FLOW CRARACE‘ERISTICS OF SHELLED
CORN THRGUGH CEUTES

 

“rests {for 'E'Im Doqm of M. 5,
MICHIGAN STATE UNIVERSITY

Joseph Aiken McCurdy
1963

I";

This is to certify that the

thesis entitled

Flow Cturactortatica of Shelled
Corn Through Chutes

presented by

J oaeph A. HeCurdy

has been accepted towards fulfillment
of the requirements for

H.S. degree in M0111 W63

Major professor

 

Date MLZS‘: /7é3
0 J ‘7

___ _ ____ _ _. _ __ ._ . _ _ . __ _ﬂ_*. _.

IJ LIBRARY '

a Michigan State
University

 

 

V —~—o .‘9"l

 

ABSTRACT

FLOW CHARACTERISTICS OF SHELLED CORN
THROUGH,CHUTES.

BY
Joseph Aiken McCurdy

.It is important that all parts of a grain handling system function
smoothly and with a precision that the design engineer can predict.
- Considerable work has been done on discharge of semi-fluids through
orifices in storage bins. Flow equations have been established for
various sizes and shapes of orifices. . Very little has been determined
on the flow of grains through transporting devices such as chutes.

The purpose of this work was to study the mechanical behavior
of shelled corn flowing through chutes and to develop a test procedure
utilizing suitable equipment so that the flow rates of the grain could
be accurately measured. Next, the effect of chute length on flow
characteristics was studied. Also the relationship between size and
shape of grain chutes constructed of different materials and flow
characteristics was studied. .. Finally the effect of chute angles on flow
rates of grains was determined.

Apparatus was used that had been constructed principally for the
study of grain flow.- It was selectedto accommodate chute lengths as
short as 1%- ft and as long as 7%- ft. The basic equipment consisted of a
storage bin suspended about 5 ft above the floor. - This made it possible
to move a balance beam platform scale under the storage bin for gravity
ﬂow. A second bin was made portable so that it could be elevated on

pivoted channel iron beams and powered by an electric motor driving

Jos eph Aiken Mc Curdy

a winch. This portable bin also served as a storage bin for the longer
' (7% ft) chutes since it could be elevated about 9 ft above the floor.
Yellow dent shelled corn that ranged in moisture content from 10. 19%
to 8. 38% w.b. (wet basis) was used throughout the tests.

It was found that the flow rate varied but was essentially unaffected
by the chute length. The relationship describing the ﬂow of shelled corn
through rectangular orifices was determined. The flow rate was found
to be proportional to the sine of the chute angle. The pr0portionality
constant was determined for the various chute angles and was found to
be-constant only for the same size orifices. The ﬂow rates at the
various chute angles were found to be equal to flow rates through orifices
placed horizontally in bins, as determined by Ewalt, multiplied by the
sine of the angle.

. It became apparent during the tests that semi-ﬂuids flowing from
a storage bin are inﬂuenced by the velocities prior to ﬂowing through
the orifice in the chute. With the orifice placed in the chute 6 in. from
the storage bin the resulting approach velocity increased theflow by
1.42 over the flow with the orifice in the end of the chute.

The depth of cornflowing in a chute varied with the length of the
chute and was independent of the chute angle. . Different chutematerials
did not appear to influence the depth of shelled corn ﬂowing in chutes

at various angles beyond 25 deg.

Approved 1 f 5%

FLOW CHARACTERISTICS OF SHELLED CORN
THROUGH CHUTES

By

Jo s eph Aiken Mc Cur dy

A THESIS

Submitted to the College of Agriculture
Michigan State University
in partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE

Department of Agricultural Engineering

1963

AC KNOW LEDGME NTS

The author expresses his sincere gratitude to Doctor‘F. H. Buelow
of the Agricultural Engineering Department for his guidance and many
helpful suggestions during the course of this study. Grateful acknowledg-
ment is also expressed for the help and consideration of the other
members of the guidance committee, Doctor C. F. Schuller and Doctor
C. W. Hall.

The author is indebted to Doctor A. W. Farrall, chairman of the
Agricultural Engineering Department for his support of the project and
making a research assistantship available. Gratitude is due Doctor M.. L.
Esmay for helpful suggestions in initiating a program of study and making
arrangements for the assistantship.

.Sincere thanks go to Mr. J. B. Cawood, mechanical technician,
for his assistance in adapting the test equipment. Appreciation is
expressed to Mr- Jerry Stafford, Swine Farm Manager, for making the
shelled corn available and to others for contributing time and assistance.

The author would also like to express his appreciation to his wife
Dorothy and family for their patience, encouragement and typing as sist-
ance which helped make completion of the» inve stigation possible.

***********

ii

TABLE. OF CONTENTS

INTRODUCTION 0 O O O O O O O O O O O O O O O O O O O

iii

- REVIEW OF LITERATURE ...................
APPARATUS . ............... . . . . . .....
METHOD OF PROCEDURE ............ . . .....
, Chute Lengths ..................... .. . .
Chute‘Angles........................
Corn. Depth in Chutes ....................
ANALYSIS OF DATA ..... . .................
‘ Results of Tests on Effect of Chute Length .........
[Effect of Chute Angles on Rate of Flow. . . ...... . .

-‘ Results of Tests on: Depth of Flow in Chutes . . ......
SUMMARY ............................
- CONCLUSIONS ......................... .
RECOMMENDATIONS FOR FURTHER STUDY ........ .
'REFERENCES ............... . ..........
APPENDIX AO O O O O O O O O ....... O ......... O

16
21
22
22
23
24
‘24
27
35
41
43
45

46

48

LIST OF TABLES

TABLE Page

1.. Percent difference from the mean flow rate between
short (1%- ft) and long (7%- ft) wood chutes at various
angles with the chute orificeq1%-x 6 in. . . . . . . . . . 25

2.. Percent difference from the mean flow rate between
short (1%- ft) and long (7%- ft) steel chutes at various
angles with the chute orifice li—x 6 in. . . . . . . . . . 25

3. Percent difference from the mean flow rate between
short (1%- ft) and long (7%- ft) wood chutes at various
angles with the chute orifice 2 x 6 in. . . . . . . . . . Z6

4.. Percent difference from the mean flow rate between
~ short (1%- ft) and long (7%- ft) steel chutes at various
angles with the chute orifice 2 x 6 in. ., . . . . . . . . 26

5.- Constanﬁ, K values as determined by the equation
K = -.— for wood chutes at various angles and
A sip .
chuteorllcesmes................... .31

6.. ConstanEK values as determined by the equation
K = -—:— for steel chutes at various angles and
A slp0 .
chuteor11ce812es................... 32

7. A comparison of the standard deviation and coefficient
of variation of the constant K for wood and steel
chutes 1%— and 7&- ft long withli- x 6 in. and 2 x 6' in.
orifices........................... 33

8.. Comparison of the flow rate in wood chutes with the
chute orifices inside and outside the storage bin . . . . 33

9.. Flow of shelled corn through a 1%- x 6 in. orifice in
woodchutes...................... 49

10.- Flow of shelled corn through a 2 x 6 in. orifice in
woodchutes....... ...... .......... 49

iv

LIST OF TABLES -Continued

TABLE

11..

12.

13..

14.

15.

16..

17..

18..

Flow of shelled corn through a 1%- x 6 in. orifice in

' steel Chutes. O O O O O O O O O O O O O O O O O O O O- O O O

Flow of shelled corn through a 2 x 6 in. orifice in
steelchutes.......g.................

Flow of shelled corn through a 2 x 6 in. orifice in
woodchutes.........................

Flow of shelled corn through a 3 x 6 in. orifice in
Steel ChutesO O O O O O O O O O O O O O O O O O O O O O O O

Depth of shelled corn flowing at various distances from
the orifice in wood chutes with an. orifice 1%- x 6 in . .. .

Depth of shelled corn flowing at various distances from
the orifice in steel chutes with an orifice 1%- x 6 in . . .

Depth of shelled corn flowing at various distances from
the orifice in a wood chute with an orifice 2 x 6 in . . .

Depth of shelled corn ﬂowing at various distances from
the orifice in a ‘Steel chute with an orifice 2x 6 in . . . .

Page

50

50

.51

51

52

52

53

53

FIGURE

1

20

3O

10

ll.

12.

LIST OF FIGURES

.~ An over-all view of the apparatus showing the storage

bin suspended over the portable bin and the discharge
being weighed on the platform scales. . . . . . . . . . .

The portable bin is raised on pivoted channel beams to
dump the shelled corn into the storage bin. . . . . . . .

A depth gage graduated in 0.01 in. was used to measure
the depth of corn flowing in the chutes using different
orifice SizeSO O O O O O O O O O O O O O O O 0 O O‘ O O O O O

. A plywood gate was used to start and stop the flow of

corn through the chute orifice as the flow was timed
With a Stop watCh O O O O O O O O O O O O O‘ O Ov O O O O O O

. A long wood chute is shown connected to the raised

portable bin. The corn flows into a scale bin that was
hand dumped into the lowered portable bin. .' . . . . . .

