‘ Thesis for the Degree 93% Pia D ‘l ”i ‘
MICHIGAN STATE umveasmf:
7’ 9 john Rowlaafi Davas
,195815'

 

 

 

 

 

This is to certify that the

thesis entitled

CHARACTERISTICS OF FLOW IN IRRIGATION FURROWS

presented bg

John Rowland Davis

has been accepted towards fulfillment

of the requirements for

Ph. D. degree in Agrl. Engineering

47%

May or professor

Date January 114-, 1959

LIBRARY

Michigan State
University

 

 

 

 

 

CHARACTERISTICS OF FLOW IN IRRIGATION FURROWS

by

John Rowland Davis

AN ABSTRACT

Submitted to the School for Advanced Graduate Studies of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of

the requirements for the degree of
' DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1958

Approved WW

 

 

John R. Davis

The efficient use and distribution of irrigation water is
predicated upon a knowledge of the behavior of water flow in
irrigation systems. unfortunately, the interactions of flowing
water, soils and crops have been difficult to analyze; resulting
in a general inability to express these interactions quantitatively
and accurately. Only recently have researchers become aware of the
need for more precise designs and descriptive mathematical tools,
and have been encouraged to study the basic variables and fundamental
principles of the hydraulics of surface irrigation systems. This
study was an attempt to describe or define some of the hydraulic
aspects of flow in irrigation furrows, to contribute to a better
understanding of furrow irrigation and the ultimate achievement of
more efficient use of water.

The basic variables involved in this problem were (1) the
infiltration phenomenon, and (2) flow regimes in small earth channels.
Considerable achievements have been made in the field of infiltration
and flow of water through soils, but the effects of the geometry of a
furrow irrigation system have been only superficially investigated.
Studies to date have indicated that furrow shape and depth of water
affect infiltration rates and wetting patterns to a considerable degree.

The characteristics of non-uniform flow in a channel with erosive
boundaries have not been studied to any extent, except for some work
on furrow erosion. Several workers have attempted to define or predict
flow of water in irrigation borders, but these methods have met with

varying degrees of success.

 

 

 

John R. Davis

The most critical part of a furrow system design is the rate of
advance of water down a furrow, for this affects not only the distri-
bution of water but also the erosion hazard, the water requirement of
the system, and the operation and management of the system. The main
purpose of this study was the development of a mathematical expression
for rate of advance and a description of the variability of the
individual components of this expression.

The rate of advance equation, based on a conservation of mass,
was developed and applied to field measurements at two locations in
California during the 1958 irrigation season. These locations
represented two distinctly different soil types and cropping systems.
Data from other workers were also used to discern whether or not the
equation would prove satisfactory with limited measurements.

Comparisons of observed and calculated rate of advance showed that
the equation was capable of predicting rate of advance accurately under
a variety of conditions. The fact that the equation could be used
successfully to describe the flow in a furrow was significant in
itself, but the fact that the equation also designated the relative
importance of the variables involved was of great importance.

Studies of furrow infiltration in a sand model resulted in the
conclusion that furrow geometry and water depth affected the
infiltration rate considerably. Although infiltration was correlated
with water depth, the relative potency of such parameters as wetted
perimeter and top width was much greater than that of water depth.

Furrow spacing was not correlated with infiltration rate.

 

 

 

 

 

 

 

John R. Davis

Field measurements with the Hamilton furrow infiltrometer
indicated that this instrument might be useful in describing
infiltration from a furrow; but that the change in furrow shape,
the movement of water and sediments in a flowing furrow, and the
seasonal effects may alter any relationships appreciably.

Studies of furrow shape at Davis, California, indicated that
furrow shape is likely to be a function of soil texture and structure
and the flow rate. Generally, higher flow rates created a flatter

bottom in a furrow; which did not change during subsequent
irrigations. Furrow shape and hydraulic roughness appeared to be
related. This led to the hypothesis that a furrow channel may
conform to a certain shape or attain a certain hydraulic radius
and area depending on the flow rate. Should this be a valid
hypothesis, it would then become possible to predict the shape and
size of a furrow as affected by flow rate and seasonal variation in
roughness, for any soil condition. This would result in an even
more practical and widespread use of the rate of advance equation.

The rate of advance equation developed should prove an extremely
valuable tool for the design and evaluation of furrow irrigation
systems. It will certainly promote a better understanding of the
flow characteristics of furrows and should stimulate further research

in the fundamental aspects of surface irrigation hydraulics.

 

 

 

CHARACTERISTICS OF FLOW IN IRRIGATION FURROWS

by

John Rowland Davis

A THESIS

Submitted to the School for Advanced Graduate Studies of
Michigan State university of Agriculture and
Applied Science in partial fulfillment of

the requirements for the degree of
DOCTOR OF PHILOSOPHY

Department of Agricultural Engineering

1958

Approved (/fE:;/S;2é2;;jjf;;;;;2:;f€::’1L—//

 

 

 

 

G /52 3 2
a pic/e!
John Rowland Davis
candidate for the degree of
Doctor of Philosophy

Final Examination:

Dissertation: Characteristics of Flow in Irrigation Furrows

Outline of Studies:

Major Subject: Agricultural Engineering
Minor Subjects: Mathematics
Soil Science
Biographical Items:
Born: December 19, 1927, Minneapolis, Minnesota
Undergraduate Studies: University of Minnesota, BSAE, 1949
Graduate Studies: University of Minnesota, MSAE, 1951
Michigan State University, 1952-1955
Purdue University, 1955-1957
Experience:

1949-1950 Graduate Assistant, Agricultural Engineering Department,
university of Minnesota.

1950-1951 Hydraulic Engineer, U.S. Geological Survey, Water
Resources Division, Quality of Water Branch, Lincoln, Nebraska.

1951-1955 Instructor, Agricultural Engineering Department,
Michigan State University.

1955-1957 Assistant Professor, Agricultural Engineering Department,
Purdue University, Lafayette, Indiana.

1957 - present Lecturer and Acting Associate Irrigation Engineer,
Irrigation Department, University of California, Davis, California.
Indiana Water Resources Study Committee, 1955-1957.

Member of:

American Society of Agricultural Engineers

Sigma Pi Sigma, Physics honorary

Pi Mu Epsilon, Mathematics honorary

The Society of Sigma Xi, Science honorary
Sprinkler Irrigation Association, Technical MEmber

 

 

 

ACKNOWLEDGEMENTS

The author wishes to acknowledge above all other things, the
professional and moral influence of Prof. Ernest H. Kidder, who has

so unselfishly given his time and skill to his profession and the

development of young staff members. The author also expresses

sincere thanks to him for the patient supervision of an interrupted

graduate program.
The author is pleased to acknowledge the leadership of Prof. A.

w. Farrell, Head of the Agricultural Engineering Department, whose

capable administration has resulted in a stimulating and friendly

atmosphere for professional development.
The writer also wishes to express thanks to the other members
of the original graduate committee: Dr. W. D. Baten, Dr. R. D. Spence,
and Dr. L. M. Turk; for their suggestions and guidance during early
phases of the graduate program.
A special note of gratitude is due Prof. G. E. Spencer, Head of

the Agricultural Engineering Department at Purdue University and
Prof. R. M. Hagan, Chairman of the Irrigation Department at the

University of California, for their constant encouragement and
forbearance during the course of these studies. Special thanks are

due also to Drs. Warren A. Hall and Gilbert Levine, who reviewed parts

of the manuscript and made many helpful suggestions.
The most heartfelt thanks go to the writer's wife, Lois, and

children; whose faith that some day the requirements for the degree

might be completed was of constant encouragement.

 

 

   

TABLE OF CONTENTS

 

Page
INTRODUCTION............................................. 1
The Problem..................... ....... ............. l
The Objective............................ .......... 4
REVIEW OF LITERATURE..................................... 6
Movement of water through soils..... .......... ...... 6
Infiltration of water into soils.................... 13
Movement of water into soil from furrows ........ .... 16
Principles and design of furrow irrigation systems.. 33
Theoretical analysis of furrow irrigation........... 41
Theoretical analysis of border irrigation........... 42
METHODOLOGY AND DERIVATION OF EQUATIONS........ ..... ..... 48
Derivation of the equation......................... 48
DESCRIPTION OF FIELD AND LABORATORY STUDIES....... ..... .. 58
Field studies in Tulare County................. . .. 58
Field studies at Davis.............................. 63
Furrow model studies................................ 63
PRESENTATION AND ANALYSIS OF DATA........................ 70
Applicability of the furrow equation................ 70
Furrow infiltration................................. 86
Furrow shape and hydraulic roughness................ 94
SUMMARY AND CONCLUSIONS.................................. 108
RECOMMENDATIONS FOR FUTURE WORK.......................... 113
APPENDIX................................................. 116
.... 121

REFERENCES CITED...‘one...stucco...oaooooooooooooo...

 

 

 

 

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r - s r ) 4 ~ - I r K r
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. - a s - I . ‘ ~ u a , a .
e ' , . > n v’ - ~ - ‘ . a u < - r 5 - a < 1 . p , -

 

Figure

1.

12.

13.

14.

LIST OF FIGURES

Schematic illustration of the relation between
total infiltration, surface storage, and distance

down a furrow......................................
Furrow infiltrometer in operation. Top shows the

water supply tanks and stage recorder, bottom
shows the furrow infiltrometer and float valves....

A view through the drying fan showing the back of
a model tank which had been tipped forward for

drying.............................................
Front view of a model tank immediately after a
measurement, showing the location of the water
supply cylinders and the valves....................
Close-up view of the front of a model tank,

showing the furrow and the method of making the
positions of the wetting front.....................

Comparisons of observed and calculated rates of
advance of water in furrows........................

Comparisons of observed and calculated rates of
advance of water in furrows........................

Comparisons of observed and calculated rates of
advance of water in furrows........................

Comparisons of observed and calculated rates of
advance of water in furrows........................

Comparisons of observed and calculated rates of
advance of water in furrows........................

Comparisons of observed and calculated rates of
advance of water in furrows........................

Comparisons of observed and calculated rates of
advance of water in furrows........................

Comparisons of observed and calculated rates of
advance of water in furrows........................
A comparison of observed and calculated rates of
advance of water in furrows, using limited

infiltration data...cocoon.nohoot-oooooooooooooooooc

Page

50

61

65

67

68

75

76

77

78

79

80

81

84

85

 

 

Figure

15.

16.

17.

18.

19.

20.

21.

 

LIST OF FIGURES (continued)

Page
Total infiltration of water from model furrows,
as a function of elapsed time...................... 88
Total infiltration of water from model furrows,
89

as a function of elapsed time............. ........

Relation between the ratio of depth of water in

a furrow infiltrometer to the depth of water in

a flowing furrow and an infiltration factor F,

showing seasonal variability....................... 93
Typical furrow cross sections, showing the effects

of stream size and number of irrigation on

furrow shape....................................... 96
Relation between velocity of water in furrows

and Manning's roughness coefficient, for Yolo

silty clay loam.................................... 101
Relation between velocity of water in furrows

and Manning's roughness coefficient, for Cajon

fine sandy loam................................... 104

 

Relation between flow rate in furrows and Manning's
roughness coefficient, for Cajon fine sandy loam... 105

 

 

 

 

 

Table

II

III

IV

 

LIST OF TABLES

Values of the infiltration function g1, where
gi=in- (i- 2)“; i ZZooooooonnoo-toocooo-oo

Infiltration equations for Cajon fine sandy loam
and Yolo silty clay loam........................

Effects of furrow parameters on the rate of
infiltration.‘O.tDO00"....ODOOOOIOCOOOOOOOOO.II

Correlations of infiltration rate with furrow
parameters...O0.0I...OOI.COI0.00QOOQOOOCOIOOQOIC

Page

56

71

9O

91

 

 

 

 

 

INTRODUCTION
The Problem

A sound engineering approach to the design of surface irrigation
systems has been seriously inhibited for some time by a lack of
understanding of the factors affecting the flow of water over soils.
The inability to express some of these factors quantatively and
accurately has resulted in inefficient, impractical designs; and only
recently have researchers been encouraged to study the basic variables
and underlying principles of the hydraulics of surface irrigation
systems.

The objective of efficient surface irrigation is to distribute a
design depth of water over the soil surface with a minimum of soil
erosion, in such a manner that water is stored uniformly within the
root zone of the crap. The efficient use of irrigation water; and
the effects of irrigation on soil compaction, soil salinity, soil
fertility and proper drainage are all affected by this ultimate
objective. Efficient water distribution is dependent on the design
and operation of the irrigation system, and is thus predicated upon a
clear understanding of the hydraulics of irrigation systems.

A committee on the hydraulics of surface irrigation in the
American Society of Agricultural Engineers (32) expressed these views
quite aptly in defining the position and scope of the committee.
Reports of this committee and a recent paper by Hansen (33) further
defined the basic variables in hydraulics of surface irrigation and

Presented a review of literature which have been included in this

 

 

 

 

dissertation. These variables are listed and discussed as follows:

1.

N

3'

4.

Rate of application

The rate at which water is applied controls the depth of
application and the uniformity with which water is applied.
The principal need here is for improved methods of

measurement and delivery of water.

Roughness characteristics

The roughness of the channel governs not only the flow
characteristics but also the intake function. The major
need today is for the evaluation of an effective
coefficient of roughness for Open channel flow in borders
and furrows, and the factors that affect the value of this

coefficient.

Intake rate

One of the most complex aspects of the hydraulics of
surface irrigation is the variable rate at which water
enters the soil. The major need here is for careful
analysis of factors involved in water intake, particularly
at soil moisture contents more realistic to irrigation.
Standardization of techniques for measuring intake rate
and careful analysis and interpretation of data will be

required.

Shape of the flow channel

The characteristics of any fluid flow are modified by the
shape of the flow channel. This effect is complex for

furrow irrigation. Careful attention needs to be given to

 

 

- 3 -

a shape factor in characterizing flow and intake
function.

5. Slope of the land surface
The slope of the land has a major influence upon the

rate at which water moves over the surface. The

 

desirability of variable slope in a field irrigation
system is being given some thought, and considerable
effort is being made toward the solution of the problems

of erosion in furrows.

0‘

. Fluid characteristics
Fluid properties cannot be ignored, because of the effects
of viscosity and density on flow of water through soils
and in channels.
7. Rate of advance
The rate that water moves over the surface is of basic
importance and is one of the most important characteristics
of surface irrigation systems. It is this characteristic,
in fact, that is used as the chief criteria for the
determination of distribution efficiency. The interpre—
tation of rate of advance data depends upon the entire
hydraulics of the system, and will be difficult to complete
until the hydraulics of the flow are evaluated.
8. Surface profile shape
The profile of water flowing in an Open unlined channel
has a definite shape, which is affected by slope, roughness,

velocity, depth and infiltration of water into the soil.

 

 

Knowledge of the surface shape is necessary to evaluate
channel storage.

Hansen (33) cited the further importance of knowledge of the
hydraulics of surface irrigation, because of the inherent short-
comings of the field-trial method now being employed by the Soil
Conservation Service. This casts no reflection on the $08, but it
is inherent in any field trial that the results are limited only to
the field and to the conditions existing at the time of the test.
Extrapolation to other fields or to a future condition is difficult
and hazardous. Only after sound practical mathematical expressions
describing the hydraulic features of flow have been developed and the
basic variables involved in the system are evaluated will the results
of field trials be more meaningful and be used satisfactorily to
predict future behavior or conditions on other lands.

The problem, then, was to define, determine and relate the above
factors affecting the hydraulics of surface irrigation systems. The
correlation and integration of these basic variables will then provide
a sound and significant solution to problems of design and evaluation,
and will assist in stimulating a united, coordinated effort for the

betterment of irrigated agriculture.

The Objective

The rate of advance of water in irrigation furrows is an important
Phase of irrigation hydraulics, and represents the integration of all
Other factors for a solution of the design problem. The objective of

this study was to present a mathematical analysis of flow in furrows,

 

 

 

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-. ‘ . ‘ ‘ , . . 1 .ilrlnlrluill .1! l.|. .. I». . . . .. . . . .. . l...

 

and a numerical solution for rate of advance in furrows. Although
other authors have presented various mathematical expressions for
rate of advance in borders, it was hardly likely that the same
expressions would be valid for furrows. Thus, a mathematical
analysis of furrow flow appeared warranted.

One should recognize that any theoretical analysis at the
present time possesses several limitations, due to the fact that the
full effects of variables such as roughness, surface profile, furrow
shape and intake functions are yet unknown and indeterminate to a
degree. However, a pr0posed analytical method should help to point
out current deficiencies in existing data and, at the same time,
provide a better working tool for the practicing engineer than a
field trial methods

A secondary objective of the study was the analysis of the effects
of furrow shape and furrow spacing on the intake function. Because of
the wide variability in soils, this part of the study should be con-
sidered as only preliminary; but the results should be indicative of
the effects of these furrow parameters. To fulfill this objective, a
model study was justified to provide a greater degree of control of
the variables involved.

It was anticipated that the latter study would facilitate the
usefulness of the mathematical expression developed for rate of
advance. Future studies on channel roughness, surface profile and
furrow shape will better define the applicability of the equations

and provide an even sounder approach to the solution of the problem.

 

 

,-u II In: I. . Illrlul .I.! .

 

 

 

REVIEW OF LITERATURE

Movement of water throu h soils
N

Because of the importance of water movement through soils in the
fields of irrigation and hydrology, it has been studied extensively
under both field and laboratory conditions. Many equations, both
theoretical and empirical, have been deveIOped to define the flow of
gases and liquids through porous media; and as a result, some
discrepancies in data and in interpretation of data appear in the
literature. Some equations are quite complex and difficult to
interpret; others are simplified to the point that inaccuracies in
their application are likely to occur. Most of the pertinent research
in this field was reviewed to enhance a more complete understanding of
the infiltration phenomenon.

Israelson (35) and Dallavalle (19) listed a number of flow
equations and defined the parameters involved, with emphasis particularly
on Darcy's equation. Richards (64) recently defined a number of terms
used in the field of soil moisture and made definite recommendations
regarding the usage of these terms. Jacob (38) also discussed the
question of the function of the permeability coefficient and its
associated nomenclature. Also, a number of authors; namely Israelson
(34), Richards (62) (63), Russell and Klute (67), and Slater (69);
have attempted to explain the concepts of water movement through soils
by the use of simple hydrodynamical analyses.

Richards defined Darcy's Law as follows:

Q = ks (H‘+ e)/e

 

 

 

 

where Q = volume of water passed in unit time

s - area of filter bed

e = thickness of bed

H = height of water on the filter

k = coefficient depending on the soil

Originally, Darcy's equation was deve10ped empirically for the

saturated flow of water through filter sands. Since then, however,
it has been proved that it is applicable also for unsaturated flow
through soils. This evidently prompted Childs' remarks in his
discussion of Richards' paper that he prefers Darcy's Law as V = - k
grad ¢, which expresses more explicitly the potential gradient under
conditions of unsaturated flow.