. Long steel chutes were similarly mounted to measure

the flow rates through-different orifices and the depth
of corn at various locations along the chute. . . .. . . .

. Flow rate of shelled corn through wood chutes 1%- and 7%-

ft long with various orifice sizes and chute angles . . .

.- Flow rate of shelled corn through steel chutes 1%- and 7-5-

ft long with various orifice sizes and chute angles . . .

. Depth of corn ﬂowing in a 7%. ft wood chute at angles of

25, 3o, 45 and 60 deg with a ii-x 6 in. orifice . . . .. .

.. Depth of corn flowing in a 7%- ft steel chute at angles of

25,. 30,45 and 60 deg with a 1%- x 6 in- orifice . . . . .

Depth of corn. flowing in a 7%- ft wood chute at angles of
25, 30, 45 and 60 deg with a 2 x 6 in- orifice . . . . . .

Depth of corn flowing in ap7é- ft steel chute at angles of
25,. 30, 45 and 60 deg with a 2 x 6 in. orifice . . . . . .

vi

Page

17

17

18

18

20

20

28

29

,37

38

39

4O

 

The author is shown timing the rate of flow
of shelled corn through a short (1%- ft) wood
chute using a 1%— x 6 in. orifice in the chute.

INTRODUCTION

Whenever grain is made to move from one point to another a flow
pattern is established. In transporting grains from the harvest field
to final processing this flow pattern is reestablished many times. It is
important that all parts of a grain handling system function smoothly
and with a precision that the design engineer can predict.

Cereal grains can neither be classified as a solid nor a liquid.
Previous work has shown that flow from a bin through an orifice is inde-
pendent of the grain depth. Flow formulas have been established for
various sizes and shapes of orifices. Very little has been determined
on the flow of grains through transporting devices such as chutes.- For
automatic control, it is important that information be available for
designing all parts of a grain handling system.

Considerable work has been done in the chemical engineering field
where there is interest in the flow of cracking catalysts, fertilizers, ‘
concentrates and other materials. All of these works relate to discharge
through orifices in storage bins. - Very little, if any, information is
available on the flow. of semi-fluids in chutes.

This study was conducted to determine the different flow character-
istics of shelled corn through chutes. . Corn ranks third in world grain
production and about half of the total world corn crop is harvested in the
United States. With the increased use of picker-sheller type corn
harvesters, grain handling has become a task of considerable magnitude.
A Specific information is needed on the performance of different chute
materials, the effect of location and angle of the orifice and the effect

of angle on grain velocities and flow depths in the chutes.

The objectives of this investigation were: (1) To investigate the
mechanical behavior of corn flowing through chutes, (2) To study the
relationship between length of grain chutes and flow characteristics,

(3) To study the relationship between size and shape of grain chutes
and ﬂow characteristics, (4) To study the relationship between the
slope of grain chutes and ﬂow characteristics.

. Since flow through grain chutes is dependent on the flow through
the orifices in the storage bin it should be possible to determine these
relationships. This information would supplement existing knowledge
of grain ﬂow through orifices and provide design parameters for chutes.
These same parameters should be valuable in further studies of specific

characteristics and rheological properties of corn.

- REVIEW OF LITERATURE

Considerable-information is available on semi-fluid flow from
various storages such as bins, bunkers and silos. ~ Flow from storage
is an important step in moving semi-fluids to final processing butit
is equallyimportant that design information be available for chutes
and other transporting devices. .Lack of knowledge of flow character-
istics of semi-fluids in chutes often necessitates a trial and error
vapproach.

Hudson (1950) in his contribution to the Chemical Engineers'
Handbook stated that the simplest chute--the straight through--by trial
may be found to be on too flat a slope so that the material will back up
or on too steep a slope so that the material will accelerate. «If the
slope. is too flat the difficulty may be corrected by flooring the chute
with a thin sheet of stainless steel or aluminum or with plate glass.

If it-is too steep the equivalent of a reduced slope may be secured by
bolting cross angles to the bottom of the chute. - Sometimes the available
head is altogether too- small to permit an inclined chute that will permit
flow. . The correction may be a vibrating chute, usually by an electro-
magnetic unit. The chute then may be horizontal.

- Hudson commented further that long inclined straight chutes may
be objectionable because they scatter dust. Thus bituminous coal when
dry flows readily on an incline of 36 deg, but if it is damp or- if the
chuteiis rusted it will not flow. So itis usual to. specify a 43 to 45 deg
slope. . Coal will flow on this slope even when quite damp but will build
up speed and shatter or scatter dust. Because this difficulty holds true
for many granular materials, long straight chutes are avoided when it

is possible to do so where degradation or dust is to be prevented.

3

An alternative frequently used for anthracite coal is a vertical box chute
with steps projecting alternately from two opposite sides. The material
cascades with little degradation. Spiral chutes are also applicable to
vertical lowering where gentle handling is desired. They are suited to
either bulk or packaged materials.

One of the first mathematical expressions of laws governing the
flow of solid particles was the result of investigations by Deming and
Mehring (1929). The flow of fertilizers, lead shot, glass beads, and
some varieties of seed through truncated cones was investigated to provide
data for the design of fertilizer distributors, seed drills and storage

bins. Their equation was the following:

— ——;:-5—— [0.201+(0.392-2.58 sin%- ¢)( 29' + 0.130 + 0.161p-ll (1)
Do: d D0

T = time of flow (hr/ton)

p = tan 0;, O = static angle of repose (deg)
D0 = orifice diameter (ft)

Dp = particle diameter (ft)

angle of the cone (deg)

‘9.
ll

9--
ll

density of the material (lbs/ft3)

This equation was found applicable for cone angles up to ( 1r -2c1)
where c, was the angle of repose in radians.
Takahasi (1934) developed an empirical equation for the flow of

spherical forms of equal size as follows:

II)

V —;- [f(p1)d-z'5 + a-Dd'3'5] (2)

Where:
V = time for flow of unit volume (min/ft3)

D = mean diameter of particles (in)

d = orifice diameter (in)
a = constant
g = gravitational acceleration (32. 2 ft/secz)

furl) = Tan 0; 0 = kinetic angle of repose (deg)

This equation is limited to a ratio of D/d equal to three or greater and
no specific accuracy was claimed for this equation.

Further experiments on the flow of catalyst particles were con-
ducted by Newton, at all. (1945). They observed the flow toward an
orifice in vertical models using multicolored pellets. When the depth
exceeded 1. 5 times the diameter of the orifice there was an apparent
angle of repose equal to 71 deg as compared to a static angle of repose
of 34 deg. The following simplified equation was found for the rate of

flow of the catalyst:

, F = 8.50 DZ°96 H°°°4 (3)
Where:

F = flow rate (lb/min)

H = head (ft)

D = orifice diameter (in)

This formula was considered valid as long as the diameter of the
orifice was greater than 6 times the particle diameter.

Work on the deve10pment of equipment to measure the flow
properties of bulk solids was undertaken by Jenike (1958). . He suggested
that bulk solids such as ore, coal, cement, ﬂour, cocoa and soil can be
represented by a frictional, cohesive, plastic-solid.- He derived a
mathematical theory of flow leading to flow, no-flow criteria. The theory
was applied to the design of bins, hoppers and storage piles for gravity
flow- He suggested that while there are, and always will be, solids
which are not suitable for gravity flow, the vast majority of them will

flow if the bins and feeders are designed correctly. Jenike (1962) is

continuing his work on a mathematical study of the steady state flow
of bulk solids.

. Further work on the rate of discharge through orifices has been
reported by Franklin and Johanson (1955). An equation was derived for
flow of glass beads, lead shot, cracking catalyst and puffed rice.

Their equation for horizontal orifices was:

 

 

W _ PS 132.93
(6.288 + 23. 16) (d + 1.889) - 44.9 (4)
Where:
W = flow rate (lb/min)

P3 = true density (1b/ft3)

tan 0; 0 = kinetic angle of friction (deg)

1:
II

diameter of orifice (in)

il

CL
ll

averagescreen size of particles (in)

Particle size ranged from 0. 03 to 0. 2 in. with densities ranging
from 7. 3 to 676 lb/ft3. Orifice diameters ranged from 0. 236 to 2. 28 in.
An accuracy of i 7% was found between theoretical and experimental data.

Initial work on the effect of inclining the orifice was reported.

A flow rate for an inclined orifice was given as:

 

W9 _ WéOLZO: c: 1 cos 0 (5)
Where:

Wo = discharge rate at angle 0 (lb/min)

Wo = discharge rate at 0 = 900 (lb/min)

0 = inclination of orifice to horizontal (deg)

o. = internal kinetic angle of repose (deg)

Internal kinetic angle of repose was defined as the angle formed by
the plane at which particles change direction of motion with the horizontal
when rotated in a cyclinder. The surface static angle of repose was

defined as the maximum angular deviation from horizontal of the surface

of a static pile of granular material. Surface kinetic angle of repose
was defined as the s10pe of a continuously moving surface of a pile
of granular material. _

The apparatus consisted of a rotating drum 1 ft in diameter and
8 in.. long, with axis fixed in a horizontalposition and a plastic window
through which surface static, surface kinetic and internal kinetic angles
of repose were observed. The use of internal kinetic angle of repose
gave better correlation of the flow rate data than did use of either
static or surface kinetic angle.

Two formulae, based on dimensional analysis, have been proposed
for calculating the rate of discharge of granular materialsthrough

orifices. The equation proposed by Fowler and Glastonbury (1959) is:

 

 

W. 1 = 0.236 ( Dh )°-"’5 ~ (6)
p3 A «l 2g Dh ds
Where:
W = weight discharged per second (lb/sec)
pB = bulk density (lb/ft3)

A F orifice area (sq in)

4 x area of orifice

D = . .
h hydraulic diameter, ( perimeter )

 

ds = spherical diameter of particle (in)

Granular materials such as sand, sugar, rape seed, wheat and
rice were tested using circular, rectangular, triangular, hexagonal,
pentagonal and square orifices. The accuracy was found to be 1'- 10%.

A simplified form of the Fowler‘s equation was proposed by Rose
and Tanaka (1959):

W

 

- _1?_ . -°'s
_ 0.16 (d - 3)° 3 0 (0) (z-5) (7)

Where:

= rate of flow (lb/min)

= diameter of orifice (in)

diameter of particles (in)

= density (lb/ft3)

= acceleration of gravity (32. 2 ft/secz)

= angle of the cone (deg)

Nombdug
II

= shape factor of the particles

51

The shape factor Z was not defined by Rose and Tanaka but was con-

coefficient that depends on the material and the cone angle 0

sidered equal to 6 for spheres and 8 to 25 for discs.

. Tests were made on steel balls, silica sand, steel discs and some
fertilizers. Bridging was noted when the minimum dimension of the
opening was approximately equal to 3 particle diameters. -Results indi-
cated that the rate of discharge was independent of the true value of the
coefficient of friction of the material but dependent upon the cohesive
strength and proportional to D7” 5 (D = orifice diameter). - Flow was
also independent of the nature of the material provided the particle shapes
were substantially similar.

Brown and Hawksley (1953) made a thorough examination of the
mechanism of flow of solids through orifices. Theysshowed that there
were at least five distinct regions of movement near the orifice and
that the upper surface of the solids did not move until a considerable
dilation of the packing had occurred. They did not however give any
equation to explain the flow.

Later“ Brown and Richards (1959) made further tests on the flow of
glass beads and sand through orifices and developed the following
equations:

~ Flow through rectangular orifice:

l
Q=2.72AHTLV (8)

Flow through a circular orifice:
Q: 2.24 Dz-Sw (9)
Where:
Q = flow (gm/sec)

A =.- orifice area (cmz)
4 x area of orifice

 

H = perimetral diameter, ( . ) cm
perimeter
W = j!— (dimensionless unit)
8H2-
g = acceleration of gravity (cm/secz)
D = diameter of orifice (cm)

With '4’ equal to 0. 3 the accuracy was i 50%. The ratio of D/P
was limited to 20 to 30. 7 (D = diameter of a circular orifice in cm, ,
P = mean particle diameter in cm.) Contrary to Jenike's theory, these
experiments indicated that the flow rate was independent of the tightness
,or the original packing. Flow from narrow vessels was inﬂuenced by
friction on walls and interlocking of particles owing to the proximity of
the walls. Other conclusions were:
1. Fine particles discharge more rapidly than coarse particles.
2.. Spherical particles ﬂowed more rapidly than angular particles.
3. Rectangular orifices discharged at about the same rate as an
elliptical orifice of the same area but both were appreciably
slower than flow from a circular orifice. -

. Ketchum (1919) was one of the earliest to investigate the flow of
agricultural grains. His work showed that the rate of discharge of
wheat through an orifice was independent of the head over the orifice
and varied in direct proportion to the cube of the orifice diameter.

- This flow phenomenon was explained by Ketchum as follows: The wheat
grains in the bin tend to form a dome over the orifice which supports
the weight above it. The surface of this dome is actually the surface of

rupture. When the orifice is opened the grain flows out of the space below

10

the dome and the space is filled up by grains dropping from the top of

the dome. . As these grains drop, others take their place in the dome.

. Experiments with glass bins showed that the grain from the center of

the bin discharges first. This drops through the top of the dome while

the grain in the lower part of the dome discharges last.

. Further work by Ketchum on grain ﬂow showed that the coefficient

of friction of wheat on wheat was 0. 501; the coefficient of friction of

wheat on the bin wall was 0. 307, while the tangent of the angle of repose

of wheat was 0.421. (Other conclusions drawn were:

1.

The pressure of grain on bin walls and bottoms follows a law
which is entirely different from the law of the pressure of
fluids.

The lateral pressure of grain on bin walls is less than the
vertical pressure and usually ranges from 0. 3 to 0. 6 of the
vertical pressure.

The ratio of lateral to vertical pressures is not a constant,
but varies with different grains and bins.

The pressure of moving grain is only slightly greater than
the pressure of grain at rest.

Discharge gates in bins should be located at or near the

center of the bin.

. If the discharge gates are located in the sides of the bins the

lateral pressure due to moving grain-is decreased near the
discharge gate and is materially increased on the side opposite

the gate.

. The maximum lateral pressures occur immediately after filling

and are slightly greater in a bin filled rapidly than. a bin filled
slowly. Maximum lateral pressures occur in deep bins during

filling.

11

Hinkley (1926) classified dry sand, wheat and other granular
materials as semi-fluids and confirmed Ketchum's observation that flow
of grain from an orifice is proportional to the cube of the area of the
orifice and is independent of the head.

Anderson and Alcock (1954) described grain flow into and out of
storage. Grain tends to separate into heavier and lighter components
when poured into or drawn from a bin. When entering a bin the grain
falls freely to the surface of the pile, but the heavier grains fall straight
down, whereas, the lighter material floats outward. This tends to
cause chaff, dust .and lighter particles to accumulate near the bin walls.
When the stream of heavy grain reaches the pile, smaller particles are
trapped between the larger kernels and remain at the center of the conical
pile, while the kernels of grain flow away down the slope. This produces
a core of high-dockage grain in the center of the pile. When the grain is
drawn from the bin, the lighter particles tend to lose their places in
the ﬂowing stream and thus leave the bin last.

Barre (1958) further described the action of emptying a bin of
grain. The column of grain directly over a discharge leaves first and
gradually widens as it reaches the funnel-shaped grain surface. ' The bulk
of grain then turns itself inside out. This pattern of ﬂow is referred to
as funnelflow. . In a very steep sloped hopper the whole mass of grain
flows down simultaneously. The ﬂowing core increases in diameter
until all the material in the h0pper is included. . This flow pattern is
referred to as mass ﬂow.

- Common grains under some circumstances and conditions can very
easily become relatively non-free ﬂowing owing to the presence of dust,
cracked grain and foreign material. Damp grain exhibits poorer flow
properties than dry grain. . To make material ﬂowable its bulk strength
must be overcome and the material allowed to become loose. Bulk

strength can be kept to a minimum by using vertical partitions at the

12

center of the bin, by using supporting shelves at vertical intervals on
the bin wall and by using a supporting shelf in the center of the hopper.
Spreaders under the filling spout reduce impact and keep pressures to
a minimum.

- O'Callaghan (1960) distinguished two modes of flow in beds of
grain under the action of gravity. One mode has been associated with
- "shallow" and the other with "deep" beds. . He observed that in a ﬂat-
bottomed bin some of the grain remains stationary at the walls of the
container, when grain flows continuously in a moving bed between inlet
and discharge orifices. The rupture line between the stationary and
moving grain was found to be represented by a logarithmic spiral.

Other conclusions were:

1. The proportion of the total grain volume that is occupied by
stationary grain is greater in a shallow bed than in a deep
bed, when the inlet and discharge orifices are on thecenter-
line of the container.

2. Inclined hopper sides at the approach to the discharge orifice
do not alter the general shape of the rupture line from that
which develops in a flat bottomed container.

3. .In a shallow bed grain flows more freely at the center than
at the sides and mixing of the grain takes place.

4.. In a deep bed, moving vertically downward, grain flows
uniformly except near the discharge orifice, where doming
takes place.

5.. Flow of grain from two sources to a commondiacharge orifice
is influenced by the action of the wedge of grain formed by one
source on that formed by the other.

6.- Flow of grain around an obstruction is inﬂuenced by the

wedges of grain formed below the obstruction.

13

'Lorenzen (1959) investigated the moisture effect on granular
friction of small grains. In the normal moisture range of 7 to 13% there
was found in general no major change in the mean static coefficients of
friction. The same was found true of kinetic coefficients of friction.