Gardner and Hsieh (25) defined three types of velocity of water
movement through soils, and stated that the factors affecting flow
velocity were: magnitude of the moving force, size of channels,
inertia of the moving water and frictional forces. As expressed in
their paper, Darcy's Law represents macroscopic velocity, which they
define as the volume rate of flow divided by the bulk cross-sectional
area. Thus V macro = - K V93, where c3 is the moisture potential and

V7¢ is then the potential gradient. In saturated soils, ¢ = _3__ +-gz
where P is the hydrostatic pressure, 2 is the vertical distancS‘Zbove
the plane in which ¢ is to be determined, and Q'w is the density of
water. In unsaturated flow, V more = - Kf V Q, where Q =W + (6. The
symbolkP is the moisture potential due to surface tension and ¢ is the
gravitational potential. The factor f is dimensionless and varies from

zero to one, depending on the moisture content. They further defined

 

 

 

 

 

the value of f as a result of determining dye-track velocities in
blotting paper. Gardner invalidated this latter work, however, by
stating that dye movements cannot be easily related to rate of flow,
and do not properly reflect the true rate of water movement (77).
Hansen (31) presented several expansions of Darcy's equations
for movement of water through soil during irrigation, based on the
volume of water stored in the soil. For horizontal flow, he derived

the expression
2t

Q

where .Q is the volume rate of flow
n is the soil porosity
S = degree of saturation after wetting--degree of
saturation before wetting
A is the area, normal to the distance x, through which
the water passes
P

ht = head loss in distance x, or =.—
w

Thus, the rate of movement, I HIE was expressed as I =«//§£%§EE5
t:
and if Kt, n, S and ht are constant, the rate of movement is a function
of the recripocal of the square root of time. Thus, as time increases,
I decreases and will be asymptotic to zero at large values of time.

For upward flow, the potential gradient was expressed as

 

where y is the vertical coordinate measured in the direction of

movement. Then Q = KtA (ht ' y) and as y approaches ht, I approaches
Y
zero. Thus, there will be a definite limit to the extent of upward

movement of water.

 

 

 

 

 

 

 

 

For downward flow, the potential gradient was expressed as
lljgez, and assuming ht constant, Q = KtA (E; + 1). Where ht does
Y

not increase with time, (fig +‘1) approaches one as time and y increase.
Thus, I will approach the value of Kt as time increases. Hence, for
soils where the infiltration rate approaches a constant, that constant
rate can be interpreted as an effective transmission hydraulic
conductivity under the existing conditions. This has been verified
by the work of others (7) (51).

These equations as proposed by Hansen perhaps could be effectively
employed for the solution of two-dimensional flow into and through
soils, and may have a considerable bearing on the understanding of flow
of water into soils from furrows or point sources.

Hansen also found that the rate of entry into moist soils was less
than in dryer soils; and that the wetting front appeared to be an
effective, restrictive layer to downward movement of water, due
primarily to the energy loss in the wetting front.

The classic experiments of Bodman and Colman (8) (16) have served
to define soil moisture-depth relationships and infiltration-time
relationships which have been recognized and adopted by many workers
in this field. Their studies were conducted with tubes made of
special, short cylinders 5 mm. high, such that the entire column of
soil could be sliced into thin samples for soil moisture determinations.

Their results showed that the infiltration-time relation assumed

the form h = Kt“, where n is positive but less than unity. The more
important result, however, was the classification of soil moisture
distribution within the soil column. Four distinct zones of soil

moisture were noted:

 

 

 

 

 

 

 

l. The surface layer of soil approximately one cm. deep reached
approximately pore Space saturation. In silt loam, apparent
supper-saturation was noted, evidently due to swelling of the
soil upon wetting.

2. Below the saturated surface layer, soil moisture content de-
decreased with depth until it reached a value about half way
between moisture equivalent and pore space saturation. Soil
moisture contents in this zone were not exceeded upon further
penetration of infiltering water. Hansen (31) called this
zone the transmission zone, and stated that within this zone,
the moisture content was essential constant (approximately 80
percent saturation). Because of the approximate linear re-
lationship between moisture content and hydraulic conductivity
over this range of saturation, it is then possible that a
simple expression for hydraulic conductivity in terms of
moisture content can be obtained to represent effective trans-
missibility of this transmission zone. Also, because the
moisture potential-depth curves of the transmitting zone
maintain a constant type of configuration, a constant hydraulic
conductivity is implied.

 

3. Below the transmission zone, moisture content decreased with
depth until dry soil was reached. This in turn caused a de-
crease in hydraulic conductivity. Within this zone, called
the wetting zone, downward progress of the wetting front
was accompanied with an increasing moisture content of the
soil. In a moist soil, the wetting zone was of greater
length than in a dry soil; due principally to the greater
hydraulic conductivity or a smaller loss of potential per
unit length.

 

4. The wetting zone terminated abruptly at the wetting front.
In every case in Bodman and Colman's experiments, water moved
into air dry soil as a distinct wet wave, and there was no 1
visual evidence of any diffusion of moisture ahead of the ;
obviously wetted soil. Because of the high potential loss
in the wetting front, this appeared to be an effective,
restrictive layer to downward movement of water. In moist
soils, the potential loss was smaller; hence, the wetting
front advanced more rapidly when the soil was wet. Its
moisture content was characteristic of the soil and was
probably independent of the depth of the wetted soil.

Bodman and Colman also pointed out that decreased in observed

infiltration rates with time were due to a decrease in moisture potential

 

 

 

 

 

 

- 11 -

gradient, reSulting primarily from an increasing depth of penetration.

It thus appears feasible that an equation in the form of the infiltration
equation could also be used to describe the advance of the wetting front.
It was also evident that moisture potential conditions represent the

chief factors influencing changes in infiltration rates and that the

 

other factors usually cited operate as a modifying influence.

Regarding texturally layed columns, less permeable layers limited
entry into the soil surface regardless of whether they laid above or
below the more permeable one. If the less permeable layer occupies the
lower position, a positive hydrostatic pressure will develop in the
layer above. This pressure increases with time, but shows no influence
on the rate of water entry into the lower layer. Examples of this
phenomenon are the case of hillside seeps, where the less permeable
soil slopes in the direction of the hillside; and the irrigation of
hardpan soils, where ultimate water logging of the soil results if too
much water is applied.

More recent work by Miller and Felix (51) fully substantiated
Badman and Colman's results. In fact, they also concluded that the
average velocity of flow through the transmitting zone must be very
nearly equal to the infiltration rate. They found that the hydraulic
gradient in the transmitting zone was relatively uniform, greater than
unity and decreased with time to unity as a limit. The gradients of
various materials differed at corresponding stages of infiltration.
For Yolo loam, for example, the hydraulic gradient, dh/dl, equalled
1.25.

Numerous authors have attempted various mathematical expansions

 

 

 

 

 

 

 

-12..

of Darcy's equation. Gardner and Widtsoe (26), for example, used the
form of Darcy's equation V = K P V G, where
V = mean velocity at a point in the soil

9 = moisture density at the point

 

K = a proportionality constant

Q = the sum of three potentials
The development of their equations, however, applied more to soil
moisture conditions in a soil column after drainage than it did to
water penetration during irrigation.

One of the assumptions of Gardner and Widtsoe was the fact that
the inherent moisture conductivity of the soil was independent of the
moisture content. This is true, but only because the moisture content
of the transmission zone in a soil is essentially constant. Klute (40)

pointed out that the conductivity of an unsaturated medium will depend

 

on the moisture content and will decrease with decreasing moisture
content. This does not invalidate any of the other work of Gardner
and Widtsoe, but it does serve to point out differences in the
characteristics between soils.

Bodman and Edlefson (6) presented rather fundamental observations
on soil moisture movement and the basic functions of forces acting on
soil moisture. More recently, Philip (58) (S9) (60) presented several
mathematical interpretations of the theory of infiltration, but his
developments were somewhat difficult to follow. A more practical
mathematical manipulation of Darcy's equation has been presented in
several of Hall's papers (28) (29), in which more simplified

mathematics was employed to define infiltration into soils. Hall's

 

 

 

 

- 13 -

paper on one-dimensional infiltration was limited, however, to an
expression for the depth of penetration of the saturated surface.
This is relatively unimportant in irrigation practice, because as
Badman and Colman point out, the depth from the soil surface to the

bottom of the shallow layer of saturated soil remains fairly constant.

 

Infiltration of water into soils

 

A number of investigators have studied the effects of various
factors influencing infiltration into soils, but the results usually
apply only to the soils under consideration. This is true particularly
in cases where chemical as well as physical factors are involved, such
as in the irrigated saline soils in the western United States.

Scofield (68) reported in great detail the effects of soil chemistry
on water movement through soils, and others (5) (27) (50) have deter-

mined the effect of various infiltration patterns on the resultant

 

salt accumulation and salt distribution in soils. Because this
dissertation was concerned with only the mechanics of flow, consideration
was not given to other modifying factors such as salinity.

A large number of factors affect infiltration, as pointed out by
Lewis and Powers (46), who discussed the effects of a number of
variables on infiltration rates. In an earlier paper, Lewis (43)
stressed the importance of knowing infiltration rates, and discussed
results of infiltration tests with single-ring infiltrometers.

Studies of a great number of soils by Free, Browning and Musgrave (24)
involved the determination of infiltration rates on 68 different soil
sites, and a statistical evaluation of the manner in which measureable

soil factors affect infiltration.

 

 

 

 

 

 

 

 

- 14 -

Their results showed that the general form of the infiltration
equation I = bta was applicable; and that b varied from unity to
0.0087 and a from 0.04 to 0.82. Results of the regression analyses
showed that the following factors have a positive influence on
infiltration:

Total porosity

Non-capillary porosity

Aggregation of soil particles

Organic matter content

pH

Moisture equivalent of the surface soil
Conversely, the following factors have a negative influence on
infiltration:

Silt and clay content

Clay content

Dispersion ratio

Moisture equivalent of subsoil

Volume weight

Suspension
These analyses and the statistical treatments have served as a general
reference for many workers in this field. Krimgold and Beenhouwer (41),
for example, used these data as a basis for a general classification
of soils into five categories of infiltration characteristics. Unless
field determinations are possible, this is the only manner in which
the data can be treated--that is, a general qualitative approach,
rather than a strict quantitative treatment. Even though Free, Browning
and Musgrave conducted an exhaustive study on 68 soils, it is quite
improbable that the infiltration rates are the same on these soils

today, and is certainly unlikely that these results, other than the

generalizations, would apply to other soils.
The technique of measurement of infiltration has been only partially

investigated. A number of years ago, Lewis and Neal (45) conducted

 

 

 

 

W-«w- , - , , , , 1 7‘7 ,
- 15 -

infiltration studies on soil cylinders of varying diameter. Although
they found a general equation for infiltration as a function of soil
porosity, they were free to admit that they had difficulty in getting
comparable results.

More recently, Burgy and Luthin (15) investigated the validity of
results from single and double ring infiltrometers in a non-stratified
soil at or near field capacity. Their results showed conclusively the
high degree of variability one would encounter with the ring
infiltrometers. They found that six single-ring infiltrometers
randomly spaced gave an average value that was within 30 percent of
the true mean. Even when an arbitrary rejection technique was applied
to the data, the adjusted ring rates were only within approximately
25 percent of the true rates. The authors pointed out, however, that
these adjusted rates might be considered quite close in such a variable
system as the soil. Thus, as the authors implied, the ring infiltrometer
is an instrument or a technique that will produce results for a point
location in a usually variable medium. Some descripancy still exists,
however, in the physical dimensions and techniques employed in using
the ring infiltrometer even for a single point.

Aronovici (3) recently reported the results of a model study of
ring infiltrometers, in which he was able to observe the wetting
patterns in soil placed in a glass-front tank. His study pertained
particularly to the effects of variations in soil profile, ring depth
and ring diameter on infiltration velocity, and illustrated quite
effectively the influence of these parameters on infiltration from rings.

Aronovici found that the infiltration velocity decreased with an increase

 

 

 

 

 

 

-15-

in the infiltrometer depth and with an increase in ring diameter.
Also, as the initial soil moisture content increased, the rate and
magnitude of infiltration velocity decreased, as might be expected.
The relationship between ring diameter and infiltration velocity was
curvilinear; that is, the rate of decrease of infiltration velocity
was about 1.3 cm. per hour per inch of increase in diameter up to

four inches, but decreased only 0.05 cm. per hour for each increase in
diameter beyond four inches.

An interesting result of the wetting front observations was the
relation between the diameter of the ring and the horizontal distance
from a vertical projection of the ring to the wet-dry soil interface.
This distance was almost the same regardless of the ring diameter, and
appeared to be the primary reason for the inverse relationship between
infiltration velocities and ring diameter.

These studies have served to emphasize the need for standardization
of technique for infiltration measurements. Inasmuch as the single-
ring infiltrometer is convenient and most widely used, standardization
of technique becomes even more important. Thus, it is imperative that
the researcher realize the limitations of infiltration data and
techniques. In a sense, the above reviews justified the use of a
general infiltration equation in the following theoretical developments.
0n the other hand, the use of such infiltration data was bound to
result in a general develoPment that should be applied with some caution

and discretion.

Movement of water into soil from furrows

W

The movement of water into soils from furrows is complicated by

 

 

 

 

 

 

- 17 -

the fact that the dimensions of the soil surface are variable, the
water is moving across this surface at some velocity, and the nature
of the surface changes from one irrigation to the next, due to
degradation and aggregation in the bottom of the furrow. Aronovici (2)
mentioned that furrow silting, erosion, soil-particle rearrangement
and deterioration of soil structure were contributing factors in alter-
ing infiltration patterns during the season. In evaluating the
reliability of the ring infiltrometer as an index of irrigation furrow
infiltration, Aronovici stated that neither ring infiltrometers nor
permeameter measurements on soil cores gave rates equivalent to furrow
infiltration rates. The ratios of furrow to ring infiltration rates
varied from 1:1 to 9:1, depending on site conditions and duration of
observations; but in all cases, furrow infiltration was always higher
than ring infiltration. Aronovici (4) later stated that cylinder
infiltrometers were not at all applicable to furrow studies, and
strongly suggested the use of the Hamilton furrow infiltrometer.
Considerable differences in individual furrow performance are
usually found. This will be true especially in furrow irrigation in
orchards, when the center furrows perform differently than those
adjacent to trees. Aronovici (2) stated that the reduction in wetted
front area of the center furrow (and consequently a reduction in
infiltration) was caused by the influence of water moving out from
furrows on either side. This was essentially the influence of furrow
spacing, although many authors do not treat it as such. Another

significant difference in furrow infiltration is due to mechanical

 

 

 

 

 

-18-

compaction of the soil in the bottom or sides of the furrow.

One of the more important aspects of Aronovici's results was the
fact that the furrow width or total wetted surface area appeared to
have no direct bearing on the infiltration rate from a furrow on a
wetted area basis. He reasoned that the lateral flow of water from
the furrow is more dependent upon the water contact with furrow sides
and capillary flow laterally than the width of the furrow. Instances
were cited where infiltration rates were higher in narrow furrows than
in broad furrows.

The Hamilton furrow infiltrometer to which Aronovici referred was
described in a recent paper by Bondurant (10). Bondurant‘s statement
of the problem was similar to this author's, in that a need exists
for determining infiltration before irrigation water is available on
the farm, and that the cylinder infiltrometers are difficult to
correlate with furrow infiltration rates. His paper described in
detail a furrow infiltrometer, its operation, and some field infiltro-
meter studies. Bondurant claimed that a comparison of data from the
furrow infiltrometer and from inflow-outflow measurements showed a
close agreement in most of his trials, but the data shown in his paper
revealed a rather poor agreement and only a general correlation. The
infiltrometer, however, has the advantage of being useful for any
shape of furrow and also takes into account the differences in
permeability and areas of the sides and bottom of the furrow.

Bondurant also found a relationship between the stream size and
wetted area, for furrows of a given slope. According to his analysis,
the following stream size, slope and stream width relationship was

obtained:

 

 

 

 

 

 

-19-

Y = 5.35 x0'285

where Y is the stream width in inches
X is the stream size in gallons per minute divided by
the slope in percent

The above relationship was a result of studies in the Republican
Valley on V-shaped furrows with side slopes averaging about 4 to 1,
and will likely be different in areas of different soils and different
furrow shape.

One possible error in Bondurant's paper that was common in a
number of other papers also, was an assumption that the water entering
the soil from a furrow is distributed over an area equivalent to the
length of the furrow infiltrometer (one foot) times the furrow spacing.
It is possible that the actual area through which water passes is
smaller than the area indicated by the furrow spacing, depending upon
the soil. This would tend to increase the field intake rate over
that which is usually shown.

In an earlier study, Bondurant (9) verified the poor correlation
between ring infiltrometers and inflow-outflow measurements, particularly
when the surface soil was not the least permeable horizon. His studies
on three major soil types showed that on a sandy loam soil, in which
the least permeable horizon was the 6" - 9" depth, the intake rate as
determined from the single ring infiltrometer was not a close
approximation of the intake rate obtained by surface flow measurements.
The furrow intake rate divided by the percentage of furrow covered by
the irrigating stream was more nearly the same as the intake rate

obtained with single ring infiltrometers. Where the surface soil was

 

 

 

 

 

 

- 20 -

the least permeable horizon, the average intake rates obtained by the
two methods were very nearly the same.

The Soil Conservation Service has used an intake rate correlation
between cylinder infiltrometers and furrow intake rates in the Northern
Great Plains for about three years, in spite of the usually poor
correlation. Phelan (57) stated that it has been used purely as a
guide in planning farms upon which it was impossible to make furrow
intake studies, and made no claim for the accuracy of the correlation.
He further stated that the curves were developed in the middle range
with intake rates of about one inch per hour and stream sizes between
5 and 15 gallons per minute. Additional work is underway to consider
the effect of slope on the correlation.

A number of studies have been made on seepage from ditches and
infiltration from furrows. One of the earliest studies was that made
by Loughridge (47) in orchards near Riverside, California. He observed
wetting patterns in the soil from trenches six feet deep dug across
furrows and trees, to give a trench 90 feet long and 3 feet wide.

Water was conveyed over the trench with small wooden flumes.

Loughridge observed the difference in wetting patterns from
shallow and deep furrows (the depth of water in the furrow was about
one-half inch in each case), and found that the depth of percolation
and spread of water were far greater under the deep furrow--the ratio
being about 2 to 1. He concluded that the real advantage of deep
furrows lies in increasing the height of soil through which water from
furrows would have to rise by capillarity to reach the surface, thus

decreasing evaporation loss and increasing the amount of water retained

 

 

 

 

 

_ 21 -

by the soil. These conclusions were modified by subsequent work of
others (5) (50) (76), however, particularly when salt concentrations
in the furrow bed are likely.

Loughridge's studies were also limited by the fact that a very
small stream of water was used, resulting in a slow rate of advance
of water down the furrows. Under these conditions, he described the
form of the curve made by wet soil from the head of the furrow to
the end: the depth of percolation was 26 feet at a distance of
30 feet from the head ditch. The curve ascended abruptly toward the
surface at a point one-fourth the length of the furrows from the head
ditch. From this point to the end of the furrow the depth of penetration
was quite small, and was nearly uniform to the end of the furrow. This
type of wetting pattern would result in an inefficient distribution of
water.

Browning and Milam (14) investigated the use of small contour
furrows for conservation of soil and water on sloping pastures in
West Virginia, and cited most of the literature available at that
time (in 1940). They cited Conti's work, the results of which showed
a vertical penetration of water four times as rapid as lateral pene-
tration in soils of uniform compaction; and Whitfield and Fly's work,
the results of which showed that the wetted area of contour furrows
in heavy clay loam soil extended about 10 inches on each side of
the furrow. In Browning and Milan's study, the results showed
conclusively that water did not move laterally as far as 12 inches
during the 12 to 24 hour tests. They observed quite a variation in

the time for water to reach the tensiometers placed six inches away

 

 

 

 

 

 

 

 

- 22 -

from the furrows; but usually water reached the downhill ones first,
as would be expected, due to the more rapid movement of water in a
downhill direction. Cross sections of the wetted soil showed that
the wetted area assumed an inverted cone pattern.