In the high moisture range from 13 to 20% the influence of moisture on
the mean coefficient was more pronounced and is especially apparent for
wheat and corn. The angle of repose for wheat in this moisture range
increases by 31% and for corn by 20%.

In these tests the steel surface used was unquestionably smoother
than the wood surface, however, the coefficient for corn on wood was
lower than for corn on steel. It was surmised that cohesion influenced
this coefficient for corn on steel because of the flat form of the kernel.

- Cohesion is an elusive factor in that there is at present no practical
method of determining where friction ends and cohesion begins.

It was also determined that grain running shallow will produce
more drag per unit weight of the given grain than grain running deep.

It was apparent that a state of smoothness is reached beyond which
further polishing has little effect.

Welschof (1961) measured the rate of ﬂow of oats, wheat, granular
fertilizers and dry sand. Circular and rectangular orifices were tested
where the orifice diameters varied from 5 to 100 mm and the particle
diameters varied from 0. l to 5. 0 mm. Equations for the ﬂow of wheat
were developed by Welchof for both circular and rectangular orifices.

Attempts were made to measure the static pressure in the openings. ‘
The equations given applied only to wheat and were not valid for other
grains or other semi-fluid materials. 6 The use of these equations re-
quired the measurement of physical properties which would be difficult
to obtain. A coefficient of discharge, the angle of internal friction of
the grain, bulk density and a correction for the orifice diameter which

accounted for the constriction of the orifice during flow were all needed

14

for application of the equations. The values obtained for wheat agreed
closely with the formulas as long as the ratio of the orifice diameter
to the grain diameter remained large.
. Stahl (1950) developed equations for the rate of ﬂow of grains
through horizontal discharge openings.
. For circular orifices:
Q = 0.1753 13’ (10)

For rectangular orifices:

Q = 0.2232W (WL) (11)
Where:

Q = flow rate (bu/min)

D = diameter of orifice (in)

W: width of orifice (in)

L = length of orifice (in)

These relationships were printed in a technical bulletin published
by the American Society of Agricultural Engineers (1948). Stahl also
stated that the ﬂow through vertical openings was one-third the rate
through horizontal apertures. This appears to be based on the ratio
of lateral to vertical pressures in a bin.

Work by Ewalt (1962) produced some equations that are unique
for corn. The derived relationships were found to have a maximum
standard deviation of difference of i 3. 24% when compared with experi-
mental measurements for widths greater than 1. 5 inches. - The equations
formulated for shelled corn of the moisture content listed follow:

Horizontal Openings:

Round orifice Q = 0. 1196D3410; MC = 8.4% d.b.

- _ 12
Rectangular orifice Q = 0.1531W1'67‘L1’40; MC = 12.1% d.b. ( )
Vertical openings:
Round orifice Q = 0.0351D3°3°; MC = 12.72% d.b.
(13)

Rectangular orifice Q = 0. 0573W1‘75L1'5°; MC = 12. 72% d. b.

15

Since none of the equations have exponents of the same power, a
fixed ratio could not be determined between the horizontal and vertical
openings. This refutes the assumption made by Stahl that ﬂow from a
vertical orifice is one-third of the ﬂow from a horizontal orifice of
the same size and shape. Also the assumption that the area affects the
flow rate appears invalid in light of the results found in this research.
The effect of both the width and length appeared more important.

Tests on the increase in the slope of the bottom of the bin showed
a slight increase in the flow rate of the grain. . This held true as long
as the flow remained funnel flow. At 52. 5 deg mass flow, as defined
by Barre (1958)., occurred and the ﬂow rate decreased below that
recorded at 40 deg.

The moisture content appeared to have a bearing upon the ﬂow
rate of the grain. .48 the moisture content increased, the flow rate
tended to decrease. . Increased moisture content appeared to increase
the friction coefficient of corn on corn. Thus, the flow rate of the corn
decreased.

- Two tests were conducted to evaluate the effect ofhead on the flow
of grain. Little, if any, variation occurred in the flow rate at different
grain depths. This confirmed previous results that ﬂow rate is not '
affected by [the depth of grain.

No definite tests were conducted to determine the ratio of the orifice
diameter to the mean particle size that would cause bridging. However,
bridging did occur when the minimum dimension of the orifice was less
than approximately three particle diameters.

Although the literature review produced some equations for semi-
fluid flow there was a lack of information on the flow characteristic
through transporting devices such as chutes. ~ No equations were found
relating the size of the orifice Opening, chute length or chute angle to
the rate of semi-fluid flow. . Much of the information available requires

parameters that are not readily available for shelled corn.

APPARATUS

In choosing equipment for this research problem several con-
siderations were kept in mind. - The apparatus was selected to
accommodate chute lengths as short as 2ft and aslong as 8 ft. To
eliminate product variations and minimize a storage problem a small
batch was tested over and over againmany times. - Only very minimum
damage to the grain could be tolerated andtherefore samples were dis-
carded when damage appeared.

. Storage was provided in an 8 ft3 bin (1 x 2 x 4 ft) supported 5 ft
off the floor. -See Figure 1. This support made it possible to place a
balance beam ‘Toledo scale on a moveable base under the storage bin.
The bin was framed with 2 x 4 in. lumber and lined with «i- in. plywood.
The front and back panels (12 x 48 in) were removable. Rods through
the sides at top and bottom held these panels in place. An opening in
the front panel was provided with a sliding door to retain the corn
while the bin was being loaded and the various chutes installed.

. A second (24 x 30 x 24 in) portable bin alternately received the
discharge from the shorter Chutes and returned the shelled corn to the
storage. ~ See Figure 2. - Elevation was accomplished by attaching this
bin to the ends of a pair of 3 in. channel iron beams pivoted 81 in. off
the floor. {A steel cable, from a power winch attached at the opposite
end of the beams, raised and lowered the portable bin. The steel beams
were detached during weighing. A double-pole, double throw switch
was used to control the %- horsepower motor.

To provide additional height for the longer chutes the portable bin
was raised on the steel beams. The longer chutes were then attached
and the flow was measured into a third bin set on the: scales. See Figures
3 and 4. ~ When the portable bin was lowered it was refilled by manually

dumping the scale bin.

16

17

 

Fig. 1 - An over-all view of the apparatus

showing the storage bin, ortable
bin and platform sca es.

 

Fig. 2 - The portable bin is raised on
pivoted channel beams to dump the
shelled corn into the storage bin.

18

 

Fig. 3 - A depth gage graduated in 0. 01 in.
was used to measure the depth of corn
flowing in the chutes.

- "TIBET « ‘"
.2 l ', I
o ." (i ”It. '
w ' ' (“.2 .. ..

I .

    

   
 
  

  

 

. lit‘!"

Fig. 4 - A plywood gate was used to
control the flow of corn through
the chute orifice.

19

All angles were carefully measured before each run using a pro-
tractor head for a combination square withattachedlevel. An angle of
25 deg from horizontal was selected as the shallowest angle tomeasure
ﬂow, and the equipment restricted the steepest angle to 72 deg. - Care
was taken to clamp the bins and chutes in place firmly to insure that
the angle did not change during a test.

The corn flow was controlled in. the chutes with »a plywood orifice
6'in.. from the inlet end of the chutes. ~ This orifice was formed by clamp-
ing a i— in. plywood block so that the desired opening was proVided. ‘ The
resulting orifice was kept perpendicular to the chute bottom and the size
of the opening was checked before each flow trial. Care was taken to
keep the leading edge of the plywood orifice square. . The slidingdoor
from the storage bin was kept open wide enough to insure that the chute
orifice was covered withcorn at all times. - Flow through the orifice
was manually started and stopped by sliding a plywood gate up and down
to open and close the orifice. - Time was measured with-a stopwatch.

_ The balance beam‘ Toledo scale, used to weigh the corn, had a
capacity of 200‘1b. .It was possible toread weights to the nearest l/8’lb.
. Calibration of this scale showed readings of 1 oz light at l to 6 1b;

2 oz heavy at 50 to 75 1b; and 4 oz light at 100 to 175 lb. . Tareweights
of the portable bin allowed runs of 100 to 125 lb of corn.

A depth gage was used to measure the depth of corn at various
locations along the chute. This gage was graduated in 0.01 in. and
could be read‘i 0.02 in. . See Figure 5. . Depth was judged at the point
where corn would just strike the end of the depth gage.

- The moisture content of the grain was checked periodically by using
a Steinlite capacitancetype moisture meter, model 400G. .Air tempera-
tures and relative humidities of the test room were determined using a

sling psychometer and psychrometric chart.

20

 

Fig. 5 .- Corn flowing from the portable
bin through the long wood chute
and into the scale bin.

 

Fig. 6 - A long steel chute mounted to
measure the flow rates and the depths
of corn flowing in the chutes.

, METHOD OF PROCEDURE

Yellow dent shelled corn that had been dried with heated air was
obtained from the Swine Farm of Michigan State University. - This corn
'was cleaned to remove most of the cracked kernels and crushed cob.
Thorough cleaning was not attempted, however, to more closely
simulate normal operating conditions. The resulting density was 56.0
pounds per bushel. Moisture content for the grain ranged from 10. 19
to 8. 38% w. b. (wet basis) throughout the tests.