One of the more exhaustive field studies of seepage from ditches

 

was reported recently by Rohwer and Stout (65), and should be applicable
to furrow irrigation problems. Their studies were concerned mainly
with the relative seepage of the sides and bottom of canals, and the
factors influencing seepage rates. Methods of measuring seepage were
also discussed, with the comment that the inflow-outflow method was
preferred because of the longer section of channel available for
observation. In general, they found that the actual losses from
canals were far less than the maximum possible, due to partial sealing
of the bed material. They also stated that seepage was only loosely
correlated with depth of water in the canal, and that the effect of
water temperature on seepage was quite small.

Individual trials showed considerable soil influences on
seepage. For example, in Holtville silty clay loam, side seepage
exceeded bottom seepage; but in Meloland fine sandy loam, side seepage
was less than bottom seepage. This difference was attributed to
differences in soil permeability or in underlying strata. In another
case at Davis, California, seepage rates from the bottom of a trench
decreased with time. The total seepage increased with time,
emphasizing the effect of seepage through the sides of the canal.
However, tests in January of the following year showed that the seepage

rate from the bottom of the trench exceeded that from the sides and

 

 
 

 

 

 

 

 

- 23 -

ends--contrary to previous findings. Rohwer and Stout reasoned that
the changes that caused this reversal must have occurred in the sides.

In pool experiments, they mentioned that flow velocities as low
as 0.05 feet per second increased the rate of percolation. If this
was true, the absence of stream velocity might cause some errors with
the furrow infiltrometer, and some adjustment might be necessary to
consider water velocity, particularly if the shape of the furrow were
affected by the velocity.

Muskat (52) discussed in great detail the flow of fluids through
porous media and presented specific solutions for drainage from ditches
and seepage from canals into sands with deep or shallow water tables.
He derived several equations for the seepage flux, Q, from ditches;
assuming that the potential can be expressed as (K/u) (p-rgy). If the
porous medium was of very great thickness, the maximum width of the
sheet of liquid seeping down into the porous medium was B1 = Q = B + 2H,
where B1 was the width of the sheet of seeping liquid, Q was the seepage
flux, B was the width of the stream, and H was the depth of water. He
also presented equations for the free surface streamlines, which define
the value of Bl’

When the normal ground water level was at a relatively shallow
depth, the streamlines assumed a horizontal rather than a vertical
trend. In this case, a complex variable relation defined the problem,
and after suitable manipulation of the equations for the free surface
streamlines, the equation B = Q + 2H was written. Thus here, also,

a knowledge of the width and depth of the ditch will give the seepage

flux out of it. In the first case, the equipotentials at great depths

 

 

 

 

 

 

were horizontal parallel lines; in the latter case, the equipotentials
at great depths were curves depending on the seepage flux and the depth
of water in the ditch.
Perhaps a more precise determination of seepage of water into
sands with deep-lying water tables was given by the equation Q = B + ZHK/K',
where K and K' are the complete elliptic integrals of the first kind
with moduli K*, l-k*2. Muskat suggested that the calculation is most

readily carried out by assuming Q/H, calculating the associated K*, and

then the value of B/H to which the value of Q/H corresponds. In this

 

case, K* was given by the equation K* = cos qfqu, where l/m was the
average side slope of the ditch. The maximum or asymptotic width of
the downward seeping sheet of water was then Bl = Q = B + ZHK/K'. It
is necessary in using these equations that, in the numerical
interpretation of the equivalence between the flux Q and the lengths
such as B, one must multiply the latter by k, which Muskat took as
unity.

The use of these data from Muskat were limited more or less to
saturated flow, and may not apply to cases where interference of the
wetting pattern from an adjacent furrow is probable. However, use of
the simple equation B1 = B +-2H might serve to define the extent of
lateral movement of water from furrows in homogeneous sandy soils
where no interference exists. For example, if the width of a furrow
stream were 16 inches and the water depth were 2 inches, the width of
the seeping stream would be about 20 inches, or 10 inches on each side
of the center line of the furrow. This remains to be verified, however,

by future studies of unsaturated flow in soils from furrows.

 

 
 

 

 

-25—

The movement of water from irrigation furrows has been reported
by a number of authors. Taylor (72), in advocating the use of closer
spaced furrows, recommended a spacing somewhat less than twice the
depth of rooting of the plant. He also stated that the wetting front
was sharp in dry soils and more gradual in wet soils, as would be
expected, and even less sharp for lateral movement.

Day and Luthin (20) analyzed the theory of flow from a system of
parallel irrigation furrows in a permeable soil overlying a deep gravel
substratum, by using the method of images. They derived equations for
the potential at any point in the soil and for the value of the stream
function along any chosen streamline. For the vertical limiting stream-
lines,L+J = 3:2'n q, which lie on vertical planes midway between furrows.
The total flux, Q, was equal to 4’” qK, where q was a flux coefficient
whose value could be determined from one of the equations mentioned.

Their studies also included a model study to verify the theoretical
developments. Measured values of seepage flux in this part of the study
agreed within eight percent of the calculated value, thus validating
the developed equations for seepage flux. Tensiometer measurements
also indicated approximate agreement with theory.

Variations in the soil profile also affect the pattern of water
movement from furrows, particularly the effect of soil stratification
and sand lenses. Photographs of wetting patterns in soil (1) showed a
definite increase in horizontal movement of water when the wetted area
encounters a clay layer or a coarse sand layer. In the latter case,
the overlying soil must be nearly saturated before water moves into

the sand. Similarly, if cracks in the soil are filled with sand, free

 

 

 

 

- 26 _

water will not enter the cracks until the adjacent soil is nearly
saturated, unless the cracks enter the furrow. This same conclusion
was reached by van't Woudt (74).

Haise (27) also used a photographic technique to determine flow
patterns in irrigated coarse textured soils. His studies were conducted
with a 64-inch long by 38-inch high by 24-inch wide lysimeter box with
a plate glass front, in which coarse sand had been placed. Two furrows
eight inches high and 36 inches from center to center and 24 inches
long, were made in the soil; and during the tests, water was
maintained at a constant head in the furrows. During some of the
tests, indigo carmine dye was injected at intervals along the furrow
perimeter, as a means of tracing the streamlines.

The most important observation of these studies was the fact that
soon after capillary wetting of the ridge was completed, the direction
of water movement was downward at all points. This had considerable
bearing on the movement of salts into and away from the furrow ridge.
It was found that the direction of moisture movement was independent
of textural differences, even though the rates of water movement varied
widely between soils.

After twenty minutes of irrigation, the flow lines were essentially
normal to the submerged surface of the furrow; and as shown by the
dye patterns, the flow pattern resulting from the water entering the
soil in each furrow was symmetrical at any given time.

Haise stated that it would be expected that altering any one of
the imposed conditions (head of water in the furrow, shape of furrows

and ridges, etc.) would alter the general configuration of the flow

- 27 -

pattern. As shown by his illustrations, furrow Spacing would have an
important effect also.

Regarding the movement of dye in the soil, Haise found that the
direction of water movement as indicated by dye movement in soils
already wet to approximately field capacity was less definite than in
soils in an air-dry condition. This was due to an apparent lag of the
dye behind the wetting front, which is explained in some of Bodman
and Colman's work and later by Gardner (77). As a result of these
model studies, Haise recommended that fertilizer should be placed in
the ridge several inches above the level of water in the furrow, thus
preventing excessive leaching of the soluble fertilizers to lower
depths.

Field and model studies of water movement from furrows into beds

have been concerned mainly with the movement and accumulation of salts

 

in the beds, but afford a reasonable examination of the factors
affecting water movement into soil from furrows. McGeorge and
Wharton (50) corroborated Haise's data in their studies of salt move-
ment from furrows into beds of different shapes. They found the
presence of heavy salt accumulations in the subsoils directly under
the beds, indicating a large amount of lateral movement both from the
furrow toward the center of the bed and downwards or upwards, depending
of the direction of water flow. Salt concentrations were always the
least in the furrows and highest in the center of the beds.

Wadleigh and Fireman (76) also reached this same conclusion in
studies to determine proper sampling techniques for salinity measure-

ments. They found a continual increase in soil salinity from underneath

 

 

 

 

-28-

the furrow to underneath the row and up to the surface of the soil
in the ridge, which reveals the pattern of water movement. The salt
accumulation under the row was also much greater under the "wet"
irrigation treatment than under the "dry".

More recent studies were published by Bernstein and Fireman (5),
which also corroborated the work mentioned above. They used a 32-inch
wide by 26-inch high model, and tremied air dry soil into place between
two parallel glass plates held 7/8 inch apart. Distilled water was
applied to shaped furrows with a constant level device.

They also found that when the shape of the bed was bilaterally
symmetrical and both furrows similarly irrigated, the wetting pattern
was symmetrical. The wetting fronts moved approximately ten times
more rapidly in loam than in clay; clay took 6.7 times as long for
the Wetting fronts to meet and 4.7 times as long for complete wetting
across the bed surface. In the final analysis, however, the salt
distributions were remarkably similar.

Generally, the results showed that the more perpendicular the
wetting front was to the bed surface, the greater the lateral and the
smaller the upward components in the direction of movement of the
wetting front, and the less salt was deposited in the surface of the
bed. In all cases, however, the angle between the tangent to the
wetting front and the soil surface of the bed was not a right angle.
The angle increased as the bed height decreased; the angle being 46°,
53°, and 75° for the 6", 4 1/2", and 3“ beds, respectively. These
results and the others cited showed conclusively that the pattern of

water penetration into furrow beds was affected not only by soil

 

 

 

-29-

conditions but also by the shape of the furrow and the bed. This
becomes quite important when salinity problems are likely to arise.

One of the more recent projects having a direct bearing on flow
of water into soils from furrows has been conducted under the leader—
ship of W. H. Gardner. In a recent progress report (77), Gardner
sited the results of studies of dye tracers for determining the
movement of water through soils, and concluded that dye-track velocities
cannot be used to represent average incremental water velocities.

For these studies, rectangular ceramic plates were made from
Palouse silt loam soil, into which dye was introduced at specific
intervals along the face of the plate. It was shown that the rate of
entry and advance of the wetting front obeyed the empirical equation
dQ/dt = AtB and S = EtF, but that the dye only approximated the average
flow rate for a saturated flow condition. Dye introduced into the
block just back of the wetting front was observed to catch up with the
wetted front, which suggested that through cascading motion it was
passed over the top of water containing no dye. Thus, dye movement
was not easily related to rate of flow-~but was used to trace out
streamlines in both saturated and unsaturated flow. In any respect,
it was improbable that any given soil sample would yield identical
water movement data on successive runs.

The results of Rowe (66) in contributing to this project were
particularly enlightening. He used a model of two rectangular glass
plates held one centimeter apart, and used a constant head apparatus
to measure flow and maintain the head in the furrows. The procedure

used by Rowe was the same as that used in this study, except that he

 

 

 

 

 

used soil sifted dry through a #20 sieve, whereas fine sand was used
in this study.

Rowe's data appeared to fit the equation Q = AtB for infiltration;
thus he expressed the results of the model study by showing the effects

of various factors on the values of A and B. The relative positions

 

of the curves plotted from the data were very nearly the same for both
laboratory and field data on ten soils.
The effect of initial soil moisture content on the parameters
A and B were as follows:
In Ephrata sandy loam, as the moisture content increased,
A decreased and B decreased
In Ritzville silt loam, as the moisture content increased,
A increased and B decreased
In general, there was no definite trend in the values of A with

variation in initial moisture content; the values of B decreased,

 

resulting in an expected decrease in total infiltration with time.

The effect of the depth of water in V-shaped furrows, for Quincy

sandy loam soil was as follows:

 

fith A B
3.5 cm 1.442 0.9775
6.0 1.673 0.9786
8.2 2.404 0.9610

Thus, it was apparent that there was a slight trend in A with
variations in hydrostatic head. No definite trend in values of B

with variations in head were evident.

 

 

 

 

- 31 -

The effect of the area of contact of water at constant head in

flat-bottom furrows was as follows for Ephrata sandy loam soil:

Area of Contact A B
10.60 m2 2.176 0.8404
21.46 2.926 0.8470
31.46 4.898 0.8304

Although no statistical analyses were employed, it was evident that
the value of A increased with an increasing area of contact, whereas
the value of B did not change appreciably.

From these results, it then appeared possible that the infiltration
from furrows could be described by an equation in the form of F'AtB,
where AtB represents the infiltration from a standard measurement, such
as that with a furrow infiltrometer. The function F would then be a
function of head of water in the furrow, the area of contact and the
furrow spacing.

As these data indicated, it was no longer necessary to postulate
the form of the infiltration equation for furrows. Once the values
of F are known, the infiltration of water into soil from furrows can
be readily determined.

Rowe also found that the rate of advance of the wetted front in
the vertical direction did not greatly exceed that in the horizontal
direction. The greatest difference occurred in the coarser soils, as
could be expected; and the data indicated that the gravitational field
was small in comparison with the capillary field as long as the water

source was maintained and the moisture gradient was fairly large.

 

 

 

 

- 32 -

Where the soil is sufficiently isotropic, the depth to the wetted
front may then be estimated from observations of the distance of
lateral advance of the wetted front.

The equations S = DtE and U = FtH appeared to apply in defining
the position of the wetting front with time, where S was the horizontal
distance and U was the vertical distance. For Quincy sandy loam, the

0'585 and u = 1.068 c0'596, from which

equations found were S = 1.037 t
it was evident that the lateral advance was very nearly equal to the
vertical advance. Rowe then used the equations Q = AtB and S = DtE
to derive a simple relationship between total infiltration and lateral
movement of the wetting front. This equation was Q = CSK where C = A/DK
and K = B/E.

More recent work by Nagmoush (54) corroborated Rowe's work.
Nagmoush also found that the value of the time exponent B decreased
with increasing hydrostatic pressure and A increased with increasing
hydrostatic pressure. He also observed that the vertical rate of
advance of the wetted front did not exceed greatly the horizontal, as
long as water was applied.

Nagmoush also found that it was possible to convert one dimensional
flow in soils to two and three dimensional flow, using simple conversion

factors. Averages of data on Palouse silt loam and a fine sand resulted

in the following equations:

One dimension Q = AtB S = EtF
Two dimensions Q = 2.1 Atl'SZB s = 0.78 ECO'le
Three dimensions Q = 2.5 Atl°64B S = 0.34 Eto'83F

 

 

 

 

 

 

- 33 -

These constants depended on the texture of the soil involved;
but served to illustrate the fact that regardless of the geometry of
the system, the general equation for infiltration could still be
written.

It was noted that the effects of furrow Spacing were not
considered in this study, nor was furrow shape. It was quite likely
that the wetted area of a furrow might be less significant than the
top width, and it was evident that the relation would depend also on
the relative permeabilities of the sides and bottom of the furrows.

In summarizing this section of the review, it appeared likely that
furrow dimensions will affect the rate of water movement into soils
from furrows. Although the general equation of the form Q = AtB may
be used to define total infiltration and vertical and horizontal advance
of the wetting front, the constants A and B depend upon soil texture
and structure, initial soil moisture content, head of water, and the
furrow dimensions. Because the value of B did not depend on furrow
dimensions, as reported by Rowe and Nagmoush, it may be postulated that
an equation in the form of Q = F'AtB may be employed to determine the
infiltration from any given furrow geometry in a particular soil
situation. This was the basic postulate in the later developments of

this study.

Principles and design of furrow irrigation systems

In many cropping systems, the most widespread method of irrigation
is by furrows. Brown (13) stated that more than 80 percent of the

sugar beets in California are furrow irrigated, and emphasized the

fact that no other method requires more judgement or more skill in

 

 

 

 

 

 

 

- 34 -

irrigation management than furrow irrigation. His popularized article
presented three basic essentials for furrow irrigation:

I. Furrows should be close enough together so that
wetted areas meet.

2. Water should be kept in the furrows for the time
necessary to obtain the desired penetration.

3. The length of the furrow should be such that the
difference in penetration between upper and lower
areas shall not be excessive. He did not define
his criteria, "excessive". /

He also gave some general recommendations for furrow length, depending
on soil type.

Lawrence (42) suggested that furrows be spaced to fit crOps and
standard machinery, and also suggested that wide, flat bottom furrows
can be used on uniform grades of less than 0.5 percent. Furrow grades
of 2.0 percent or more may result in excessive erosion, but this depends
on the flow of water in the furrow and the soil type. Lawrence stated
that the size of the stream should be controlled to fit the furrow
grade and soil conditions, such that the maximum non-erosive stream
would reach the end of the furrow in about one-fourth the time it
takes to irrigate the crop.

These recommendations agreed essentially with those of Griddle (7)
and Griddle, Davis, Pair and Shockley (18). These two reports gave in
detail the procedure for determining the length of furrows, sizes of
streams and spacing of furrows, but involved the common problem that

water must be already available and the land must be graded and leveled

 

 

 

 

 

IIIIIIIIIIIIIIIIIII::::_________________________________—____—________¥4447 iv' H fiflfi’
- 35 - j {.1

to perform the tests. Thus, the methods cited are more adapted to the
evaluation of irrigation systems than to the design of a furrow
irrigation system.

Griddle stated at the outset that increasing the size of the
stream in bare V-type furrows on steeper grades did not materially
increase the rate at which water infiltrates into the soil. Others
have found that this relation did not hold on flatter slopes in lighter f
soils nor where the furrows were broad or grass covered. In fact, many
workers in this field disagreed with his statement altogether.

Criddle explained the analysis of results of field tests, in
which rate of advance curves were determined for furrow streams of
various sizes. He cited the fact that the final analysis for the
permissible limit for erosion rests somewhat on personal judgement.
Regarding furrow spacing, the row crop involved usually fixes the
spacing of the furrows. One should realize, however, that in

homogeneous soils, the horizontal width of the wetted bulb of soil is

 

frequently about the same as the height of the bulb. Under these
conditions, the correct furrow spacing is somewhat less than the root
zone depth of the crop.

The authors of both publications stated emphatically that the
stream front should reach the lower ends of the furrows within
approximately one-fourth of the total time needed to refill the soil
in the root zone. This procedure would reduce the average deep
percolation loss for the full length of the furrow to about five
percent of the water stored in the root zone. A faster rate of advance

would decrease loss, but would also create problems in labor and soil

erosion.

 

 

 

 

 

IIIIIIIIIIIIIIIIIIIIIZIIT___________________________________________—____"”i ’ .:
gm

 

 

- 36 -

The maximum allowable stream, as Griddle mentioned, appears to be
a matter of good judgement. However, as a general rule, the equation
Q = 10/S may be used as an approximation; where Q is the furrow stream
in gallons per minute and S is the furrow slope in percent.

The final analysis of the problem, as outlined by Griddle,
consisted of plotting the rate at which different size streams
advance, and determining the maximum size stream and maximum time that
can be allowed for it to reach the end of the furrow. In this manner
the maximum allowable length of furrow can be determined.

Furrows present conditions most favorable to erosion, in that
loose, cultivated soil is exposed to a concentrated flow of water.
0n the other hand, the frequent cultivation creates roughness in the
channel which may tend to lower the velocity of flow. Taylor (71) used
the work of Gilbert on small channels to postulate the effect of slope,
discharge and aggregation on furrow erosion; and to present in
mathematical form the capacity for traction. He concluded that the
slope should be kept to a minimum, that the furrow width should be large
in relation to the depth, cover should be used where steep slopes are
unavoidable, and narrower furrow widths and greater depths should be
used when the cross s10pe increases.