. A ﬂow pattern for the shorter (2 ft) chutes was established from
the portable bin, to the storage bin, through the chutes and into the
lowered portable bin. After the corn was elevated in the portable bin it
flowed by gravity into the storage bin. The portable bin was then
lowered to the platform scale and the scale was adjusted to read zero.
The chutes were attached and the angle was adjusted. , The retaining door
on the storage bin was opened and the corn was allowed to fill the end of.
the. chute to the gate at the orifice. - A stop watch was started when the
orifice gate was opened and stopped when it was closed.

- For the longer (7% ft) chutes the ﬂow pattern was from the raised
portable bin, through the chutes, into a scale bin and then hand dumped
into the lowered portable bin. . Before the chutes were attached the
portable bin was clamped securely to prevent tipping. . Approximately
115 1b of shelled corn was used for each run.

As the corn was used repeatedly, damaged kernels and small dirt
particles tended to collect in the bottom and corners of the bins.

Periodically the used corn was discarded and replaced with newcorn.

21

22

Chute Lengths

 

The first tests were to find what effect chutes of different lengths
had on the ﬂow rate of the grain. Wood chutes (6 x 6 in inside
dimensions) were constructed of 3/8 in. plywood in 2 and 8 foot lengths.
The plywood was interior grade with surfaces graded A and B. The A
surface was used for the interior of the chutes and the plywood was cut
so that the corn flowed parallel with the grain of the wood.

To insure accurate metering of the corn ﬂow, plywood blocks
were installed 6 in. from the top ends of the chutes. This formed an
orifice that could easily be adjusted and manually opened and closed.
The effective lengths of the chutes were therefore reduced from 2 ft to
l. 5 ft and from 8 ft to 7. 5 ft. The plywood orifices were held in place
by 11,- in. clamping rods through the sides of the chutes. . See'Figure 6.
Care was taken to keep the orifices perpendicular to the bottom of the
chutes and running full during the tests.

The chutes were attached to the bins. The angle from the hori-
zontal was carefully measured using a protractor head for a combination
square with an attached level. The various slopes were set on the
protractor and the chute angle adjusted until the bubble on the level was
centered. . Flow rates were taken at 25, 20, 45, 60 and 72 deg for
2 ft and 8 ft wood chutes. The orifice opening was kept constant at
1%- x 6 in. Three replications were made for each‘angle. These data
of flow rate versus angle from horizontal were plotted for the two chute

lengths. See Figures 7 and 8.

Chute Angles

 

The investigation of the influence of chute angle on discharge
rates was extended to include steel chutes. Twenty gage black steel
sheets were formed into chutes (6 x 6 in. , inside dimensions) 2 ft and

8 ft long. . Plywood blocks were again used to form the orifices 6 in. from

23

the top end of the chutes. Wood spacers were attached across the top
of the chutes to insure that they would retain their shape.

Tests were made at the various angles with 1312-, 2 and 3 in. orifice
openings. The flow patterns were accomplished as before. Three

replications were made for each change in orifice opening and angle.

- Corn Depth in. Chutes

 

To measure the depth of the corn ﬂowing in the chutes a depth
gage was developed. This consisted of a steel rule graduated in 0.01 in.
and a clear plastic slide. The slide was made of rigid plastic 3 in. by
2 in. with an opening in the center through which the rule could move
up and down. See Figure 5.

. As the corn flowed through the 7-i- ft chutes the depth was
measured at the wood spacers placed at 2 in. , 6 in. , 2 ft, 5 ft and 7%- ft
along the chute. Full depth from the top of the brace to the bottom. of
the chute was carefully measured. As the corn flowed through the
chute the depth from the top of the brace to where the corn just touched
the bottom of the depth gage was recorded. The resultant corn depth
was found by subtracting the reading with the corn flowing, from the
full measured depth. Three replications at the various angles and orifice
openings were made at each location along the chutes. These data of
corn depth versus distance along the chute were plotted for 1%- and 2 in.
orifice openings at 25, 30, 45 and 60 deg.

The angle where the corn reached zero velocity was measured by
allowing the corn toﬂow and decreasing the angle to the point where
the corn would not move in the chute. Normally the corn would flow
at a depth approximately equal to 2 kernels deep at angles over 25 deg
and at a distance of 2 to 5 ft from the orifice. . It tended to run slightly
deeper as the angle was decreased. - Measurements of the chute angle
was taken at the point where the corn ceased to flow. - Both the wood

and steel chutes were tested for' zero velocity.

ANALYSIS OF DATA

Results of Tests on Effect of Chute Length

 

Tests were conducted to determine the effect of chute length on
the discharge through an orifice in rectangular wood and steel chutes.

. Shelled corn with-a moisture content of 10. 19 to 8.48% w. b.. (wet basis)
was'used. - Flow measurements were made with orifice openings. 1%- x 6
in and 2.x 6 in. for chute lengths of 1%- and 7";- ft. These chutes were
tested at angles of 25,. 30,. 45, 60 and 72 deg. I

These results indicate there is little or no difference between
the discharge of a 1%- x 6 in. orifice in the short (1%- ft) wood chute as
compared to the long. (7&- ft) chute. _. See‘Figures 7 and 8. - The percent
difference from the mean discharge ranged from 0. 19 to 1..42%_as shown
in Table 1. The discharge through the 1%- x 6 in.orifice in the steel
chutes was slightly higher in the short chutes compared to the long
chute with the percent difference from the mean ranging from 0. 50m
3. 05% as shown in Table 2. I

Using the 2 x 6 in.orifice the discharge was higher through the
long wood chute with the percent difference from the mean ranging from
0.97 to 2. 88% as shown in Table 3. - The discharge was higher in the
short steel chute using the 2 x 6 in. orifice with the percent difference
ranging from 0. 20 to 2. 77% as shown in Table 4. The, data used- in
plotting thecurves in Figures 7 and 8 are found in Tables 9-14,
Appendix A.

All of the runs weremade over a period of weeks and during this
time the temperature and relative‘humidity fluctuated. - Thus, the
moisture content varied from 10. 19 to, 8. 38% w. b. as determined by a
-‘Steinlite moisture tester. There was a slepe of about 10 deg to the

bottom of the portable bin used to elevate the grain for thelonger chutes.

24

25

TABLE 1

- Percent difference from the mean ﬂow rate
between short (1%- ft) and long (7%- ft)
wood chutes at various angles with
the chute orifice 1%: x 6 in.

 

 

 

 

M M
Angle . ,. -Flow RatesAlb/min) -Percent Difference
(deg) Short Chute Long. Chute from mean

25 108.3 108.9 ‘ 0.28

30 128.4 128.9 0.19

45 181.5 180.5 0.28

60 222.0 223.8 0.40

72 245.5 252.6 1.42
TABLE 2

(Percent difference from the mean ﬂow rate
between short (1%- ft) and, long. (77}- ft)
steel chutes at various angles'with
the chute orifice ~l-i- x 6 in.

 

 

 

 

Angle Flow Rates (lb/min) Percent Difference
--(deg) ~ Short Chute .Long- Chute from mean

25 107.7 106.5 0.50

30 140.6 132.3 3.05

45 193.3 181.9 3.04

60 236.8 223.0 3.00

72 255.4 244.9 2.10

 

26

TABLE 3

' Percent difference from the mean flow rate
between short (1%- ft) and long (7%- ft)
wood chutes at various angles with

the chute orifice 2 x 6 in.

_—.‘ .__’__ —-: r I
— i :i -

 

 

 

 

Angle Flow Rates (lb/min) Percent Difference
(deg) Short Chute Long Chute from mean

25 170.3 180.4 2.88

30 212.7 218.7 1.39

45 307.5 315.1 1.22

60 392.8 400.5 0.97

72 .430.0 441.0 1.26

TABLE 4

Percent difference from the mean ﬂow rate
between short (1%- ft) and long» (7'):- ft)
steel chutes at various angles with
the chute orifice 2 x 6 in.

 

Angle Flow Rates ‘ (lb/min) Percent Difference

 

 

(deg) Short Chute ‘Long Chute from mean
25 205.7 184.9 5.25
30 233.5 225.9 1.66
45 330.5 312.7 2.77
60 390. 2 386.6 0.46

72 442.3 440.5 0.20

 

27

Flow limitations from the side of the storage bin would not permit
tests with the short chutes using a 3 x 6 in. orifice. Tests were made,
however, on the long chutes using 3 x 6 in. orifices and angle versus
discharge rate was plotted as shown in Figures 7 and 8.

. From the results of this investigation of the effect of chute length
on the discharge rate of shelled corn, it appeared that the flow rate

was essentially unaffected by the chute length.