In a more papular article, Taylor (70) stressed a number of
advantages of broad furrows, particularly the fact that it was a more
effective water conducting channel with less susceptibility to erosion
and clogging. He recommended an effective bottom width of 20 to 24
inches on flat land and about half this width on hillside orchards.

These advantages would depend on the properties of the soil, however,

 

 

 

 

 

 

—_—“— a" {
f, ‘

-37- yr"

and cannot be considered applicable to all soils and all crops.

Later work by Israelson, Clyde, and Lauritzen (36) corroborated
Taylor's work and provided the values of constants in an equation
suggested earlier by Gardner. This equation was in the form of
E = kSnQ, where E is the rate of soil erosion from a furrow with
slope S. The authors found values of k and n in the order of 2.8
and 2.0, respectively, for silty clay loam; and 4.4 and 1.5,
reapectively, for sandy loam soil.

They also found that erosion was higher from V-shaped furrows
than from flat furrows, due to the differences in velocity of flow.
Above lepes of 3.2 percent to 3.5 percent, however, the stream in
the rectangular channel concentrated in its eroded channel and formed
a V-shaped channel. Thus the authors concluded that furrow slopes
of two percent and higher were excessive and caused harmful erosion
when streams of ten gallons per minute, were run into each furrow.

Evans and Jensen (22) conducted similar studies in North Dakota,
and developed the equation E = 0.48 SZ'3Q1°5 for furrow erosion. In
this case, Q was the runoff flow in gallons per minute, which might
be less likely to represent total erosion in the furrow than total
inflow into the furrow. In observing cultivated and undisturbed
furrows, Evans and Jensen found that the undisturbed furrows suffered
less soil loss than the disturbed furrows, the rate of advance in
undisturbed furrows was about twice as fast as in disturbed furrows,
and the infiltration rate of the undisturbed furrows was lower during
the first hour.

The fact that soil erosion may occur in furrows is an important

facet in the field of irrigation hydraulics, for erosion would affect

 

 

 

 

 

 

 

-38- - 7"

not only the infiltration rate but also the furrow shape, dimensions,
and hydraulic roughness.

Perhaps the most detailed design procedure for furrow irrigation
systems has been prepared by the Soil Conservation Service (73). This
engineering handbook summarized the adaptations, limitations and
conservation features of irrigation furrows. The recommended design
procedure was outlined as follows:

1. Determine the average intake rate. (For this purpose, curves

were shown as a guide, and related the average seasonal
intake rates for coarse to very fine soils).

2. Increase the average intake rate to allow for runoff from

 

the end of the furrow (10 to 15 percent).

3. Determine the average water application head per 100 feet

of length. (Curves relating water application head to
intake rate and furrow spacing were shown).
4. Multiply the water application head required per 100 feet
of length by the recommended length of run and divide by 100.
5. Check for erosive water application heads. The value obtained
should be 1/4 to 1/3 less than the erosive head limit.
(From Q = lO/S).
The handbook further provided recommendations for furrow spacing for
the best ratio of lateral and vertical penetration. These recommendations
were based on a grouping of soil types, and were intended primarily as
a guide.
It was quite evident that the above design procedure is not

infallible, but was intended as a reference guide to be used with

 

 

 

 

 

- 39 -

discretion by service personnel. These data provide some means of
designing an irrigation system, however, in the event that water is
not available or the soil has not been leveled.

Several Australian workers have contributed to studies on furrow
irrigation, in designating what they term a "primary flow" system.
Lyon and Pennefather (49) described the generally low efficiency (33
percent) of furrow systems and stated that higher efficiencies (70 to
80 percent) were attainable through good design and operation. They
regarded the size of flow per furrow as the most important factor and
showed a relation between flow rate per furrow and the volume water
applied to the soil surface. At low flow rates, the water applied was
quite high; as the flow rate increased the water applied decreased,
until a minimum water application was reached. As the flow rate
increased from this point, the water application remained constant.
Many other workers disagreed with this hypothesis, because of some
rather broad assumptions.

Vasey (75) derived the equation for this curve as follows:

1. The volume of water applied by ideal furrow = de/12.I

where w is the furrow spacing
d is the depth of water in inches
L is the furrow length

2. By turning the water off when it reaches the bottom end of

the furrow (primary flow), the volume of water = Qt.

3. Thus the average depth, dave = 12 Qt/wL.

4. Then plotting dave and Q, a curve was drawn that showed a

minimum value of dave for large rates of flow, which was

designated as d1.

 

 

 

 

 

- 40 -

5. If the required application was greater than d1, the flow
should not be reduced, but the other dimensions of the system
should be changed.

The errors associated with this hypothesis were due to the fact

that water storage in the furrow was neglected and because it is seldom

 

practicable to turn the water off when it reaches the bottom end of the
furrow. The shape of the curve depends also on the rate of advance
function, and may assume a form quite unlike that shown by the authors.
In discussing primary flow, Lyon and Pennefather stated that the
necessary conditions for this system can be attained by lengthening
the watering run, increasing the width and roughness of the furrow,
cultivating deeper, impeding the flow with craps, decreasing the slope
or reducing the flow. They further recommended that furrow grades

should be uniform and that furrows Should be made to suit the large

 

flows required in "flat grade watering".

Philip (61) also advocated the primary flow system in discussing
the general mechanics of the advance of water in the furrow. He
suggested that the following relations be established in future work
on furrow irrigation:

l. The relation between wetted perimeter of furrow and equivalent

 

soakage area in an infiltrometer.
2. The relationship between furrow flow and friction losses.
3. The relation between furrow shape and time of irrigation
(changing shape during the season).
These relations would be extremely useful, whether or not the primary

flow concept is accepted.

 

 

, jj,, g "”7” win, . , , q
- 41 -

Theoretical analysis of furrow irrigation

Oroszlany and Wellisch (55) proposed an unusual method for furrow
design, based on the following requirements: a closed-end furrow
system, such that the total water applied equalled the total volume

of water required to wet the soil to a uniform depth; the infiltration

 

of water was uniform along the length of the furrow; and the advancing
water in the furrow reached the end of the run at the time the flow was
cut off. They derived equations for the flow variables T, the duration
of time of application; q, the flow in the furrow; and l, the furrow
length.

They assumed that the rate of advance could be expressed by the
relation x = aqktB, where a was a function of the soil characteristics;
and assumed that the effect of soil properties on the movement of
water could be characterized by one coefficient. This was questioned
however, for not only infiltration rates but also furrow erosion and
roughness affect water movement, and these affects vary throughout the
irrigation season.

An interesting analysis was presented, however, which bears
further investigation. Results of their analyses showed that average
field slopes (for ranges of 0.0001 to 0.006) had no direct influence
on water advancement. They also mentioned that if the wetted section
at the beginning of a furrow was greater than average, the advancement
of water was slower and the constant a would decrease. This lower
value of 3 caused a higher than actual value for the infiltration rate.
Thus they compensated the error resulting from the introduction of a

lower value for the wetted area by a higher than actual infiltration

rate. Theoretically, however, this conclusion was not valid, for this

 

 

 

 

 

assumed a linear relationship between infiltration rate and volume of
surface storage in the furrow, which may not be correct.

The authors prepared a table, based on their equations, that
permitted an easy solution of the discharge-length of run-time

relationship. They suggested applying a flow of one liter per second

 

to eight or ten furrows, and recording the time required for the water
to travel 50 meters. Then using a table with this corresponding time,
one found the discharge and total time of application corresponding

to the actual length of furrow and depth of water to apply. The fact
that the authors mentioned that the constant a did not change
appreciably during the irrigation season, and that the tables were
unsatisfactory when a small flow was introduced over soil with high
infiltration or vice-verse, raised considerable doubt as to the

validity of the solutions shown.

Theoretical analysis of border irrigation

 

A number of authors have attempted to define the flow of water
in irrigated borders, with varying degrees of success and acceptance.
Several authors stated that their analysis for borders applied also
to furrows; but it was unlikely that this was the case; for wetting
patterns, infiltration phenomena and flow in the furrows are
considerably different from that in borders.

Lewis and Milne (44) derived an equation for rate of advance down
border strips, based on the assumption of constant depth of water and
varying rate of infiltration. The final form of the equation was as

follows:
t

X
cx = — Jf y (tX - ts) x' (ts) dtS +~th/L

O

 

. i II.III.1.

 

 

 

-43..

which was solved when the function y was a solution of a linear

differential equation of the n th order with constant coefficients.
Several examples were given. If y, the infiltration function,

-rt)

was defined by y = b (l - e , then

_ l _ -kt
x k (1 e %

= _3_ [t
LR (b + c)
where k = r (b + c)/c.
If y was defined by y = at + b (1 - e'rt), then

x=_9._[ l-e-et cosh6t+(—a_-.§.) e-et sinh 6t]
La c6 6

These equations do not appear to have a wide acceptance by system
designers, possibly because of their mathematical complexity and because
the infiltration data are forced to fit a predetermined functional
relationship. Also, the effect of slope and surface roughness were not
readily discernable; because they were reflected in the depth of water,
which was estimated beforehand. Their analysis, on the other hand,
has been widely accepted by researchers and has stimulated a mathematical
approach toward field irrigation analyses.

Israelson (37) presented a rather simplified approach to border
analysis and rate of advance of water in a border strip. He also
assumed a constant depth of water as it flows over the soil. Letting
A represent the area covered with water at any time t, after water was
turned on, then

q dt = y dA + IA dt
where y is the average depth of water in inches, I is the rate of
infiltration into soil of wetted area in in/hr, and t is the time

after water was turned on in hours.

 

 

:

 

- 44 -

Then rearranging and integrating,

t = 2.303 (y/I) log q/q - IA

Thus, a rather simple equation was the result. The errors
involved in this analysis were increased, however, by the assumption
of a constant infiltration rate and a uniform depth of water. The
slope and roughness of the border were reflected in the depth of the
water, as in Lewis and Milne's analysis.

Israelson recognized the fact that furrow irrigation presents a
more difficult problem, in that the water wets only part of the soil
surface. He cited this as an advantage because it lessens the
puddling of heavy soils and cultivation can begin sooner after
irrigation than with borders.

Hall's (30) analysis of border flow closely paralleled the
analysis in this dissertation. Hall considered that the volume of
water in storage above the soil surface was equal to
Vsi = b (doc +~e) xi; where c was a constant that describes the shape
of the water surface, e was a depth correction termed the puddle
factor, do was the depth of water at the head of the check, and x1 the
distance the water has advanced down the surface of the check.

The infiltration function, y(t), was defined as the total quantity
of water per unit area which has entered the soil t units of time
after water was applied initially. The increment of volume applied

to the soil A Vai was then given by

v .
‘bi = “2 [(Yi ‘ Yi—l) + (Vi-1 ‘ 33-2)] Axl

+ 1/2 [ (371-1 ~ 33-2) + (371-2 - V149] sz +....+

1/2 [ (3'2 - Y1) + (Y1 - 0)] A xi_1 +ky1 Axi

 

 

 

 

 

 

_ 45 -

where R was a constant describing the shape of the wetting front in
the soil under the element of distance A Xi' Then, by letting
ai = (y1 - yi-2)/2, and by summing the volumes of water in the soil

and in surface storage, the mass balance for the check was:

Q0 At/b = aiAxi + ai_1 sz + .... + a2 AXi-Z + (kyl + cdo + e) Axi

 

Thus, a solution for Axi was obtained by using a simple
numerical method, which Hall illustrated with an example in his paper.
An analysis of possible errors in this method showed that errors in
estimating e, c, k or n have much less effect on the result than errors
in Q0 or y(t). Likewise, Q0 was the most important for determining the
first increments of distance while y(t) was more important in determin-
ing later increments of distance, or for longer furrow runs.

Hall also compared measured advance down a border with that
calculated by assuming various values for c and k. He found that
the curve for c = k = 0.75 fell approximately on the experimental
points, demonstrating the validity of the developed equations. He
concluded that this method of computing rate of advance was well
within the accuracy of infiltrometer data.

Bouwer (12) presented a somewhat different approach to flow in
borders which was somewhat laborous in that a number of equations
were solved simultaneously to determine the infiltration of water into
the soil. Considerable errors would be present if infiltration
changed rapidly with time and if the varying depth of water on the
surface were not considered. However, the method offered some
advantages in its simplicity and could produce more accurate results

by easy manipulation of the time and distance variables.

.l.‘ ..l . ll.

 

 

 

 

_ 46 -

Bouwer suggested that the method was applicable to furrow
systems, assuming that the width of the wetted front in the soil was
a multiple of the row spacing. He did recognize the problem in doing
so, however, for he stated that some refinement can be obtained if the
effect of stream width on infiltration was known.

Ostromecki (56) reviewed the equations proposed by Skotnicki,
Zakaszewski, Kostiakow and Michalowski, which dealt with the calculation
of the time required to flood irrigation checks. He pointed out that
these equations were limited to a condition of a low water table
(several meters below ground level); and because these equations
assumed a constant rate of infiltration, the practical applications
were not always quite justifiable.

Ostromecki then proposed a differential equation for the solution
of the time of flooding, based on a variable rate of infiltration
defined by the equation W = wlTa+1. His equation was developed in
a manner similar to Hall's, in that he equated the volume of water
introduced into the check in a finite time interval [X t to the sum
of the increments of volumes of water in surface storage and soil
moisture storage, in order to calculate the increment of distance,

XXX, that the water has traveled in the check. However, in order to
derive his equations, he apparently assumed that water flows into the
lower end of the check, and fills the check with successive horizontal
increments of water depth. This premise, in the writer's opinion,
deviated considerably from field practice and may result in a
considerable error in the calculation of the volume of water stored

above the soil surface. Otherwise his technique appeared valid. He

 

 

- 47 -

did not validate the equation with any empirical field studies,
however, and merely compared this equation with that of the four
other workers mentioned.

Although all of the above methods appeared to have merit, it was
doubtful that they could be applied to furrow irrigation unless the
stream shape-infiltration function was known. Because this function
depends on the soil properties and the flow regime, the Hamilton
furrow infiltrometer may provide a satisfactory means of measuring
furrow infiltration rates which could then be substituted into the
equations presented. In any case, the adoption of any mathematical
technique of preducting rates of advance of water in furrows will
depend on its simplicity, its accuracy, and the availability of field

data.

 

 

- 43 -
METHODOLOGY AND DERIVATION OF EQUATIONS

Any approach to a rate of advance equation for irrigated furrows
may be subject to error and a varying degree of applicability.
However, the mass conservation approach, as advocated by Hall,
Israelson and Ostromecki, appealed to this author as a method less
subject to error than others and as a method fairly easily validated
by empirical studies.

Of all the methods proposed for determining the rate of advance
in borders, as discussed in the review of literature, Hall's appeared
to offer the most promise as an accurate, simple solution. NOt only
was infiltration considered as a variable function of time, but the
water surface profile was also considered in determining the storage
of water in the border. Thus, one may consider that Hall's equation
was mathematically correct; that the equation itself need not be
validated, but that the infiltration and storage functions need
evaluation. This approach leads more toward the empirical study of
these functions than the study of the equation itself.

The purpose of this dissertation was then: (1) to adapt Hall's
approach to furrow irrigation for the derivation of a single equation
for rate of advance, (2) to validate the equation in field studies,
and (3) to shed some light on the relative contributions of the

infiltration and surface storage functions.

Qgrivation of the eggation
The method used to obtain the advance of the water front was

essentially a numerical integration. When water flows into a furrow

 

 

 

 

 

- 49 -

at a rate of Q cubic feet per second, part of this volume of water
enters the soil at an intake rate 1 = i(t), a function of time after
wetting. The rest of the water fills a volume VS above the surface
of the soil. For a given roughness and furrow shape, and water
surface slope at the head of the furrow; a depth of water, do’ will
be reached such that the rate of flow down the furrow at the head end
is equal to the inflow rate~Q.
The infiltration function y(t) was defined as the total quantity

of water per unit length of furrow which has entered the soil t units

of time after water was applied initially and continuously; such that

t
y(t) =f i(t)dt.
O

The relationship between total infiltration and surface storage
is given by the curves in Figure l with time as a parameter. Downward
from a horizontal line representing the soil surface, a series of points

were plotted on a vertical axis, representing to scale the total
volume of infiltration at the end of successive, equal increments of
time. At any distance X down the furrow, the volume of water applied
to the soil was determined only by the time elapsed since water first
reached that point.

If it is presumed that on the average the infiltration character-
istics were uniform for the length of the furrow, the horizontal lines
then represent the total volume of water in the soil at the corresponding
instants in time after water reaches the point considered. At the end
of the first time increment, A t, water will have reached X1 and the
volume of water applied at X = 0 will be yl. At the end of the second

time increment, the volume of water in the soil at X = 0 will be y2,

 

 

 

 

 

 

 

 

 

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mudmmmummu on mam Souwflw wfiu CBOp muamumwm mudmwmuamu
wxeraHo> :Owumuuawmcfi monomwunmu Hz moors. msouunw
m sBOp mocmumwu pom .wmeOum muumuam .nofiumuuagwafi

HmuOu monsoon coHuunu m3» m0 coHumnuwnaaw ofiumamnom .H wuswflm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

- 51 -

the volume of water in the soil at X1 will be yl, and the water will
have reached X2. Thus the curve passing through the points (0, yz),
(X1, yl) and (X2, 0) represents the total volume of water in the soil
as a function of distance down the furrow at time t = 2 At. Other

such curves for t = 3 At, t = 4 At and t = 5 At are also shown to

illustrate the method for constructing these curves. The area between

 

any two successive curves is then equal to the total volume of water
applied to the soil during the time interval At.

In addition to the volume of water stored in the soil as described
above, there is a storage of water represented by the depth of water
in the furrow. Depending on the slope, roughness and shape of the
furrow, there is a minimum depth do necessary at the head of the
furrow to pass the flow Q down the furrow. This depth may be obtained
directly from Manning's equation or from flow equations that may be

developed later to more adequately describe the flow phenomena in

 

small rough channels.

The depth of water necessary for flow past successive points down
the furrow will decrease, however, since the total flow past these
points decreases. The water depth thus becomes a funétion of the
distance down the furrow. While the depth of water at each point can
be computed, a simpler and more general approach was to assume that
the type of function represented by the water surface was the same
for all instants of time. With this assumption, the ratio of the
actual volume of surface storage to the volume of the circumscribing
parallelopiped is a constant c, which from reasoning should be greater

than one-half but less than one.

 

 

( r .
. t . \
. I I .
I . . .y ..
. .
.. . . x
. .
..
. .
<
. _
. .
t
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.
) a
. t . .
.
t
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O
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- 52 -

The value of c would depend not only on the shape of the water
surface but also on the shape of the furrow. For example, if the
equation of the water surface happened to be a cubical parabola with
vertex on the X-axis at the point in question, the value of the

constant ratio is 0.75 for a rectangular shaped furrow; 0.375 for a

 

triangular shaped furrow, 0.321 for a semicircular shaped furrow,

and a dual constant for a trapezoidal furrow. The advantage in
expressing the volume in terms of c lies in the fact that c can always
be computed for any particular furrow shape if enough is known of the
geometry.

The volume of water calculated in the above manner was only thatl
which was necessary for the required flow to occur at the roughness
and slope of the channel, and did not include the volume of water
which must be applied to fill the pockets and minute depressions

before flow can occur. Thus for purposes of surface storage, a

 

correction must be applied to represent the volume of water which
would remain in the furrow after the water was turned off, assuming
zero infiltration. This average volume correction was termed the
puddle factor, denoted by e. It is somewhat dependent upon surface
roughness and consequently the volume of flow and water stability of
soil aggregates, but for most soil conditions, should be a fairly
constant value.

The volume of water in storage above the soil surface at any time
ti’ is than equal to

v _ = [c.f(d) +e] Ki (1)

81

 

 

 

 

 

-53—

The increment of surface storage volume which occurs during

 

any time interval is equal to the difference between the surface

storage volumes at the beginning and end of the time interval.
Thus Avgi = [c.md) + e] Axi (2)

The increment of the volume of water stored in the soil is equal

 

to the area between two successive total application curves. In
Figure 1, for the fifth time increment, this is the area whose corners
are y4, X4, X5 and y5. The area except the last three cornered element
below A XS can be determined by the trapezoidal rule. The last
element was estimated in the same manner as the surface volume by
assuming that the shape of the curve in this last element was a constant.
The ratio of the actual cross sectional area to the area of the
rectangle circumscribing it will be a constant, k, whose value should
be between one-half and one. The increment of volume applied to the
soil Avai is then given by
Avai = 1/2 [(yi - 311-1) + (33-1 - 53-2)] A X1 +
1/2 [(yi_1 - yi_2) -I- (yi_2 - yi_3)] sz + +
1/2 [(5'2 " Y1) + (Y1 "' 0)] AX1-1 + kyl AXi (3)
To simplify equation (3), one may assume that in most cases the

function = atn is a licable as ointed out by others in the review
y PP : P

 

 

of literature. In fact, as long as y is an algebraic function of t
(i.e. nontrigonometric or transcendental), this postulate does not
affect the validity of the analysis; it merely is a more simplified
form. For example, if y = atn +-bt, there would be only one more term

to include; or if y = y(t) is expansible in a power series in t, the

 

' -54-

method, though cumbersome, would still yield a workable solution.
Then, assuming that yl = a(A t)n; y2 = a(2 At)n; y3 = a(3 At)n;
y1 = a(i A c)“
Avai=l/2 [a(iAt)n- a {(i- 2) A t} n] Ax1+
l/2[a{(i-1)At}n~a{(i-3)A }]Ax +....+
1/2 [a(2 Ann] Axi_l +ka( At)n A Xi (4)
Simplifying equation (4) by factoring;
Ava, =£L42iLn [{in - (i - 2)“} Axl-i-
{(1 - 1)n - (1 - an} Ax2 + +
2n Axi_l+2k Ari] (5)
By substituting a factor defined by
gi = in - (i - 2)n where i 2 2,
Avai = 2S_A?E}_n[giAxl + gi_l A x2 + + ngxi_l + 2k Axi] (6)
By the law of conservation of matter, the quantity of water flowing
into the furrow during any time increment must be equal to the sum of the
increments of storage produced. Using equations (2) and (6), the mass

balance for the furrow during any time increment is, for i Z 2;
Q( At): —§_(_2A._t).ri [giAxl + gi_1AX2 + + ngxi_1 + 2kAxi]
+ [c.f(d) +e] Axi (7)
Presuming that the shape of the furrow is either parabolic or
V-shaped, the volume of water in surface storage can be expressed as
a function of d2. Also, since the total intake function is likely to

be characterized by cylinder or furrow infiltrometer techniques, the

intake function should be modified by a factor F to permit the use of

 

 

 

 

’55-

the equation for all conditions of furrow shape, roughness, spacing,
depth of water, etc.; such that yi = F a (i At)n. Thus equation (7),

including the above changes and rearranged, becomes

A Xi = IQ<A t) - LES-955E: [siAxl + 314sz + + gZAXi_1 (8)

 

Fa(At)n k + cdoz + e

For X1 the solution is simply

= 0(AtL
Axl Fa(At)n k + ch2 + e (9)

The value of [XXI is obtained from equation (9) and substituted into
equation (8) for i I 2 to obtain [3 X2. This value is substituted in
turn in equation (8) for i = 3 to obtain A X3.

The gi are calculated directly from the empirical total infiltration
function and are shown for various values of n in Table I. While not
necessary, the solutions of equation (8) can be determined easily with
electronic computers or with the form shown by Hall in his paper.

Equation (8) was obtained with accepted laws and equations of
hydraulics. However, certain assumptions were made in order to reduce
the labor of computations and to provide for a more general, acceptable
equation. These postulates primarily concerned the constants F, c and
k. Additional factors affecting the accuracy of the results were the
experimental accuracies with which the infiltration functions were
determined and the accuracy of the estimates of the puddle factor and
furrow roughness. None of these factors should be expected to remain
constant during the irrigation season or from year to year, except
possibly as average values.

On soils of good permeability, the volume of water stored in the

soil will usually be much larger than the volume of water in surface

 

 

 

 

 

.20
.24
.28
.32

.36

.60
.64
.68
.72
.76

.80

.84

-56-

Table I

gi=in-(i-2)n

 

82 83 84 85 86 g7 $84, 897 810
1.0281 .0449 .0289 .0216 .0173 .0144 .0124 .0110 .0098
1.0570 .0919 .0603 .0455 .0368 .0311 .0269 .0237 .0213
1.0867 .1409 .0943 .0721 .0589 .0500 .0435 .0387 .0348
1.1173 .1922 .1310 .1015 .0837 .0716 .0626 .0560 .0508
1.1487 .2457 .1708 .1340 .1115 .0961 .0847 .0761 .0692
1.1810 .3017 .2136 .1698 .1427 .1237 .1099 .0992 .0906
1.2142 .3602 .2601 .2091 .1772 .1551 .1386 .1257 .1154
1.2483 .4213 .3100 .2524 .2159 .1902 .1711 .1561 .1440
1.2834 .4851 .3638 .2999 .2588 .2298 .2080 .1908 .1768
1.3195 .5519 .4216 .3517 .3066 .2743 .2497V .2303 .2145
1.3566 .6216 .4838 .4086 .3594 .3240 .2969 .2753 .2575
1.3946 .6944 .5507 .4710 .4180 .3794 .3499 .3262 .3067
1.4340 .7705 .6222 .5387 .4827 .4416 .4097 .3839 .3627
1.4743 .8501 .6992 .6127 .5540 .5106 .4768 .4493 .4265
1.5157 .9332 .7817 .6933 .6327 .5876 .5521 .5231 .4989
1.5583 1.0204 .8701 .7812 .7195 .6730 .6363 .6063 .5810
1.6021 1.1108 .9647 .8766 .8150 .7681 .7307 .6998 .6738
1.6472 1.2056 1.0660 .9805 .9198 .8734 .8361 .8052 .7790
1.6935 1.3047 1.1744 1.0933 1.0350 .9901 .9539 .9234 .8976
1.7411 1.4082 1.2903 1.2157 1.1616 1.1194 1.0850 1.0562 1.0316
1.7901 1.5164 1.4142 1.3485 1.3002 1.2624 1.2313 1.2050 1.1826

 

 

 

 

 

-57-

storage. It therefore appeared that some error in estimating e, c,
k or surface roughness would have much less effect on the result
than errors in Q or y(t). It was also noted that while Q will be
the most important factor for determining the first increment of
distance, y(t) will be more important in determining later increments
of distance. This is an advantage, however, because more tolerance
can then be allowed for short runs than for longer runs. Where long
runs would be more efficient (low infiltration rates), the infiltration
function should be subject to less error in measurement.

Thus, an equation for rate of advance in irrigation furrows has
been written. The remainder of this dissertation will then describe
the results of certain field and laboratory tests, conducted to

demonstrate the applicability of the equation and to discern the errors

and effects of estimating e, c, k and F.

 

 

 

 

 

- 58 -
DESCRIPTION OF FIELD AND LABORATORY STUDIES

To test the applicability of the furrow equation and to determine
the effects of some variables on the coefficients in this equation,
appropriate measurements were made in the field during the summer of
1958. In addition, the equation was evaluated using data from other
workers.

A preliminary model study was also conducted in the greenhouse,
in an attempt to evaluate the effects of furrow shape, spacing and
water depth on the rate of infiltration into the furrow. This will
be described later, as it affects only a part of the problem of non-
uniform flow in furrow.

The field studies were conducted on the Marshall Wanzer ranch
in Tulare County near Farmersville, on a Cajon fine sandy loam soil;

and on the experiment fields of the University of California at Davis

on Yolo silty clay loam soil.

Field studies in Tulare County

The field work in this area was conducted in cooperation with
Mr. Alan George, Farm Adviser, who selected the fields and assisted
in the collection of field data. Two separate fields were selected
on the Wanzer Ranch; both were planted to cotton in the middle of
April, after a pre-planting application of water. The two fields,

hereinafter called the northeast and the southwest fields, had the

following treatments:

 

 

 

. .
. .
.
. .
.
: r\
I _
x t _
. .
.
. I
.
n .
. .
. ..

 

-59..

Northeast Field

Planted Cotton, April 18

Cultivated ‘ May 15, June 10, June 21

Fertilized May 26, 80 lbs. N

Irrigated June 12, 30, July 17, 31, August 13, 22
Crop history Cotton, Cotton, Field Corn, Sweet

Corn, Cotton, Cotton, Cotton

Southwest Field

Planted Cotton, April 16

Cultivated May 7, 13, June 10, June 21
Fertilized May 21, 80 lbs. N

Irrigated June 13, July 1, 18, 30, August 8, 22
CrOp history Cotton, Cotton, Corn, Cotton, Cotton,

Corn, Cotton

Each field had been recently graded, the northeast field had an average

slope of 0.195 percent for 400 feet and an average slope of 0.068

percent from 400 to 650 feet. The southwest field had an average slope

of 0.086 percent for the entire length of 520 feet, but the field con-

tained numerous slight depressions that had not been removed during

grading.

To evaluate the effects of changing soil conditions and foliage
conditions during the irrigation season, the trials were conducted

during the first, third and fifth irrigations. Ditch water of about the

same quality was applied at each irrigation; in no case was salinity a

problem in the irrigation Operation.

 

 

 

 

-60-

Before each irrigation, the infiltration rates of the soil were
determined with the Hamilton furrow infiltrometer (as described by
Bondurant). Float valves were used to maintain a constant head of
water in the furrow section and the buffers; and a Friez FW-l water
level recorder was used to record the water level in a calibrated
five-gallon pail which served as a water storage tank. These
instruments are shown in Figure 2. The furrow section was lined with
plastic film, and measurements were started when the furrow section
was full of water and the plastic was removed. Disturbance of the
soil by water flowing from the valves was prevented.

At least two infiltrometer measurements were made immediately
prior to each rate of advance measurement in each field in an area
adjacent to the test area. These measurements were conducted over
a period of time sufficient to insure that infiltration had reached
a constant value.

To evaluate the influence of flow rate (volume/time) upon rate of
advance, measurements were made with five flow rates, representing a
range from very low to very high for the soil and length of run
conditions encountered. Five adjacent furrows were irrigated with
the same flow rate; 25 furrows were irrigated in total. Because the
two fields were irrigated from a head ditch at the upper end of the
fields, it was necessary to combine various sizes of siphons or spiles
to obtain the five flow rates desired.

For the first irrigation, combinations of 3/4", 1", 1 1/2" and 2"
aluminum siphons were used to introduce water into the furrows. These

were primed by the irrigator and the time at which flow started in

 

 

 

 

-61...

 

 

 

 

 

 

 

 

Furrow infiltrometer and float valves.

 

Figure 2. Furrow infiltrometer in operation.

 

 

 

 

 

-62—

each group of furrows was noted. The rate of advance was then

determined by noting the position of the wetting front in the furrow
with resPect to stakes placed every 50 feet down the field. The flow

of water into alternate furrows from the siphons was measured with a
calibrated bucket and a stopwatch. Because this was a difficult

method, sometimes leading to questionable accuracy; the head on the
siphon was determined by leveling, and the flow calculated from rating
curves for the siphons. The flow rates than used for later calculations
were averages of the two methods employed.

During the third and fifth irrigations, spiles were used to
introduce water into the furrows from the head ditch. These were
placed in the ditch bank and allowed a much more precise measurement
of the flow with the bucket. Two to three determinations of the flow
rate were then made on alternate furrows, and the average of these
determinations employed in the later calculations.

Toward the end of each trial, the depth of water in each furrow
was determined and observations were made on the shape and width of
each furrow.

In two cases--the first irrigation in the northeast field and the
third irrigation in the southwest field--some of the data were discarded

because of major changes in the flow condition. Breaks in the head
ditch upstream resulted in excessively varied flow, sufficient to
warrant exclusion of the data. For all of the other trials, the flow

rates were presumed to be fairly constant.

 

 

 

 

 

 

- 63 -

Field studies at Davis

 

The studies at Davis were conducted in a small area which had been
planted to milo in June, and which was irrigated for the first time
at the middle of July. The measurements were made in much the same

manner as those in Tulare County, except that gated pipe was used to

 

introduce water into the furrows. Two studies were made here--on J
July 14 and August 28.

On the first date, three flow rates were introduced into three
groups of three furrows each; on the second date, three flow rates
were introduced into three groups of four furrows each. Flow measure-
ments were again made with a calibrated bucket and a stopwatch, and
the position of the wetted front in the furrow noted in 50 ft. intervals
for the length of the field.

Furrow infiltrometers were operated at the same time as the
irrigation, on adjacent furrows, with the same equipment as previously
described.

Toward the end of each irrigation, water depth and furrow width
were measured and recorded. After the second irrigation, the shape
of each furrow was determined by the method of cross sections; that
is, the difference in elevation between the water surface and the

furrow bottom was measured at one-inch intervals across the furrow.

Furrow model studies
To investigate several of the furrow parameters that might
influence the infiltration phenomenon, two model tanks were con-

structed. The tanks were about six feet long, three feet deep and

0.1 feet thick; with 1/4-inch plate glass on the front, through which

 

 

 

 

 

 

 

h

wetting patterns were observed. Both front and back of the tanks
were strongly reinforced to prevent warping or twisting, and the base
of each tank was equipped with leveling screws. A small perforated
tube wrapped with fiberglass mat was installed at the bottom of each
tank, to permit the escape of entrapped air in the soil during tests.

The plywood back of each tank was removable to facilitate placing
the sand in the tank and to allow the sand to later dry out at an
accelerated rate.

Initially, the tanks were tipped forward, with the glass front
down, and the backs were removed. Air dry sand was then placed
in the tank in uniform horizontal layers, to eliminate any horizontal
stratification when the tanks were then tipped to their original
position. The sand has been classified as an Oso Flaco fine sand,
which is a dune sand with a fairly uniformly graded particle size
distribution and with nearly spherical shaped particles.

The sand was leveled in the tanks, the back was replaced and the
tank tipped back and leveled. Several wetting and drying cycles were
performed to settle the sand. Drying was accelerated by removing the
back and blowing air over the soil surface for 24 to 48 hours, or
until the entire depth of sand was air-dry. The surface of the sand
was protected by a layer of fiberglass to avoid any disturbance by
air movement, as shown in Figure 3.

Furrows were made in the wet sand by slicing out of the sand the
size and shape of the furrow desired. The furrow sides were then
lined with several thicknesses of fiberglass mat and coarse screening,

to maintain the shape of the furrow when water was later introduced.

 

 

 

 

_ 65 -

O

. III-:uvlgl#|fl’s~ ‘3
4N)" "

x”

 

 

 

Figure 3. A view through the drying fan showing the
back of a model tank which had been tipped
forward for drying.

 

 

 

 

-66-

Water was supplied to each furrow from a 4-inch diameter plastic
cylinder approximately 24 inches high, using the principle of
Mariotte's bottle to supply water and to maintain a constant water
level in the furrow. All the water used was cold tap water, the
temperature of which did not change during the period of the study.
The water was chlorinated in the cylinders to prevent any microbial
growth in the sand.

The cylinders which were calibrated and read to the nearest 9 cc.
(.05 inch depth), were attached to a manifold of positive action valves
with tygon tubing. This arrangement permitted entry of water into as
many as seven furrows simultaneously. Figures 4 and 5 show the arrange-
ment of the tank and the cylinders. Immediately after water was
admitted to the furrows, the position of the wetting front and the
depth of the water in the supply cylinders were recorded at specific
time intervals. This was done by marking the glass front of the tank
and the side of the cylinders with a wax pencil.

Since it was difficult to prevent entirely any deflections in the
front or back of the tanks, measurements were made to determine the
magnitude of such deflections. The depth of sand was determined at
the start and toward the end of the study. In both tanks the maximum
variation in sand depth was about 9 percent of the average depth,
while the average variation was about four percent of the average
depth.

The specific variables studied were as follows:

Furrow shape

a. triangular-~6" deep, 1:1 side slopes

 

 

 

 

 

 

-67..

   

 

Figure 4. Front View of a model tank immediately
after a measurement, showing the location
of the water supply cylinders and the valves.

mm ,

 

 

- 68 -

 

 

 

 

Figure 5. Close-up view of the front of a model tank,
showing the furrow and the method of marking
the positions of the wetting front.

   

.- 69-
b. trapezoidal--6” deep, 1:1 side lepes, 4" bottom.width

Furrow Spacing
a. 18 inches
b. 36 inches

c. 72 inches

Water depth
a. 2 inches
b. 5 inches
After initial settlement of the soil in the tank had taken place,

the sand was allowed to come to an air dry condition and the tests were

 

then performed. For the 72-inch spacing, one furrow was made in the

center of the tank, and several separate tests were conducted for

J
purposes of replication. For the 36-inch spacing, half furrows were

added at each end of the tank, and again several separate tests were

conducted. For the l8-inch spacing, two more furrows were added,

 

making a total of three complete and two half-furrows in the tank.
In this case, the three furrows provided some replication, and

additional tests were not performed.

 

 

ml

1?

- 7o -
PRESENTATION AND ANALYSIS OF DATA

The data described in the previous section will be presented
in the order of the development of this study, or in the order of the
apparent need for these data. First, the applicability of the furrow
equation will be treated; that is, a comparison will be made of the
observed rate of advance and a theoretical rate of advance for all the
studies conducted.

Secondly, parts of the equation will be analyzed to determine
the magnitude of the separate factors involved. Here, the results
of the furrow infiltrometer data and their apparent fit to the
existing field conditions will be shown, as well as the results of
the furrow model studies conducted in the laboratory. The results of
measurements of furrow size and shape and the subsequent calculation
of hydraulic roughness will then be presented--all in an attempt to

provide more knowledge on the behavior of water flow in small channels

and the resulting storage of water in the furrow channel.

Applicability of the furrow equation
After each field study had been conducted, the infiltrometer data

were plotted and the equations for total infiltration were calculated.

 

In general, these equations assumed the form I = Atn. In some instances,
the slope of the curves for about the first 15 minutes of the
infiltrometer run was steeper than the curve for the remaining time;

but rather than introduce the problem of using two separate equations

for infiltration, one single equation was calculated which represented

the total infiltration for the remaining time. This should introduce

   

 

 

 

we

me

av

 

 

_ 71 -

only a small error, because the flow of water in the furrow usually
requires a considerable length of time, and the equations used should
be representative of conditions existing throughout most of the trials.
In each study, at least two separate infiltrometer determinations
were made. Two equations were thus obtained by the slope-intercept
method, and an average of the two was used for the study. The resulting

average equations are shown in Table II.