 

Effect of Chute Angle on Rate of Flow

The relationship describing the flow of shelled corn through
rectangular orifices placed in chutes at different angles was determined.
Orifice openings 6 in. wide and 1%, 2 and 3 in. high were used with
chute angles of 25, 30, 45, 60 and 72 deg. A plot of chute discharge
(lb/min) versus angle (deg) for the various orifices, Figures 7 and 8,
showed that discharge increased as the angle increased. . Several
attempts were made to describe the curved lines mathematically. .It was
observed that the curves are similar to sine curves; that is, the flow
rate appeared to be a function of the chute angle 0. .The equation then

is of the following form;

F = KA sin 0 (14)
Where:
. F = flow rate (lb/min)
K = constant for a given orifice size and shape
A = orifice area (inz)
0 = chute angle (deg)

The constant K was determined for the various orifice openings
and chute angles. .See Tables 5 and 6. The coefficient of variation ranged
from 1. 08 to 4. 22% for the different sizes and types of chutes. - See
Table 7.

Flow Rate (lb/min)

600

700

500

400

300

200

100

28

'- ®/ 0— 1%- inx 6 in x 1&- ft
A—— li-in x 6 inx 7%.ft
x 2 in-x 6 in:.x 1%- ft

 

m— 2 in-x 6 inx 7)- ft
®-—-—- 3 in-x 6 inzx 7%:ft

 

L l L l I L L . #j

 

10 ‘ 20 307 40 5.0 60 70 80 9o
Angl.e'(deg) ‘
Fig. 7 - Flow rate of shelled corn through wood chutes

1%- ft and 7%- ft long with various orifice sizes and
chute angles.

I
I

- Flow Rate (lb/min)

700

600

500

400

300

200

100

 

29

/ Q— 1%- inx6 inxlfft

 

®
A— lé-inx6inx7f-ft
x 2in7x6inx 11- ft
13...;— 21nx6inx75-ft
®-——— 3inx6inzx7i-ft

G
<8

1::

x

 

 

I l l . ‘1 i I I l l.

10 20 30 4050 60 70 80 9o
Angle (deg)

Fig. 8 -- Flow rate of shelled corn through steel chutes
1';- ft and 7%- ft long with various orifice sizes and
chute angles.

30

:Since discharge from an. orifice placed horizontally. in the bottom
of a bin and discharge from a chute 90 deg from horizontal are bothin
free fall the flow rates should be comparable. . Attempts were made to
calculate discharge rates from equations proposed by Ewalt (1962).

- His equation for a rectangular orifice positioned horizontally is as
follows:

Q : 0.1531W1.62 LL40 | (14)
- Where: i
Q = ﬂow rate of corn (bu/min)
W
L

width of the orifice (in)

length 0f the orifice (in)
By this equation a rectangular orifice 1%- x 6 in. should give a

flow. of 3.64 bu/min or 204. 0 lb/min. -Since F = Q and‘F = KA sin 0,

 

7 _ Q _ 2.04.0 _ 7 . 2 ‘
thenK — A sin 0 of K — 9 x ’1 - 22.65, where A (1n) equals the area

of the orifice and 0 equals 90 deg. - The mean of the K constants from
Tables Sand 6 for this size orifice is 28.95. . The difference between
the calculated K and measured K is 21. 8%.

- In analyzing this difference it became apparent that the grain had
an approach velocity prior to flowing throughthe orifice in the chute.
Even though care was taken to keep the orifice covered with grain during
all the tests, the velocity created by movement fromthe dome formed
in the bin to the orifice in the chute caused the flow rate to increase.

. Tests were conducted to evaluate this approach velocity. The
chute orifice was placed at the end of the chute-and inserted intorthe bin
of shelled corn. Runs were made using 1%- x 6 in. and 2 x 6 in. orifices
at 30’ and 45" deg. Three replications of each size of orifice and angle
were made. ~ Table 8 shows the comparison factor to vary from 1. 39 to
1.45 with the average equal to 1.42. This factor accounts'for the
approach velocity of the grain used in previous tests. The ﬂow through
orifices placed 6 in. from the end of the chute discharged at a rate 1.42

times faster than orifices placed in the end of the chute.

31

TABLE 5

Constant K values aigdetermined by the
equatioan = --—.-- for wood
sm 0
chutes at varlous angles and
chute orifice sizes.

 

 

 

Wood Chute Angle Flow Rate *
sizes (deg) (lb/min) K

(in x in x ft)

1%— x 6 x111,- 25 108.3 28. 50
" 30 128.4 28.40
I' 45 181.5 28.45
" 60 222.0 28.45
" 72 245.5 28.60

1%“x6 x 7;— 25 108.9 28.60
" 30 128.9 28.61
" 45 180.5 28.40
" 60 4223.8 28.59
" 72 252.6 29.45

2x6x 1%- .25 170.3 33.60
" 30 212.7 35.45
" 45 307.5 36.20
" 60 392.8 37.80
I" 72 430.0 37.65

2x6 2.7%- 25 180.4 35.60
" 30 218.7 »36.50
" 45 315.1 137.10
2' 60 400.5 38.50
" 72 441.0 38.60

 

>3
Average'K for wood chutes with 1%- x 6 in. orifice 28. 60.
Average-K for wood chutes with 2 x 6 in. orifice 36. 70.

32
TABLE 6

Constant K values 321'? determined by the
equation'K = T for steel
chutes at various angles and

chute orifice sizes

 

 

 

Steel Chute Angle - Flow Rate *
Sizes (deg) (lbs/min) K
(in x inuxft)
1%x 6 x 1;- 25 107.7 28.30
" 30 140.6 31.20
-" 45 193.3 30.28
... 60, 236.8 230.28
.H 72 255.4 29. 81
1%- x 6x 7%- 25 106, 5 28. 00
... 30 132.3 29.40
.H 45 181.9 28.58
." 60 223.0 28.62
" 72 244.9 28.62
2 x 6 x 171,- 25 205.7 40.40
" 30 233.5 38.85
.. 45 330.5 38.95
" 60 390.2 37.50
-" 72 442.3 38.70
2 x 6 x 7,1,- 25 184.9 36.45
-" 30 225.9 37.65
" 45 312.7 36.90
"' 60 386.6 37.20
4* 72 440.5 38.60

 

*
Average‘K for steel chutes with 1';- x 6 in.. orifice 29. 31.
- Average K for steel chutes with 2 x 6 in.. orifice 38. 12.

.33,

TABLE 7

A comparison of the standard deviation and
coefficient of variation of the constant
K for wood and steel chutes 1%- and 7%- ft
long with 1%- x 6 in: and 2 x 6 in.. orifices.

 

 

 

 

 

 

 

 

Chute Standard . - Coefficient
Type . Size Deviation of Variation (%)
(in x in x ft) 1
Wood 1%x6x 1%- 0.31 1.08
Wood 2x6x7i- 2.42 4.22
.Steel 1;— x 6 x 1;- 1.05 3.58
Steel 2x6x7g- 1.19 3.12
TABLE 8
Comparison of the flow rate in wood chutes
with the chute orifices inside and
outside the storage bin.
. - Discharge Discharge . Comparison
Chute Size _ Angle Orifice win-Chute Orifice in Bin Factor. *
(in. x in‘x ft) (deg) (lb/min) (lb/min)
li—x6x1i— 30 128.4 90.34 1.422..
li-x 6 x l;- 45 181.5 122.25 1.449
2x6x1%- 30 212.7 153.3 1.387
2 x 6 x 1%- 45 307.5 218.5 1.405

 

*
Average Conversion Factor 1.42

34

Since the tests were conducted with the orifice 6 in. from the end
of the chute this comparison factor must be applied to Ewalt's formula

for horizontal orifices to correlate results. Ewalt's formula then

becomes:
= 0.1531 W1°6Z “4° 1.42
o L ( ) O (16)
WithW: l.51n., L: 6 in. andO = 90
Q = 5. 15 bu/min or 288.51b/min
. Since Q = F
Then:
-Q=KAsin00rK=——g——— (.17)
A sin 0
Kz-Z—8-§-'--2 of 32.06
9 x1

The difference in K's between the average of Tables 5 and 6 and
that determined by Ewalt's equation is 10. 8% . Ewalt found for the
1%- x 6 in. orifice placed horizontally in the bin the actual measured
flow rate was 255.4 1b/min. The constant K for a 1%- x 6 in. orifice now

is:
__ 255.4

K”9x1

= 28.4.

 

. The difference between this constant and the average K from

Tables 5 and 6 for this size orifice is 0. 19%. . This indicates that Ewalt's
‘ equation is only valid for orifices wider than 1%— in. - Also the-measured
flow Q from an orifice is KA sin 0. . The constant K, however, is different
for different size orifices.

- The flow from a 2 x 6 in. orifice placed horizontally in a bin by
‘ Ewalt was 324. 8~1b/min by formula and 312. 6 lb/min by actual measure-

) ment. . Corresponding K's are 38. 33 and 37.93. These constants differ

from the average'K in Tables 5 and 6 by 2.4 and 1.4%.