Table IIA
Infiltration Equations for Cajon Fine Sandy Loam,

Wanzer Ranch, Farmersville, California

 

 

Northeast Field Southwest Field
Irrigation Equation Di Equation Di
First I = 0.0342 t0°56 0.280 1 = 0.0908 t0'31 0.278
Third I = 0.0142 t°°7°4 0.135 I = 0.0751 t0'375 0.155
Fifth I = 0.0174 t0'468 0.120 1 = 0.0562 t0'332 0.150

 

Table IIB
Infiltration Equations for Yolo Silty Clay Loam,

Davis, California

 

 

Irrigation Equation Di
First I = 0.0341 t0'625 0.17
Second I = 0.0321 t0'549 0.15

 

In each of these tables, I is expressed in cubic feet per foot length

of furrow, D1 represents the depth of water in the infiltrometer in

 

 

 

 

 

_ 72 -

feet, and t represents elapsed time in minutes.

Thus, for each study a standard measurement of infiltration was
obtained and an equation for total infiltration as a function of time
was determined. Inasmuch as these data were determined immediately
preceeding an irrigation, the equations should represent the field
conditions of moisture content and soil aggregation encountered
during the irrigation.

Two glaring errors are involved in the above assumption. First,
the area of soil isolated by the infiltrometer was not subject to
erosion, so the furrow essentially retained its shape and dimensions.
A furrow in which water is flowing, however, is Subject to soil
erosion; consequently its shape and size will change depending on its
roughness, aggregate stability and aggregate size, etc. Thus, the
furrow used for determining infiltration rates may or may not be
representative of furrows in which water is flowing.

Secondly, the depth of the water in the infiltrometer may differ
considerably from that in a flowing furrow. If the infiltrometer depth
is greater, it may be presumed that the total infiltration will be
greater than that in a flowing furrow.

In view of the fact that some determination of infiltration is

 

necessary, and the fact that no better method was available; these two
discrepancies have to be ignored. This is not serious, however,
because as other authors have pointed out, the shape of the furrow and
the depth of water in the furrow affect only the constant A in the

:1

equation I = At . Thus, if a factor F, which is a function of various

furrow parameters, were applied to the infiltration equation; a

 

 

"1

ba

Wit

est

eqt

 

tru

war

1'63

 

 

-73-

suitable equation for infiltration from furrows in which water is
flowing should result.

The equation for rate of advance, as derived in a previous
section, was as follows:

AXi = QAt - 1/2Fa(At)n[(siAX1 + gi_1Ax2 + + 324X1-1)]
Fa( At)n k + cdoz + e

 

In each trial, the depth of water flowing in the furrows was
measured; and assuming some reasonable furrow shape from observations,
the volume of water in storage in the furrow could be calculated. In
the northeast field on the Wanzer Ranch, the slope of the field changed
abruptly at a distance of 400 feet from the upper end. For this
reason, the depth of water changed in proportion to the square root of
the ratio of the two slopes; and for purposes of calculating the rate
of advance, as soon as water had reached station 4 + 00, the term
representing storage in the denominator of the equation was appropriately
revised.

In most cases a value for the puddle factor e was assumed to be
within the range of 0.001 to 0.003 cu. ft. per ft. These values are
based upon cursory observations of stationary roughness in the furrows.
With the field slopes encountered in the field studies, errors in
estimating the puddle factor should not affect the accuracy of the
equation significantly.

Assuming that the infiltration function adequately represented the
true infiltration of water into the soil, that the measured dePth 0f
water in the furrow was reasonably accurate, that the puddle factor was

- atel
reasonably representative, and that the flow rates weie accur y

 

 

 

- 74 -

determined; the only remaining unknowns in the equation were c, k,
F and Xi'

For the analyses, c was assumed equal to unity, because field
observations indicated that a constant depth of water in the furrow
was reached shortly after the wetting front had passed. No data were
available from which any other value could be justifiably selected.

The constant k and the furrow shape factor F were then combined to
reduce the number of remaining variables in the equation; thus only
F and X1 remain unknown.

For each flow measurement for each study, a factor F was assumed
and X1 was calculated. Then by trial and error, a value of F was
reached whereby X1 (calculated) was equal to Xl (observed). This
resulting value of F then remained constant throughout the calculations
for the remaining Xi' Once this initial step was performed, the
calculations proceeded rather speedily, for the denominator of the
equation and most of the numerator remained constant. Several sample
calculations are shown in the appendix.

The time A t selected for the calculations of rate of advance
was either 10 or 20 minutes, depending on the length of time the
measurements were made. For eight of the trials, two separate
calculations using both 10 and 20 minute intervals were made. There
was no difference in rate of advance due to these different time
intervals.

Comparisons of calculated rate of advance and observed rate
of advance for all of the field studies are shown in figures 6

thr°USh 12. In all cases, the calculated rate of advance was almost

 

 

 

 

 

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IN MINUTES

TIME

-76..

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

:20
FIRST IRRIGATION- SOUTHWEST FIELD -
399m *WANZER RANCH :1
' I
I 59pm V I’
I
I I
A’
no -
I‘flpfl‘
I //
so J1 20°”
I ’ g
A f
I p
.0 I) ' Z ‘
I' i
i .!
I’ I
I 1’ ” ’." i i
20 - -1 _r
I, OBSERVED
’ ---_ - CALCULATED
O i_‘__J——i____a
o n 2 3 4 s
DISTANCE m IOO FEET

Figure 7. Comparisons of observed and calculated rates of
advance of water in furrows,for indicated flow rates.

- 77 ~

 

WANZER RANCH
THIRD IRRIGATION - NORTHEAST FIELD

 

 

 

      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 
 

 

2.3899m
nor—ii, n, ,'
I
I
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..---... CALCULATED
O 1 1 l A i
0 I 2 3 4 5 5

DISTANCE IN IOO FEET

Comparisons of observed and calculated rates of advance

Figure 8.
of water in furrows, for indicated flow rates.

_____

 

 

 

~ 78 ~

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

MC
FIFTH IRRIGATION - NORTHEAST FIELD
WANZER RANCH
I20 , 3.59:9pm 5.74qpm .—
I
2 9pm ’4’
’ I
Imp“ "
m I
I. ,7
a
E
x // 7‘
so~ ‘3
E I
z / I
so I- j i
40
a, / __
OBSERVED
_.___ CALCULATED
o I 4
O I 3 4 5 6

2
DISTANCE IN IOO FEET

Figure 9. Comparisons of observed and calculated rates of advance
of water in furrows, for indicated flow rates.

 

 

-79..

 

IZOr———r exit, _ i,
FIFTH IRRIGATION WANZER RANCH 1’
I SOUTHEAST FIELD 9.389pm
Ioo» . 3'19”?"

 

 

 

 

 

 

 

 

 

 

 

80 ’ 784gpm
(I)
w .
D .
E l’
5560 '"
a ’I
m .‘
E
I- 40 _+. ,
I
II
I, : ._OBSERVED
20 I , ,, -_-CALCULATED
I I
I I I I
l I ‘ I
O I J
O I 2 3 4 5 6

DISTANCE IN IOO FEET

Figure 10. Comparisons of observed and calculated rates
of advance of water in furrows, for indicated

flow rates.

 

 

 

 

 

wrrrjww

s 80 -

 

20.2 qpm

.4°_____ FIRST IRRIGATION
CAMPBELL TRACT, DAVIS CALIF.

 
  
  
  
    

   

 

I I
I I I

H.04gpm

  

 

IOO

 

 

 

 

IN MINUTES

 

 

 

 

 

TIME

 

 

 

 

Do ;
so
¢o Fir“?
OBSERVED
20 _-_ CALCULATED _

I I

O I 2 3 4
DISTANCE IN IOO FEET

  

 

 

   
 

alculated rates of

1. ‘ s of observed and c
Figure 1 comparison for indicated flow

advance of water in furrows,
rates.

 

 

 

-81..

80

 

SECOND IRRIGATION

CAMPBELL TRACT DAVIS CALIF. " j‘MLL‘
TO

 

 

 
 
 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2qum
60v F
’/I I
I
I
so
'0
3 no
:3
2
x
2
so
MI
3
.-
/ I __OBSERVED
'0 r I _---CAI.CULATED 7
I I
” I I I I
o I I
O I 2 3 4 5

DISTANCE IN IOO FEET

Figure 12. Comparisons Of Observed and calculated rates
of advance of water in furrows, for indicated
flow rates.

 

 

 

 

 

 

- 32 _

equal to the Observed rate of advance, indicating a rather high
degree of predicting accuracy of the equation. The discrepancies

in figures 7 and 10 were due to a small rise of about 0.03 feet in
field elevation from station 2 +-50 to station 3 + 00. This was not
taken into account in the predicting equation, but it evidently
affected the observed rate of advance considerably.

It was interesting to note in these two cases that the predicted
distance down the furrow was nearly equal to the observed distance
after the flow had become more stabilized on the downstream side of
this ridge. This might indicate that the equation has a practical
use in fields where grading or leveling has been done imprOperly, or
where minor changes in grade may occur.

From the results of these seven studies one may conclude that an
equation may be available for accurately predicting the rate of advance
Of water in furrows. 0f perhaps even greater importance is the fact
that the equation defines the research areas in which additional work
is necessary, and also designates the relative importance Of the
variables affecting flow and the conditions under which the importance
may change.

To test the equation under more severe conditions of data avail-
ability, information gathered at an irrigation training conference in
1950 at Davis was selected and analyzed. These data, over which the
author had no control, consisted of rate of advance measurements and
inflow-outflow measurements for three rates of flow. The furrow inflow-
outflow measurements were used for plotting the total infiltration as

a function of time. The infiltration equation for each flow rate was

then determined.

 

 

 

 

 

_ 83 -

The outflow meaSurements using the above method are usually
made at a distance of 100 feet from the upper end of the furrow. The
instantaneous infiltration rate is then assumed equal to the difference
in flow rate between the upper end and the outflow section, divided by
the average of the times that water has flowed past each of these two
sections. The resulting infiltration rate then represents an average
or an integrated rate over the 100-foot length, rather than an
instantaneous rate at a particular point. For this reason, the
determined infiltration rate was reduced by an arbitrary factor,
similar to the F factor previously mentioned, for use in the rate-of-
advance equation.

The results of these calculations are shown in Figure 13. A
fairly good correlation between the Observed and calculated rates of
advance was again evident. Thus, the equation may be expected to
perform satisfactorily under conditions of limited data and limited
field contact.

A similar conclusion may be drawn from Figure 14, which also
represents a condition of limited field data--in this case, gathered
by another graduate student. These data were treated rather uniquely,
because three flow rates were used and only one inflow-outflow measure-
ment was made, for which the flow rate had not been indicated. An
infiltration equation was determined from the inflow-outflow data and
used in the calculations for rate of advance of the three different
flows.

It was evident in Figure 14 that the calculated rates of advance

for the 11.0 and 23.9 gpm flow rates differed considerably from the

 

 

 

 

TIME IN MINUTES

-84—

 

 

 

 

 

 

Iao 4.
T I
I60 I r
I
I I
I40 I I
I I I
I I I
I .
I I
i I
In“ | i A
luv 1 ‘
II
I

 

 

 

 

 

 

Figure 13.

4
I

TRAINING CONFERENCE
DAVIS, CALIF. I950

— OBSERVED
.. - .. CALCULATED

l l l
4 5 6
DISTANCE IN IOO FEET

Comparisons of Observed and calculated rates
of advance Of water in furrows, for indicated
flow rates.

 

 

 

 

 

 

 

 

90

.m—Wgflfl. ,V ”7,7 ,7, ._,,.‘.~.-...,..7.7 . _ . ..,_ -—.--_,,-— ,_ . V

e 85 _

 

 

60‘

M 7

DATA FROM EDUARDO JORDAN
DAVIS, CALIF, I957.

  

 

 

TIME

'0 $0n———fi~ f T

In :

t- s

D I

z /
2 40 I

a; l

 

 

 

 

 

 

 

 

 

OBSERVED
.. ._...- CALCULATED

 

 

 

 

 

Figure 14.

4 5
DISTANCE IN IOO FEET

A comparison of observed and calculated rates
of advance of water in furrows, for indicated
flow rates, using limited infiltration data.

 

 

 

- 86 -

observed, whereas the calculated rate of advance at 16.3 gpm agreed
fairly well with that for the observed rate of advance. Later, the
major professor for the graduate student stated that the inflow-outflow
measurements had been made in the furrows in which 16.3 gpm was
flowing. This was a timely statement, for it verified the fact that
the rate of advance equation will produce satisfactory results only

if valid data are used in the equation.

The rate of advance equation thus appears to be capable of
predicting an advance of water down a furrow with a fairly high degree
of accuracy. Studies on two different soil types at different times
during the irrigation season indicate that the equation is valid
under a range of field conditions. Before full use can be made of

this equation, parts of it will need further analysis.

Furrow infiltration

 

One of the hypotheses stated in the initial development of the
rate of advance equation and of this study was that the infiltration
of water from a furrow (a two dimensional system) as a function of
time was related linearly to the depth of water in the furrow, the
furrow shape and size and the furrow spacing. The model study was
conducted to evaluate this hypothesis, and to determine the relation-
ship between these factors.

Data from the field studies will be analyzed later, to evaluate
the effectiveness of the furrow infiltrometer and its relation to
existing furrow conditions.

Duplicate measurements of total infiltration of water from

simulated furrows in the model were averaged and the total infiltration

 

 

 

 

-37-

was plotted as a function of elapsed time. The results are presented
in figures 15 and 16, in which the factors of furrow shape, depth of
water and furrow spacing are identified.

The initial parts of the curves represent that time in which the
furrows were being filled with water to a predetermined depth, which
was a relatively short time compared to the total length of time of
the measurements. The remainder of the data represent the total
infiltration function after the depth of water was stabilized. Only
the latter condition was analyzed and interpreted because the initial
transitory condition would not necessarily represent the variables
under study.

Straight lines were drawn through the plotted points by eye.

The equations for these straight lines were then determined. The fact
that the resulting curves are straight lines on rectangular coordinates
was of little consequence--this merely represented a final condition
where the infiltration-rate into the sand was equal to the hydraulic
conductivity of the sand. As expressed by Hansen, this represented

the condition of a head loss per unit length (ht/y) that became so

small that the hydraulic conductivity was the only governing factor.

The equations that were determined were in the form I = Atn + B,
where n equalled unity and B represented the volume of water required
to fill the furrow and the volume of water added to the soil during
the time that ht/y was significant. For this analyses, however, the
values of B were discarded, because this represents an initial
condition which had little bearing on the relationships to be evaluated.

Thus, the equations selected were in the form I = At, from which

it was evident that the effects of the variables could be expressed by

 

 

 

 

CUMULATIVE INFILTRATION IN CC.

-33..

 

 

”fie
___._+e_-a—-———-“
_._'.—d

iii—«+—

 

 

L__._.—.._——d—
—?4——I
\
\
\
L ‘
U\ ‘
‘\
\—
‘R
‘

 

 

 

 

 

 

 

 

 

 

 

 

 

 

spec I
/
/ [2"], I
III r I}!
‘ [I ’1
I!” 1"
j?” {II
| I
‘ ’ Ir
, I,’ MODEL 37qu
2,000 ‘ 17L TRIANGULAR SHAPED FURROWS
’4’ / _,___ 2" DEPTH
5"DEPTH
I,ooo - " NUMBERS REFER TO

I FURROW SPACING.

a. IMI‘HI

L i
O I 2 3 5 6 7 8 9 I0
TIME IN MINUTES

Figure 15. Total infiltration of water from model
furrows, as a function of elapsed time.

 

 

 

 

 

 

 

-89...

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  
 

 

 

9,000; ,
I 72I a/ I I
36
Y ID
/ /
apoc , ’36
I
/ , ,’ 72
' I I [P
/ 'x x
zoos ‘ I I 1.,
. I l ,
t) I ’ A I
o I A J! I I
E ' I 1’ ’
I
2 was " ’1
2 I 1 I
v; / IP
I I
I: I I
'3 5.000 / 3 (y,
E h’ ’1
E I ’III
u: C) ;d’4?/’
z 'I-
O- ,9
:5 I? ’r’
A
2 I II}
3 I;
o l/
I
MODEL STUDY
TRAPEZOIDAL SHAPED FURROWS
___ 2"DEPTH
5" DEPTH

NUMBERS REFER TO
FURROW SPACING.

 

 

I
3 4 5 6 7 a 9*
TIME IN MINUTES

Figure 16. Total infiltration of water from model
furrows, as a function of elapsed time.

 

...u I...\lll.IDJ II. UIIIII. 5.114.: i....|.:
. n . n.

- 90 -

the values of A--the slope of the line representing total infiltration.

The effects of the three variables are shown in Table III.

Table III

Effects of Furrow Parameters on the Rate of Infiltration

Rate of Infiltration in cc/min

 

 

Shape of furrow Furrow Spacing
18 in. 36 in. 72 in.
water depth water depth water depth
2 in. 5 in. 2 in. 5 in. 2 in. 5 in.
Triangular* 11.78 22.90 10.18 17.60 11.22 24.05
Trapezoidal 13.10 18.95 12.69 17.60 11.40 19.85
Average 12.44 20.92 11.44 17.60 11.31 21.95

 

 

*Corrected for difference in the thickness of the tanks, where the
I

thickness of the tank for triangular furrows was 0.928 times that for I
I

I

trapezoidal furrows. I

 

A multiple regression analysis Was applied to these data, which
represented 12 separate conditions or combinations of the various
furrow parameters. For this analysis, X1 represented wetted parameter,
X2 represented top width, X3 represented water depth, X4 represented
furrow spacing and Y represents the slope of the total infiltration
curve. The resulting regression equation was as follows:

Y = 3.2019 X1 - 3.3739 X2 + 0.5065 X3 + 0.0075 X4 + 6.1148

The correlation coefficient for this equation was Ry.1234 = 0.9163,

Which was significant at the one percent level. Table IV shows the

correlations of infiltration rate with Xi'

 

 

 

 

 

- 91 -

Table IV

Correlations of Infiltration Rate with Furrow Parameters

Wetted Perimeter Top Width Depth Spacing

 

Correlations of Y with X's 0.7935 0.7179 0.9119 0.0367
Standard regressions of 3.2500 -2.6338 0.1646 0.0367

Y on X's

 

Since the value of Ry.1234 was little larger than Ry.3’ small
advantage was gained by the multiple regression so far as estimating
infiltration rate was concerned. One might as well use the simple
linear regression of infiltration rate on depth of water. If the
shape and spacing are ignored, the total regression would then be

Y = 2.83 X3 +-6.03
for the data gathered in these studies.

The regression coefficients of the multiple regression showed that
the wetted perimeter and top width were more effective in forecasting
infiltration rate than depth of water. Thus even though the infiltra-

tion rate was highly correlated with depth, the contribution of an

increasing depth to an increasing rate was small in comparison to the

furrow size and Shape. This was consistent with potential theory,

Which shows that an increase in head exerts only a small Influence on

the total potential.

From these results, one may conclude that: (l) infiltration rate

' a d
was linearly related to depth of water and to the wetted perimeter n

top width of the furrow, (2) furrow spacing had little effect on

ere
infiltration rate, even when the wetted soil masses tended to interf ,

 

 

 

 

 

 

 

-92-

(3) the relative potency of wetted perimeter and top width in
estimating infiltration rate was much greater than that of water
depth, and (4) the depth of water was highly correlated with
infiltration rate, and a simple linear regression could be used with
fair accuracy.

These conclusions were based upon rather restricted conditions,
where the wetted perimeter and top width were directly related to
water depth, and where no soil stratification existed. In a layered
soil, or where the permeability of the sides of a furrow is different
than that of the bottom of the furrow, these relations just developed
may not exist and the above conclusions may not be valid.

To test these theories under field conditions, data taken from
the studies at the Wanzer Ranch and at Davis were analyzed. Assuming
that the rate-of-advance equations were valid, the factor F should
represent some measure of the infiltration phenomenon in flowing
furrows in comparison to that in the furrow infiltrometer. This
factor thus provides some basis for these analyses. Ratios of depth
0f water in the flowing furrow to the depth of water in the furrow
infiltrometer were calculated, and plotted with the factor F that was
found to result in a fairly accurate rate of advance prediction. This

relation is shown in Figure 17, from which it was evident that as the

depth of water in the furrow increased in relation to the depth of

water in the infiltrometer, the value of F also increased. In all

‘ ' ' l to or
caSes, the infiltration rate in the flow1ng furrow was equa

less than the infiltration ratio measured in the infiltrometer.

If F was a reliable measure of actual furrow infiltration rates,

these data also indicated that the condition of the furrow (time of

 

l
I
u
I
n
.

 

 

 

 

 

INFILTRATION FACTOR "F "

-93..

 

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

'-° ifs I I7?—
I { '
0.94.NE[R 'BVA”’QT I ; 4 l
’ 9 j i
l , .
0.8 4: T T T
I I I
I 1 j
0.7 w IL f f
‘I f j :
.. LI. / a;
/
—fi’n. ‘4 [3 = l '. l
95 , 5’“/ + / 3 I
a ‘ l I
0J4 ‘ I ll
0.3 41 1
E _NORTHEAST FIELD
0.2 ‘y ___-soumIIIEST FIELD —
s ‘ NUMBERS REFER To TIIE
0.I r NUMBER OF IRRIGATIONS —
o l I I I l
0 02 0.4 0.6 0.8 m I2 L4 I.6 l8

RATIO OF DEPTH OF WATER IN Fiowmc
FURROWS To THAT IN AN INFILTROMETER.

Figure 17.

Relation between the ratio of depth of water
in a furrow infiltrometer to the depth of
water in a flowing furrow and an infiltration
factor F, showing seasonal variability.

 

 

 

-94-

season) had a considerable bearing on the relation of the infiltration
rates in the furrow to that in the infiltrometer. If this was correct,
the effects of soil surface sealing by the velocity of flowing water
varied thrOughout the season, such that the soil surface in a furrow
had a tendency to seal more easily later in the season than earlier.

The rather meager data from the studies at Davis indicated the
opposite--that the factor F increased with a decrease in the ratio of
depth in the furrow to depth in the infiltrometer.

Although the results of all of these comparisons were rather
inconclusive, it appeared probable that the infiltration rate of a
furrow was related to the depth of water in a furrow infiltrometer;
but that this relationship was affected greatly by the condition of
the soil in the furrow and by soil texture and structure. The non-
linear relationship of F and df/di indicated that the infiltration
from the sides of the furrows might be higher than that of the bottoms.
This effect, and the effects of tractor wheel compaction and surface
sealing thus prevented direct application of the results of the model
study to the conditions of these field studies.

In any event, much additional work will be necessary before the
furrow infiltrometer can be used successfully to accurately predict
the infiltration from a flowing furrow. Qualitatively, the infiltrometer
may prove a useful tool, but for a rigorous qualitative analysis, many

factors need consideration.

Furrow shape and hydraulic roughness
Because infiltration varies with wetted perimeter, top width, depth

of water, and the relative permeabilities and areas of the bottom and

 

 

 

 

 

 

- 95 _

sides of the furrow; and because the storage of water in a furrow
has an influence on the rate of advance; it was desirable to develop
some relationship between stream size, furrow shape and water depth.

Bondurant attempted such a correlation in the Republican Valley
in Nebraska, and found the following relationship:

Y = 5.35 XO'285
where Y is the stream width in inches and X is the stream size in
gallons per minute divided by the slope in percent. One can hardly
expect, however, that these data would apply to other conditions of
soil texture and structure and hydraulic roughness.

When data for two irrigations at Davis were expressed in similar
fashion, no such relationship existed. Using stream size and slope
data from Davis in Bondurant's equation resulted in calculated stream
widths that were nearly 70 percent greater than those measured in the
field.

Certainly some relation between stream size or stream velocity
and furrow size, shape and width existed; but this relation was
likely affected by aggregate size and stability and hydraulic roughness
of the furrow. Thus Bondurant's equation must be treated as a special
case which may not be applicable to other soil or cropping conditions.

Studies of changes in furrow shape were conducted at Davis on
Yolo silty clay loam soil, in the same area in which the rate of
advance studies were made. Furrow cross sections were measured before
any irrigation after the furrows were made; and after each of two
successive irrigations. Typical results of these measurements are

shown in Figure 18.

 

 

 

~96-

    

BEFORE IRRIGATION

FIRST IRRIGATION SECONO IRRIGATION

 

 

 

 

 

I
I
I
l
I
|

2|. 4 gpm 27.42 gpm 5

 

 

30.75 gpm 42.I5 gpm

SCALE:
I“ HORIZONTALLY- 5.0"
I“ VERTICALLY -2.4“

Figure 18. Typical furrow cross sections, showing the effects
of stream size and number of irrigation on furrow
shape.

 

 

 

- 97 -

Initially, the furrows were V-shaped furrows, with side slopes
of about 2:1. Flows of about 12 gallons per minute did not alter
this shape appreciably, but a slight flattening of the sides was
noticeable. Flow rates of about 25 gallons per minute created a
trapezoidal shaped furrow with a distinctly flatter bottom, but with
about the same side slopes. Higher flows did not change this
trapezoidal section appreciably.

It appeared that once the change in furrow shape has taken place,
additional irrigations did not influence the resulting shape to any
extent, as shown by the lack of difference between the first and
second irrigations. Similar observations were made on the Wanzer
Ranch on the sandy loam soil.

Thus, the shape of an irrigated furrow could be presumed to be a
function of soil type, soil structure, aggregate stability, furrow
flow or furrow velocity, the initial furrow shape and the number of
irrigations. After the initial irrigation without any intervening
cultivation, it is probable that the only factors that would influence
furrow shape are furrow flow to a small extent and furrow roughness,
including that roughness caused by vegetative trash in the furrow.
Furrow flows that would be erosive would certainly alter the shape,
but this condition should be avoided at all times.

Based on these data, one might conclude that the prediction of a
furrow shape based on soil conditions and furrow flow is possible.
These studies showed that the prediction may be more difficult for
the first irrigation than for subsequent irrigations, and showed also

that furrows tended to form trapezoidal or parabolic shapes with

 

 

 

 

 

 

- 93 -

increasing flow, in silty clay loam soil. No definite relationship
between furrow size and shape and flow rate was apparent in these
studies.

These same measurements were used also as a means of evaluating
hydraulic roughness in furrows. As small, earth-lined channels,
furrows represent a condition whereby the characteristics of the
channel change with time, soil conditions, crepping conditions, and
flow rate. Because of the influence of these factors, the rate of
advance of water down the furrow due to surface storage in the furrow
can be extremely variable and subject to a multitude of conditions.

The purpose of this part of the study was to determine the
magnitude of hydraulic roughness and the effect of flow rate on rough-
ness. Presumably, the relation between r0ughness and velocity can be
expressed in a manner similar to the classical expressions for friction
in pipes as a function of Reynolds Number. That is, the friction loss
is a function also of e/d, which represents the magnitude of small
projections in relation to the diameter of the pipe.

In furrows, the roughnesses (mainly clods) are sufficiently large

in relation to furrow depth to warrant such an approach. However, at

 

high flow rates, the velocity of flow tends to smooth the furrow and
dissipate the cloddiness, which reduces the roughness of the furrow.
On the other hand, high flow rates alter the shape of furrow to a
generally less efficient hydraulic section, as shown previously. Also,
the leaves of some crops, such as potatoes and sugar beets, may hang
into the furrow to create some retardance on the surface of the water.

Thus, the flow regimes in irrigation furrows are extremely varied

and rather difficult to evaluate. The problem of flow characteristics

 

 

 

- 99 -

in small channels under conditions of moving boundaries itself is a
relatively new concept, especially when the change in the boundary is
a function of the flow. Some data are presented herein, however, as

a means of introducing the problem and adding to the knowledge of this

 

phenomenon.

At Davis, the same furrows which were measured for rate of advance
were used for determinations of hydraulic roughness. The technique
used involved the measurement of flow into each furrow, the measure-
ment of the cross-sectional area of each furrow, and the determination
of the slope of the water surface. Water was directed into twelve
furrows in three flow rates for a sufficient length of time to insure
uniform flow in a 50 ft. length of furrow, which was marked with
stakes about 100 feet from the head end of the furrows. As soon as
the flow had stabilized in this section, small metal markers were
inserted in the side of each furrow to mark the water level in the
furrow at each end of the section. The flow was then turned off
and the measurements of the furrow cross-section and water surface
slope were made several days later.

This procedure was followed because measurements of furrow cross
sections when water was flowing were extremely inaccurate. The rather
mushy, soft bottom almost prohibited measurements of depth and the
furrows were easily disturbed. Although the method used was subject
to some inaccuracy, it was probably more accurate than others.

The cross-sectional shape of each furrow at both ends of the
test section was plotted and the wetted perimeter and area determined.

These were then averaged to arrive at a representative area and wetted

 

 

 

- 100 -

perimeter for each furrow. By substituting the known parameters of
flow rate, area, wetted perimeter and slope into Manning's equation,
the roughness factor n was then calculated. Summaries of this analysis
are shown in Appendix III.

The results of this analysis are shown in Figure 19, which
expresses the calculated n as a function of furrow velocity for two
irrigations. N0 disturbance of the soil took place between irrigations.
It seems quite evident that the hypothesis expressed earlier was
correct; that is, the hydraulic roughness was a function of flow rate,
or rather, the flow velocity. As the velocity of flow increased, the
roughness coefficient decreased, probably due to a smoothing of the
clods in the furrow. Because the same relationship existed for the
second irrigation as for the first, it appeared that the aggregates
in the furrow either no longer existed or had already stabilized, and
that the crop of milo had no effect on the roughness.

The slope of the line in Figure 19 was almost minus one. For
these conditions n may be expressed as n = CV-l. If this expression

is substituted into Manning's equation, the following equation results:

1 ___ 1.286 R2/3 Sl/2

Considering that S was constant, and C was constant, then the hydraulic
radius was a constant and did not depend on the velocity or the flow
rate. One may conclude from this that for these soil conditions, the
hydraulic radius was independent of the velocity or of the flow rate,
and that the soil conditions were such that a constant relation between

area and wetted perimeter existed for all flow rates.

 

 

 

 

 

 

 

MANNING'S "N"

- 101 -

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.06
.05 a
(3
C)
.04 \0
.I
.osI
C i.
c).
' .
I.
.02
I.
CAMPBELL TRACT
DAVIS, CALIF. p
0 FIRST IRRIGATION
0 SECOND IRRIGATION
I I '
.0:
02 03 0.4 05 0.5 0.7 03 09 Lo

VELOCITY IN FEET PER SECOND

Figure 19. Relation between velocity of water in furrows
and Manning's roughness coefficient, for Yolo

silty clay loam.

 

 

 

 

- 102 -

Thus, if the general furrow shape as a function of flow rate can
be determined; it becomes possible to estimate the depth of water in
the furrow for any given flow, and to calculate the volume of water
in storage in the furrow. Additional studies are certainly needed to
verify this conclusion, however.

Another interesting facet of this study was the fact that initial
roughness appeared to have little effect on the value of the
calculated roughness coefficient. Due to compaction by the tractor
when the furrows were made, the furrows were alternately smooth and
extremely rough. However, the effects of this initial cloddiness or
roughness were not evident in the calculated value of n except for
minor trends at low flow rates and at high flow rates. On the average,
the values of n for the rough furrows were 12 percent higher than
those for the smooth furrows, for both irrigations. This was within
the experimental error, however.

Although the studies at the Wanzer Ranch were not intended for
the evaluation of hydraulic roughness, the data collected have proved
of some use in this respect. Measurements of flow rates and depth of
water in the furrows were made, and used primarily in the rate of
advance equation. Inasmuch as the calculated rate of advance very
nearly approximated the observed advance, it was presumed that the
quantity of water in surface storage had been estimated fairly
accurately, and that the volume of water per foot of furrow was equal
to the area of the channel.

Most of the furrows in this sandy loam soil approached a

trapezoidal or parabolic shape, even at low flows. Thus, in order to

 

 

 

 

- 103 -

calculate the values of the roughness coefficient, the hydraulic
radius was assumed equal to the depth of flow. Errors in the order
of 20 percent may result from this assumption, so the results should
be treated with caution and interpreted only as possible trends.

Substituting the depth for hydraulic radius, the slepe of the
soil surface for the water surface, and the estimated surface storage
per foot of furrow for area into Manning‘s equation; n was calculated.
The results are shown in figures 20 and 21, which express the calculated
n as a function of velocity and flow rate, respectively.

These results were approximately the same as those for the studies
at Davis, in that increasing the velocity decreased the hydraulic
roughness of the furrow. In Figure 20, the slope of the line was
approximately -0.75, and n was then expressed as n = CV-0’75. When
this expression was substituted into Manning's equation, the hydraulic
radius became a function of the velocity to the 3/8 power, and velocity
a function of the square of the slope.

This relationship between n and V would presumably permit a trial
and error solution for water depth if the shape of the furrow were
known. In fact, the resulting equation Q = kAR8/3 32 could be used
quite simply for this determination.

Figure 21 expresses the relation between n and the flow rate, Q.

1/3

, which if substituted into Manning's equation resulted

in the equation Q = mA3/2 RSB/é. If a known slope is assumed, these

Here, n = gQ-

two equations for flow rate may then be solved simultaneously for the
two unknowns R and A, for any flow rate.
AThese results and conclusions would certainly not apply to other

soils, but indicate that it may be possible to apply this method of

 

 

 

 

NANNING‘s "N“

-104-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

.26
I
6

.00 a \ ‘6“ ,,
.c: —
.03-— a

mum RANCH

-— NORTHEAST FIELD a I

.02 --- SOUTHWEST FIELD

a 00 .IO .20 30 .40 -IIO 00 w

VELOCITY IN FEET PER sECOND

Figure 20.

 

Relation between velocity of water in furrows
and Manning's roughness coefficient, for Cajon

fine sandy loam.

 

 

 

 

 

MANNING’S “N“

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

e 105 ~
.20
-
\
\\
.I0 -
. ‘
,0. ;\ ‘ =I FIFTH
‘_ \
MI: 0‘ -——— “
"N ‘ stFTH
.04 _—
93 ‘s e ‘ THIRD
‘0 “ FIRST
.02 WANZER RANCH
__ NORTHEAST FIELD
--— SOUTHWEST FIELD
.OI
2 3 4 5 s 7 89I0 20 30
FLOW RATE IN GALLONS PER MINUTE

Figure 21. Relation between flow rate in furrows
and Manning's roughness coefficient,
for Cajon fine sandy loam.

 

 

 

- 106 ~

analysis to other soils if these relationships between V, Q, and

n are known. The fact that no relationship existed between Q and n
for the Yolo silty clay loam invalidated this last statement, but the
results from the studies at the Wanzer Ranch provided enough
justification for additional studies of these effects.

Figure 21 also points out that the relation between Q and n
changed during the irrigation season, and shows that the value of n
tended to increase as the season progressed. This conclusion agrees
with the unpublished work of Mech at Prosser, Washington, in which he
showed increases in the value of n during an irrigation season for
sugar beets. He reasoned that this was due to the increased vegetative
growth extending into the channel and to the secession of cultivating
and ditching. CrOps such as alfalfa and wheat showed a fairly uniform
n throughout the season.

Although the vegetative growth of cotton did not extend much into
the furrow, the shedding blossoms and the weeds which were hoed fell
into the furrow, creating the same effect.

From these two studies of furrow roughness, it was apparent that
the introduction of a non-erosive furrow stream resulted in some
Stable shape and Size of furrow which remained relatively unchanged
during the irrigation season. Predictions of furrow area and hydraulic
but additional studies on

radius for any flow rate may be possible,

other soil conditions will be necessary. The effect of vegetation

Extending into the furrow and vegetative trash in the furrow changed

the hydraulic roughness during the irrigation season, but had little

effect on the roughness of the furrow itself.

 

 

 

 

 

- 107 -

Determinations of surface storage in the furrow are much more
important than infiltration volumes on soils of low permeability.
In this situation, some error in estimating the infiltration function
will be less critical than errors in estimating hydraulic roughness
and furrow area. On the other hand, on soils of good permeability,
some errors in estimating e, c or n will have much less effect on
the result than errors in flow rate or infiltration rates. Accurate
estimates of surface storage may be more critical at higher rates of
flow, if the volume of water in the furrow becomes greater in
proportion to infiltration volume. This will depend considerably on
the existing soil conditions in the furrow.

Thus, a need exists for evaluating these two components of the
rate of advance equation (infiltration and surface storage) as a
function of soil physical preperties, to determine the allowable
errors of measurement and the relative significance of the two

factors.

 

 

 

 

 

 

 

 

 

- 108 -
SUMMARY AND CONCLUSIONS

A general mathematical expression, based on the conservation of
mass, was derived to define the flow of water in irrigated furrows.
Although the principle of mass conservation cannot be argued, the
individual components of the expression can. This study was
initiated to present a mathematical expression of flow in furrows,
and to determine the factors that affect the application of the
equation; specifically, to evaluate the phenomenon of infiltration
from furrows and to evaluate the hydraulic factors that affect the
storage of water in the furrow.

The conclusions of this study were based on field measurements at
two soil locations during the irrigation season of 1958, and on measure-

ments of infiltration in a furrow model tank. These conclusions are

 

summarized as follows: ‘I

1. An equation for accurately predicting the advance of surface
water in irrigated furrows was derived. Field studies conducted in
two different soil areas with two different crOps during an irrigation
season proved the reliability and accuracy of the equation under
variable conditions of soil and flow rates.

2. Comparisons of observed and calculated rate of advance showed
that the equation may be applied to fields of non-uniform slopes or
Slightly irregular slopes. The equation also performed well with
rather limited data, provided that valid measurements were used.

3. Studies of furrow infiltration in a sand model resulted in
infiltration equations in the form I = Atn where I is the total

infiltration after time t. The effects of water depth, furrow shape

 

 

- 109 -

and furrow spacing on this equation were evaluated by regression
analysis, which verified the hypothesis that these factors were
related linearly to infiltration rate.

4. This analysis showed that water depth only slightly affected
the infiltration rate, but was highly correlated with infiltration rate.
Wetted perimeter and top width affected infiltration rates to a much
greater degree than the water depth.

5. Furrow spacing had little effect on the infiltration rate
from a single furrow, and was not correlated with infiltration rate.

6. The resulting multiple regression equation was highly
significant in predicting infiltration rates; however, a simple
linear regression of infiltration rate on water depth proved just as
accurate. One might thus conclude that infiltration rates determined
with a furrow infiltrometer might be used satisfactorily for
estimating infiltration rates for furrows in which water is flowing
at the same or any other depth.

7. Field measurements with the Hamilton furrow infiltrometer
indicated that this instrument might serve well as a tool for
qualitative analyses, but that considerably more work is necessary
before it can be used in a strictly quantitative manner.

8. A furrow factor F, applied to the infiltration equations
determined with the infiltrometer, appeared to satisfactorily describe
any differences in infiltration between infiltrometer and a flowing
furrow. As the depth of flowing water increased, the value of F
also increased; but this increase and the magnitude of F were

affected by the time of the season or the condition of the furrow.