. Similarly the flow from a 3 x 6 in. orifice placed horizontally in a

bin by Ewalt was 888. 0 lb/min by formula and 931. 0 lb/min by actual

35

measurement. - Corresponding K's are 49.4 and 51. 7. These constants
differ from the average-K computed from Tables 8 and 9 by 7.5 and 3. 18%
These results indicate that flow rates determined by the equation

F = KA sin 0 are nearly equal to ﬂow rates as determined by the equation:
Q = 0.1531w1-67- LL40 sin 0 (1.3)

with the chute angle over 25 deg and W greater than 1%- in.

-Since the value of K depends on the size of the orifice it would be
more convenient to use the equation for Q which applies to any size. of
orifice. . Also the values for the constant K in Tables 5 and 6 are valid
only for equipment similar to that used in these tests with chute angles
between 25 and 90‘ deg. — The constants were found to differ by a factor

of 1.42 from flow rates as determined by Ewalt.

. Results of Tests on Depth of Flow inChutes

 

Tests were run to determine the depth of corn at various points
along the chutes set at different angles and using the different orifice
sizes- The measurements were made with a depth gage graduated in 0. 01
in. . (See page 19 for a more detailed description of the depth gage.)

Readings were taken at the orifice and at 5 points along the long
(7% ft) wood chutes. . Depth of corn versus distance along the chute was
plotted for 25,. 30,. 45 and 60 deg angles, Figure 9. wWith a chute orifice
of 1%- x 6 in. the depth appeared to remain constant beyond about 2 ft
from the orifice regardless of the angle over 25 deg. - Using a 2x 6 in.
orifice, Figure 10, the corn reached a constant depth at about 5 ft from
the orifice.

. An additional series of tests was conducted to determine the effect
of the chute material on the depth of flow. - Readings were taken-at‘the

orifice and at the same locations along a (7% ft) steel chute using the same

36

chute angles. A plot of depth of corn versus distance along the chute,

. Figure 11,. showed a relationship similar to the wood chute. Usingthe
same size orifices, similar depths occurred at about the same location
along the metal chute. - The corn depth was slightly less in the metal
chute than in the wood chute using a 1%- x 6 in.orifice. . See Tables 15
and 16, Appendix A.- However, the opposite relationship occurred in
comparing the wood and steel chutes using a 2 x 6 in.orifice. Figure 12.
. See also Tables 17 and 18, Appendix A.. It appeared that the chute

material had-little effect on the depth of flow in the chutes.

, Corn Depths (in)

37

Chute Angles

 

1.3 —

1.2 _ O. 25 deg
A——- 30 deg

1.1 " x— .45 deg

3* 6'0: deg

 

 

 

 

mad

 

 

O3-
.25
.17
J I L J 4L 1 I
0 1 2 3 4 5 6 7' 8

Chute Length from Orifice (ft)

Fig. 9 - -Depth of corn flowing in a 7%- ft woo‘d chute at angles
of 25,. 30, 45 and 60 deg with a 1.1- x 6 in. orifice.

Corn Depth (in)

 

38

 

 

Chute Angles

 

 

 

 

 

’ O 25 deg
F A 30 deg
K 45 deg
13 60 deg
\§ ‘ al at :i ~
)-
l l 1 l L l L
1 3 4 5 6 7 8

-Chute Length from Orifice (ft)

I

Fig. 10 -. Depth of corn ﬂowing in ae7§r ft wood chute at angles

of 25,. 30, 45 and 60 deg with a 2 x 6 in.orifice.

Corn Depth (in)

39

Chute Angles

 

7 @—
a
,1 A—
X
I.
a—

 

Chute Length from Orifice (ft)

25 deg
30 deg

45 deg
60 deg

 

Fig. 11 --Depth of corn ﬂowing in a 7%- ft steel chute at angles

of 25, 30, 45 and 60 deg with a 11, x 6 in.orifice.

Corn Depth (in)

1.3

1.2

40

Chute Angles

 

 

 

 

 

. O— 25 deg

- A—- 30 deg
X 45 deg

b D— 60 deg

p.

b

L—

).

l L l J l _l J
1 2 3 4 5 6

» Chute Length from Orifice (ft)

Fig- 12 - Depth of corn ﬂowing in a 7;- ft steel chute at angles
of 25, 30, 45 and 60 deg with a ‘2; x 6 in.orifice.

. SUMMARY

It is important that all parts of a grain handling system function
smoothly and with a precision that the design engineer can predict.
Considerable work has been done on discharge of semi-fluids through
orifices in storage bins. Very little information is available on the
ﬂow of semi-fluids in chutes. . Information has been obtained on the
performance of different chute materials, the effect of location and
angle of the chute orifice at the bin location and the effect of chute
angle on grain velocities and flow depths in the chutes.

. Several equations have been proposed describing the relationships
involved in grain ﬂow through orifices placed in bins. . Lack of knowl-
edge of ﬂow of semi-fluids in transporting devices such as chutes often
necessitates a trial and error approach.

The purposes of this work were (1) to attempt to determine the
mechanical behavior of shelled corn through chutes, (2) to study the
relationship between length of grain chutes and ﬂow characteristics,

. (3) to- study the relationship between size and shape of grain chutes and
flow characteristics and (4) to study the relationship between the slope
of grain chutes and ﬂow characteristics.

Apparatus was used that had been constructed principally for the
study of grain ﬂow. . It was selected to-accommodate chute lengths as
short as 2 ft and as long as 8 ft. The basic equipment consisted of a
storage bin suspended about 5 ft off the floor. This made it possible to
-movea balance beam platform scale under the storage bin for gravity
flow. A second portable bin was elevated on pivoted channel iron beams
and powered by an electric motor driving a winch. - The short (2 ft)

chutes were attached to the storage bin and the ﬂow rates were determined

41

42

as the grain flowed into the portable bin. The grain was thenelevated
and dumped into the storage bin. The'longer (8 ft) chutes were attached
to the elevated storage bin and the flow rates were measured into a
third bin placed on the scale. Hand dumping into the portable bin com-
pleted the flow pattern. Yellow dent shelled corn that ranged in
.moisture content from 10.19 to .8. 38% w. b. was used throughout the
tests.

. The ﬂow varied but was essentially unaffected by the chute length.
The relationship describing the ﬂow of shelled corn through rectangular
orifices was determined. - The ﬂow was found to depend on a constant,
the area of the orifice and the sine of the chute angle. - The constant K

was determined by the equation K = and was found to vary with

__F_
A sin 0
the size of the orifice. . The coefficient of variation for the various
orifice sizes ranged from 1. 08 to 4. 22%.
It became apparent during the tests that semi-fluids ﬂowing from

a storage bin are influenced by the velocities prior to flowing through
the orifice in the chute. With the orifice placed in the chute 6 in..from
the storage bin this approach velocity increased the ﬂow 1.42 times
the flow with the orifice in the end of the chute.

- The depth of corn flowing in a chute varied with the length of the
chute and was independent of the chute angle. - It could not be determined

that chutematerial effected the depth of corn in comparing the ﬂow in

wood and steel chutes with various size orifices.

CONCLUSIONS

1. The rate of ﬂow was found to be independent of the chute length

with the chute angle over 25 deg. . Some variation was found when com-
paring the ﬂow rate through 117 ft and 7%- ft chutes with different size
orifices. However, no relationship of flow rate to chute length could

be established.

2. The relationship describing the flow of shelled corn through rectangu-
lar orifices placed in chutes at different angles was found to be:
F = KA sin 0
- Where:
F = flow rate (lb/min)
K = constant for a given orifice size and shape
A
0

orifice ar ea (inz)

chute angle (deg)
K was found to increase by 1.42 with the orifice placed 6 in.. from the

end of the chute as compared to the orifice in the end of the chute.

3. The flow rate equation for rectangular orifices may be written as
follows:

F = 0.1531w1-62 L1°4° sin 0
At angles over 25 deg, the flow rate F was found to be equal to flow
rates through horizontal orifices as determined by Ewalt, multiplied by
the sine of the angle. His equation for a rectangular orifice positioned
horizontally is as follows:

Q ___ 0.153 W1.62 LL40
Where:

- Q = flow rate of shelled corn (bu/min)
W = width of orifice (in)
L = length of orifice (in)
43

44

4. The depth of shelled corn flowing in chutes was found to vary with the
distance from the orifice and was found to remain constant beyond 2 ft
from the orifice using a 1%- x 6 in. orifice. - Depth remained constant

beyond 5 ft from the orifice using a 2 x 6 in. orifice.

5. With the same orifice opening, the depth of shelled corn ﬂowing in
chutes was found to be independent of the chute angle beyong 25 deg.
As the angle was increased the shelled corn appeared to flow faster but

at the same depth as other angles.

6. Different chute materials did not appear to influence the depth of

shelled corn flowing in the chutes at various chute angles beyond 25 deg.

RECOMMENDATIONS FOR FURTHER STUDY

- An attempt should be made to relate the hydraulic jump that

apparently occurs with grain ﬂowing in a chute toﬂuid flow equations.