 

 

 

 

 

 

 

- 110 -

9. The movements, distribution and deposition of sediments in a
furrow appeared to affect the relation between the infiltrometer
infiltration and that from a flowing furrow. These effects, combined
with differences in permeability between the bottom and sides of
furrows, prevented a direct application of data from the tank models
and also created problems in the use of the furrow infiltrometer.

10. Studies of furrow shapes at Davis showed that changes from a
V-shape to a trapezoidal or parabolic shape were likely to occur
during the first irrigation after furrows are formed. Subsequent
irrigations did not alter the shape appreciably.

11. The rate of flow of water into a furrow affected the shape
considerably. Up to a certain point, increasing flow tended to result
in a furrow with a flatter bottom. These studies also indicated that
prediction of furrow shape may be possible, if factors such as soil
texture, soil structure, aggregate stability, furrow flow and initial
shape can be evaluated. Bondurant's equation for furrow shape did
not appear applicable to the soils evaluated in this study.

12. Calculations of hydraulic roughness of furrows showed that
roughness was a function of the flow velocity, such that higher
velocities reSulted in lower values of Manning's "n". This was probably
due to a smoothing of the clods or soil obstructions in the furrow.
The relation between roughness and flow velocity appeared to remain
constant during the irrigation season, and was affected to only a
slight degree by the initial roughness of the furrow. The magnitude
of "n" and its relation to flow velocity appeared to be about the

same for the two soils studied.

 

 

 

 

 

 

 

 

 

- lll -

13. The hydraulic roughness of a furrow was inversely related
to velocity, in the studies at Davis, and the hydraulic radius was
essentially constant and independent of the flow rate. Studies
at the Wanzer Ranch showed, however, that on a sandy loam soil the
relation between Manning's "n" and flow rate, together with the
relation between "n" and flow velocity resulted in two simultaneous
equations involving Q, A, R and slope, thus, if the slope and flow
rate are known, the area and hydraulic radius of the furrow may be
calculated. This conclusion needs further verification for other
soil conditions, however.

14. For the same flow rate, the value of hydraulic roughness
increased during the irrigation season. This was probably due to the
effects of overhanging vegetation and trash in the furrows. The
over-all values of n varied from about 0.01 to 0.18 depending on flow

velocity.

The most significant conclusion of this study was the fact that a
simple equation, based on conservation of mass, may be used to
accurately predict the rate of advance of a water front in an irrigated
furrow. This equation may then provide a means whereby an irrigation
system can be better designed or evaluated, and should result in a
much better understanding of the contributions of the infiltration and
flow phenomena.

A rather striking but inconclusive part of the study was the fact
that for the two soils studied, the shape of the furrow channel tended
to become stable for a certain rate of flow. This leads to the

possibility that hydraulic radius may either be constant or may be

 

 

 

 

 

 

- 112 ~

estimated if the flow rate and slope are known. If this conclusion
can be verified, solutions of the rate of advance equation can be

made on the basis of infiltration alone, or for general textural

soil groupings. This would certainly enhance irrigation system design
and would result in an ultimate use of recognized design techniques

based on sound engineering principles.

 

 

 

 

 

- 113 -
RECOMMENDATIONS FOR FUTURE WORK

Future research in the field of the hydraulics of irrigation
systems should be concerned with two aSpects: the flow of water

from irrigation furrows into the surrounding soil and the hydraulics

 

of flow in small, rough channels.

The former involves the determination of the influence of furrow
shape, size, spacing and water depth on the infiltration of water
into stratified, heterogeneous soils. Particular emphasis should be

placed on infiltration theory, but considerable field work should be

 

done to evaluate the effects of flow velocity and sediment deposition
or removal on the infiltration phenomena.

Some improvements in the techniques of measuring infiltration are
quite desirable. Standardization of instruments and procedures are
vitally needed for infiltration studies. Some method of measuring the
flow rate in an irrigated furrow would also be extremely useful, for
such a tool would provide a means of collecting not only infiltration
data but also data concerning the hydraulics of the furrow channel.

The ultimate goal of any such infiltration studies should be
toward a more complete understanding of the geometric factors affecting
infiltration into soils. This work, combined with research on other
‘modifying factors, would certainly enhance the develOpment of more
efficient furrow irrigation systems.

The hydraulics of flow in small rough channels can be divided into
two phases: a study of the characteristics of flow in small channels

with fixed boundaries and artificial roughness, and studies of flow

 

 

 

 
 

 

 

- 114 -

regimes in small channels under conditions of moving boundaries. The
latter deserves particular immediate attention, because this affects
also the infiltration characteristics of the furrow.

The relationships between flow rate, flow velocity, furrow
shape, furrow size and hydraulic roughness certainly need to be
established for many soil conditions. The results of this study
indicate the possibility that in a certain soil, a definite hydraulic
radius and area may exist for a given flow velocity or flow rate. If
this is true, studies on this aspect are needed immediately to
simplify the design procedures that would then follow.

These studies could well be conducted in a variable slope flume
in which different soils can be placed, using limited field studies to
verify any theories developed in the laboratory. The problem could
perhaps be effectively approached by the use of dimensional analysis.

Studies of channels using artificial roughness, including that
caused by vegetation, would be an invaluable aid in determining the
effects of seasonal plant growth and roughness geometry on furrow
flow characteristics. These studies should be undertaken to supplement
any progress made in evaluating the effects of furrow flow on furrow
shape and aggregate size.

The most important work in the future involves the integration of
all these physical factors into a mathematical tool whereby the
distribution efficiency of furrow systems can be made optimum.
Engineers should recognize that this tool will provide the key for
optimum design of irrigation systems and efficient, economic water

use and distribution; and will provide the only basis upon which

 

 

 

 

 

 

- 115 -

automation may be applied to surface irrigation systems. Future
studies should be directed toward this definite goal, and should
be developed on a broad fundamental basis if irrigated agriculture
is to survive the technical evolution in agriculture and the

increasing demand for water resources.

 

 

 

 

 

 

 

 

- 116 -

APPENDIX

I. Sample Calculations of Rate of Advance in Furrows

A. First Irrigation on Wanzer Farm, Northeast Field

Given:

Q = 3.28 gpm
1 = 0.0342 t0'56

Depth of flow = 0.08 ft.

Furrow area = 0.0353 sq. ft.
At = 10 min.

Q (At) - 3%93 [giAxl + gi_1Ax2 + + SZAXi_1]

 

Fa( A t)n + cdo2 + e

F = 0.22. Then

wax» - 10 - 60 =
0.22 ' 0.124 + 0.0353 + 0.001 0.0636

4.38

 

= 69 ft.

 

 

= 41.3 ft.

41'3) = 36.8 ft.

 

 

= 33.5 ft.

4.38 - 0.01365 (1.4743 - 69) = 47.2 ft.
0.0636

4.38 - 0.01365 (0.8501 - 69 +-1.4743 - 47.2)
0.0636

4.38 - 0.01365 (0.6992 - 69 + 0.8501 - 47.2

+ 1.4743 .

0.0636

4.38 - 0.01365 (0.6127 - 69 + 0.6992 - 47.2

+ 0.8501 - 41.3 + 1.4743 ~ 36.§)

0.0636 ‘

4.38 ~ 0.01365 (0.5540 ' 69 + 0.6127 3 47.2

+ 0.6992
+ 1.4743

0.0636

n

41.3 + 0.8501 - 36.8

33.5) = 31.0 ft.

 

 

 

 

 

 

 

 

. J-. o. '
, . 1.. .
,\ . .
.
.
. .
, . . v
' I
. ... ___—-1--.
4
I
a 1 - I I
. ' “ ‘
. _ . .
a n I ‘ v
. - ..
. .. . . ~
.
. . , .
. . , - --.... i.-. . .....-_. -. ’. .-_..__-.v——
I
. . . ..
. . ‘.. , / _ . ...
. ‘ I .~ ‘
o a. . _. ..-.. "
.
.
Q . ‘ V
' c . "' ~ "
‘ .
a ' , a
, . :..--...--.—... .- "‘ '
\.
. u
. . ‘ .
.- . ..
A I . C -.
n ' l
I I . ‘
' ' . l u
, . :1—~—.__-.__ .‘ - .6 4

B.

- 117 -

First Irrigation on Campbell Tract, Davis, California

Given = Q = 32.8 gpm
1 = 0.0341 t0°625
Furrow area = 0.208 sq. ft.

At = 20 min.

AXi = Q(At) " Fa£2A,t_.2_n [giAxl + gi_1AX2 + 000 + ngXi‘l]

 

Fa( At)n + cdo2 + e

Assume F = 1.08. Then

Ax = 32.8/448.6 .20 ~ 60 . ..___,87.8 _ 195 ft.
1.08 - 0.222 + 0.208 + 0.002 0.4500

 

 

 

 

AXz = 87.8 - 0.12 (1.5423 - 195)
0.4500
- ~ . - 115
Ax3 = 87.8 0.12 (0.9874 195 + 1 5423 ) = 96 ft.
0.4500
Ax = 87.8 - 0.12 (0.8369 - 195 + 0.9874 . 115
4 + 1.5423 - 96) = 82 ft.
0.4500
87.8 - 0.12 (0.7483 - 195 + 0.8369 - 115
4X5 = + 0.9874 - 96 + 1.5423 . 82) = 72 ft.

 

0.4500

 

 

 

.-__—/.-.

_
.
_
i
—
.
_

 

,_..—a

II.

- 118 -

Summary of Rate of Advance Calculations

A. Wanzer Ranch

 

 

 

No. of Field Q, F Surface Depth in Depth in
Irrigation gpm storage,ft infil., ft. furrow, ft.
1 NE 3.28 0.22 0.0353 0.28 0.08
19.7
21.2 .55 .0652 0.28 .11
1 SW 3 0.55 0.033 0.278 0.13
5 .48 .044 .278 15
12 .55 .051 .278 .16
14 .50 .071 .278 .19
20 .595 .079 .278 .20
3 NE 2.28 0.26 0.050 0.135 0.05
3.99 .29 .063 .135 .096
8.9 .35 .055 .135 .086
17.6 .55 .089 .135 .12 .
25.4 .48 .126 .135 .144 5
5 NE 2.36 0.29 0.073 0.12 0.09
3.39 .36 .073 .12 .12
5.74 .425 .114 .12 .17 I
10.62 .50 .140 .12 .15 2
30.0 1.00 .232 .12 .21
5 SW 2.97 0.48 0.067 0.15 0.10
4.17 .46 .067 .15 .11
7.84 .60 .126 .15 .15
9.5 .60 .118 .15 .15
15.79 1.00 .102 .15 .18
B. Campbell Tract, Davis
No. of Q, F Surface Depth in Depth in
Irrigation gpm storage,ft2 infil., ft. furrow, ft.
1 11.04 0.63 0.076 0.17 --
20.2 .72 .175 .17 --
32.8 1.08 .208 .17 --
2 11.88 0.70 0.061 0.15 0.11
24.4 .40 .130 .15 .14
30.75 .50 .157 .15 .12

 

 

t

._
.
.
.

c.

o
.
a
.

 

- 119 -

III. Summary of Hydraulic Roughness Calculations

A. ‘Campbell Tract, Davis, Second Irrigation

Slope = 0.2 percent

 

Furrow Q, gpm Area,ft2 Wetted Velocity, n
No. perimeter,ft. ft./sec.
1 11.88 0.066 0.833 0.40 0.030 4
2 11.88 .084 .938 .31 .042 ‘
3 11.88 .066 .818 .40 .031
4 11.88 .072 .901 .37 .034
5 21.4 .112 1.084 .43 .034
6 21.4 .107 1.021 .45 .033
7 21.4 .136 1.147 .35 .046
8 21.4 .128 1.169 .38 .041
9 30.75 .097 .991 .71 .020
10 30.75 .112 1.050 .61 .024
11 30.75 .118 1.047 .58 .027
12 30.75 .167 1.282 .41 .042

 

B. Campbell Tract, Davis, Third Irrigation

 

Furrow Q, gpm Area,ft2 Wetted Slope, Velocity,- n
No. perimeter,ft. percent ft./sec.
1 13.88 0.037 0.717 0.206 0.84 0.011
2 13.88 .069 .904 .288 .45 .032
3 13.88 .065 .868 .262 .48 .028
4 13.88 .054 .819 .176 .57 .018
5 27.42 .102 1.108 .278 .60 .027
6 27.42 .124 1.145 .270 .49 .036
7 27.42 .108 1.118 .252 .56 .028
8 27.42 .103 1.106 .206 .59 .023
9 42.15 .104 1.098 .224 .90 .016
10 42.15 .125 1.135 .238 .75 .022
11 42.15 .120 1.186 .206 .79 .018

12 42.15 .170 1.553 .264 .55 .032

 

 

 

 

.1-
.
1
,\.|| .

 

 

- 120 -

C. Wanzer Ranch

 

Irrigation Field Q, Area, Wetted Velocity n ‘
gpm sq.ft. perimeter, ft. ft./sec.
1 NE 3.28 0.035 0.08 0.21 0.059
20.0 .065 .12 .68 .023
1 sw 3 0.033 0.13 0.20 0.055 1
5 .044 .15 .25 .049 _
12 .051 .16 .52 .025
14 .071 .19 .44 .033
20 .079 .20 .56 .026
3 NE 2.28 0.051 0.05 0.10 0.089
3.99 .063 .096 .14 .098
8.9 .055 .086 .36 .036
17.6 .089 .12 .44 .036
25.4 .126 .144 .45 .040
5 NE 2.36 0.073 0.09 0.07 0.182 1
3.39 .073 .12 .10 .155 g
5.74 .114 .17 .11 .180 1
10.62 .140 .15 .17 .110 2
30.0 .233 .21 .29 .081 g 1
5 sw 2.97 0.067 0.10 0.10 0.095 E
4.17 .067 .11 .14 .072
7.84 .126 .15 .14 .089
9.5 .118 .15 .18 .069 '
15.79 .102 .18 .34 .040

 

 

10.

ll.

12.

13.

14.

- 121 -

LITERATURE

Anon. The interesting things that happen when water meets a new
soil strata. Sunset, pp. 230, 233, Oct., 1954.

Aronovici, V. S. The application of the ring infiltrometer to
diagnosis of irrigation problems in southern California.
Trans. A.G.U. 35: 813-820, 1954.

Aronovici, V. S. Model study of ring infiltrometer performance
under low initial soil moisture. Soil Sci. Soc. Amer. Proc.
19: 1-6, 1955.

Aronovici, V. S. Personal correspondence, 1957.

Bernstein, L. and M. Fireman. Laboratory studies on salt
distribution in furrow irrigated soil with special reference
to the pre-emergence period. Soil Science 83: 249-263, 1957.

Bodman, G. B. and N. E. Edlefson. The soil moisture system. Soil
Science 38: 425—444, 1934.

Badman, G. B. Factors affecting downward movement of water in
soils. Paper presented before the 16th annual meeting of
the American Soil Survey Association Committee on Forest
Soils, Dec. 3, 1935, Chicago, Ill.

Bodman, G. B. and E. A. Colman. Moisture and energy conditions
during downward entry of water into soils. Soil Sci. Soc.
Amer. Proc. 8: 116-122, 1943.

Bondurant, J. A. Two methods of measuring water intake in
irrigated furrows. M.S. Thesis, University of Nebraska,
Dept. of Agricultural Engineering, 1951.

Bondurant, J. A. Developing a furrow infiltrometer. Agr. Engr.
38: 602-604, 1957.

Bondurant, J. A. Personal correspondence, 1957.

Bouwer, H. Infiltration patterns for surface irrigation. Agr.
Engr. 38: 662-664, 676, 1957.

Brown, J. B. Principles of furrow irrigation. Spreckels Sugar
Beet Bulletin 6(8): 49, 53-54, 1942.

Browning, G. M. and F. M. Milam. The lateral movement of water
in relation to pasture contour furrows. Soil Sci. Soc. Amer.
Proc. 5: 386-389, 1940.

 

15.

16.

19.

20.

21.

22.

23.

24'.

25.
26.
27?.
28.

29.

- 122 -

Burgy, R. H. and J. N. Luthin. A test of the single and double
ring types of infiltrometers. Trans. A.G.U. 37: 189-191, 1956.

Colman, E. A. and G. B. Bodman. Moisture and energy conditions
during downward entry of water into moist and layered soils.
Soil Sci. Soc. Amer. Proc. 9: 3-11, 1944.

Griddle, W. D. A practical method of determining proper length of
runs, sizes of furrow streams and spacing of furrows on
irrigated lands, Soil Conservation Service, U.S.D.A., October,
1950.

Griddle, W. D., S. Davis, C. H. Pair and D. G. Shockley. Methods
for evaluating irrigation systems. Agriculture Handbook No. 82,
Soil Conservation Service, U.S.D.A., 1956.

Dallavalle, J. M. Micrometrics. Second edition. Pitman
Publishing Corp., New York, 1948.

Day, P. R. and J. N. Luthin. Sand model experiments on the
distribution of water pressure under an unlined canal. Soil
Sci. Soc. Amer. Proc. 18: 133-136, 1954.

Edlefson, N. E. Committee on physics of soil moisture, 1939-1940.
(Soil porosity in relation to gaseous and water movement) Trans.
A.G.U. 22: 414-433, 1940.

Evans, N. A. and M. E. Jensen. Erosion under furrow irrigation.
No. Dak. Agr. Exp. Sta. Bimonthly Bulletin 15: 7-13, Sept.,
Oct., 1952.

Fox, R. L., J. T. Phelan and W. D. Criddle. Design of subirrigation
systems. Agr. Engr. 37: 103-107, 1956.

Free, G. R., G. M. Browning and G. w. Musgrave. Relative
‘infiltration and related physical characteristics of certain
soils. U.S.D.A. Tech. Bul. 729, July, 1940.

Gardner, W. H. and Hseih. Water velocity in unsaturated porous
materials. Soil Sci. Soc. Amer. Proc. 20: 157-161, 1956.

Gardner, Willard and J. A. Widtsoe. The movement of soil
moisture. Soil Science 11: 215-232, 1921.

Haise, H. R. Flow pattern studies in irrigated coarse-textured
soils. Soil Sci. Soc. Amer. Proc. 13: 83-89, 1948.

Hall, w. A. Theoretical aSpects of water spreading. Agr. Engr.
36: 394-397, 1955.

Hall, W. A. Permeability and infiltration relationships in one
dimensional infiltration in a uniform soil. Trans. A.G.U.
37: 602-604, 1956.

 

 

 

 

 

30.

31.

32.

33.

34.

35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

- 123 -

Hall, W. A. Estimating irrigation border flow. Agr. Engr. 37:
263-265, 1956.

Hansen, V. E. Infiltration and soil water movement during
irrigation. Soil Science 79: 93-105, 1955.

Hansen, V. E. Report of Committee on the Hydraulics of Surface
Irrigation. Presented at meeting of American Society of
Agricultural Engineers, Dec. 11, 1956, Chicago, Ill.

Hansen, V. E. Hydraulics of irrigation water application as
affected by soils and other factors. Paper presented to
First Intersociety Conference on Irrigation and Drainage,
April 30, 1957, San Francisco, Calif.

Israelson, 0. W. The application of hydrodynamics to irrigation
and drainage problems. Hilgardia 2: 479-528, 1927.

Israelson, O. W. Coordination of research concerning flow of
water in soils. Agr. Engr. 12: 1931.

Israelson, 0. W., G. D. Clyde and C. W. Lauritzen. Soil erosion
in small irrigation furrows. Utah Agr. Exp. Sta. Bul. 320,
1-39, 1946.

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-124-

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77. Washington Agr. Exp. Sta. Progress report for regional
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