. Studies should be made to determine the influence of approach

velocities to the ﬂow rates through» orifices.

More direct methods of measuring the velocities of grains in chutes

should be studied.

Theinfluence of corrosion of construction materials and films formed
by dust and other foreign matter on flow rate in chutes should be

studied.

Work. should be done to determine flow rate equations for grains

other than shelled corn.

1 Tests should be conducted to determine the effect of moisture on

the flow rate of grains.

.4 Further work should be done on the effect of chute materials on

the flow rate'of grain.

.45

REFERENCES

Anderson, J- A. , and A. W. Alcock
1954. Storage of Cereal Grains and Their Products
Am. Soc. of Cereal Chemists, Minneapolis,

Minn.:515
ASAE
1948. - Engineering data on grain storage. Agr. Eng.
Data 1:1-11

Barre, H. J.

1958. . Flow of bulk granular materials. Agricultural
Engineering 39 (9):534-536, 539,- Sept.

Brown, R. L..and P. GT W.-Hawka1ey

1947. The internal flow of granular masses. Fuel 26:
159

Brown, R. L., and J. C. Richards
1959. . Exploration study of the flow of granules through

apertures. . Trans.- Instn. of Chem.- Engrs. ,- London.
37:108-119

Deming, W. E., and A. L. Mehring
1929. The gravitational flow of fertilizers and other

comminuted solids. Industr. and Engng.. Chem.
21 (7):661-665, July

Fowler, R. T., and J. R. Glastonbury
1959. The flow of granular solids through orifices.
Chem. Engng.-Sci. 10 (3):150-156

Franklin, F. C., and L. N. Johanson
1955. Flow of granular material through a circular ori-
fice. .Chem. Eng. Sci. 4 (3):119-129

Hinchley, J. W.

1926. - EncycloEdia Britannica. - Chemical Engineering
5:348

46

47

Hudson, Wilbur G.
1950. - Chemical Erﬂneers' Handbook, 3rd ed. McGraw-Hill
Inc. , New York:1361-1362

 

Jenike, A. W. ,~ P. J- Elsey and R. H. Woolley
1960. - Flow properties of bulk solids. . Paper - Amer.
.Soc.for Testing Engrs. :14 June

Jenike, A. W.
1954. Better design for bulk handling. . Chem. Eng.
61 (12) Part 2:175-180, Dec.

. Ketchum, M. S.
1919. The Design of Walls, Bins and Grain. Elevators
3rd ed. -McGraw-Hill Book Co. ,> New York:556

 

Lorenzen, R. T.

1959. . Moisture effect on granular friction of small
grain. ASAE Paper, 59-416

Newton, R. H. , G- S- Dunhan and T. R. Simpson
1945. Trans. of Amer. Inst. Chem. Engng. 41:218

O'Callaghan, J. R.
1960. . Internal Flow in moving bins of granular material.
Jour. of Ag. Eng. Res. (JAER) 5 (2):200-217

Rose, H. E., and T. Tanaka
1959. . Rate of discharge of granular materials from bins
and hoppers. Engineer, London 208 (10):465-469,
Oct.

Stahl, B. .
1950. - Grain storage design. USDA Circ. 834 (based on
data in Eng. Data on Grain Storage, Agr.. Eng.
-Data 1:1-11, 1948):23

Takahasi, K. ; .
1934. .Inst. of Phys. and Chem. Research, Tokyo.
. Scientific papers. 26 (1):11-20 No. 540

Welschof, G.

1961. Beitrag zur Messung der Ausflussmengen k6rniger
Guter mit Blenden und Diisen (translated) Institut
fiir Landtechnik, Stuttgart - Hohenheim,
Landtechnische Forschung 11, H. 5:138-141

APPENDIX A

EXPERIMENT AL RESULTS

48

49

TABLE 9

Flow of shelled corn through a
1%- x 6 in. orifice in wood chutes.

 

 

 

 

Chute Size Angle Flow Rates

(inx inrx ft) , (deg) * (lb/min)

1%— x 6 x1%— 25 108.2 108. 5 108.3
30 125.0 123.9 125.0
45 181.5 181.5 181.0
60 221.5 223.0 221.5
72 250.0 241.0 245.5

1%- x 6 x 7-1. 25 108.8 109.0 109.0
30 127.8 128.5 130.5
45 179.6 181.9 180.0
60 224.5 223.3 223.5
72 250.0‘ 253.9 253.9

TABLElO

 

Flow of shelled corn through a
2 x 6 in. orifice in wood chutes.

 

Chute Size Angle Flow'Rates

(inx in x ft) (deg) (lb/min)

2 x 6 x 1;— 25 170.0 170.8 170.0
30 215.5 212.0 210.5
45 304.6 310.9 307. 1
60 401.7 381.7 395.0
72 437.0 424.0 429.0

2 x 6 x 7%- 25 180.8 180.8 179.6
30 213. 1 225.0 218.0
45 313.8 317. l - 314.3
60 393.3 400.8 407.5
72 436.0 435.0 ' 452.0

 

50

TABLE 11

. Flow of shelled corn through a
1%- x 6 in orifice in steel chutes.

w

 

 

 

Flow of shelled corn through-a
2 x 6 in. orifice in steel chutes.

Chute Size Angle Flow Rates

(in x in x ft) . (deg) (lb/min)

1%x6 x1%- 25 104.1 108.2 110.9
30 138.9 141.8 141.2
45 193.1 195.0 191.7
60 238.0 238.5 234.0
72 254.3 256.0 257.1

1-5-x6x7-g- 25 101.8 107.7 110.0
30 132.2 139.9 132.8
45 182.9 182.5 180.4
60 224.0 225.0 223.0
72 254.4 236.4 243.8

TABLElZ

 

Chute Size ‘Angle - Flow Rates

((inx in xft) (dig) (lymin)

2x6x1i- 25 205.0 205.4 206.8
30 233.0 233.5 234.0
45 330.0 331.4 330.0
60 407.0 401.5 405.8
72 389.8 446.0 387.0

2 x 6 x 75- 25 186.7 183. 5 184.6
30 229.0 222.2 226.4
45 314.9 312.9 310.4
60 386.7 385.7 387.5
72 434.6 437.0 450.0

 

51

TABLE 1 3

Flow of shelled corn through a
3 x 6 in orifice in wood chutes.

 

 

 

 

Chute'Size Angle * Flow Rates
(in x in x ft) (dej) (lb/min)
3 x6 x7%- 25 375.8 383.3 1373.3
30 478.0 470. 0 478.0
45 725.0 676.7 681.3
60 982.5 1035. 0 1020.0
TABLE 14

Flow of shelled corn through a
3 x 6 in. orifice in steel chutes.

 

 

Chute Size Angle Flow Rates

(in x in x ft) (dej) (lb/min)

3 x 6 x71- . 25 400.8 426. 7 427.5
30 497.0 481.0 501.0

45 692.0 675.0 698.3

 

52

TABLE 15

Depths of shelled corn flowing at various
distances from the orifice in wood
chutes with an orifice 1%- x 6 in.

 

C orn Depths (in)

 

 

 

Chute Size Angle Chute Length
(in x in x ft) (deg) 2'in 6'in 2‘ft 5’ft 7*ﬁ
1%x6x7‘i- 25 .82 .64 .44 .43 .48
30 . 87 .66 .44 .43 .45
45 . 84 .67 .47 .44 .45
60 . 87 .65 .47 .47 --
TABLE 16

Depths of shelled corn flowing at various
distances from the orifice in steel
chutes with an orifice 1%- x 6 in.

Corn. Depths (in)

 

 

Chute Size Angle ' Chute‘Length ‘

(in x in x ft) (deg) 2 in 6 in 2 ft 5 ft (7%- ft

1%x6x7i- 25 .80 .63 .47 .43 .42
30 .77 .62 .45 .41 .39
45 .81 .62 .42 .42 .41
60 .82 .64 .44 .42 .43

 

53

TABLE 17

Depths of shelled corn flowing at various
distances from the orifice in wood
chutes with an orifice 2 x 6 in.

W

C orn Depths (in)

 

 

 

Chute Size Angle . Chute Length
(in x in x ft) (deg) 2 in 6 in 2 ft 5 ft 7%- ft
2x6x7;— 25 1.19 .93 .62 .49 .47
30 1.19 .94 .64 .49 .48
45 1.17 .88 .63 .50 .47
60 1.25 .96 .63 .49 .49
TABLE 18

Depths of shelled corn flowing at various
distances from the orifice in steel
chutes with an orifice 2 x 6 in.

 

Corn. Degths (in)

 

 

Chute Size. Angle Chute Length .

(in x in x ft) ‘ (deg) 2 in 6 in f 2 ft 5 ft 7%- ft

2x6x7-1; .25 1.18 .88 .60 .50 .47
30 1.16 .89 .61 .50 .49
45 1.17 .88 .59 .49 .48

60 1.18 .89 .59 .51 .50

 

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