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FLOW OF SHELLED CORN THROUGH
ORIFICES IN GRAIN BINS

by
DALE JOHN EWAL'I'

ABSTRACT

Submitted to the Colleges of Agriculture and Engineering of
Michigan State University of Agriculture and
Applied Science in partial fulfillment of
the requirements for the degree of

IMASTER OF SCIENCE
IN
AGRICULTURAL ENGINEERING

Department of Agricultural Engineering

Approval \Ef'21V/ (ji/‘tél/éﬁ:b¢1’

 

ABSTRACT

The design of materials handling systems could be greatly improved
if more data were available that accurately described the flow of grain
through an opening. This would allow engineers to better design bins as
a part of a system that could be expected to operate independently as
desired. Such systems would be a definite aid in grain storage.

A review of literature revealed that some work had been done in the
area of semi—fluid flow. Stahl (1950) advanced some equations based on
work done with wheat which indicated that flow was proportional to the
cube of the diameter of an opening and independent of the head. He also
indicated that the flow from a vertical orifice was one-third that from
a horizontal opening. Other investigators agreed that a logarithmic
relationship would describe grain flow and that flow was prOportional to
some function of the diameter of the discharge orifice. -

The purpose of this work was first to develop a test procedure
utilizing suitable equipment so that the flow rates of various grains
could be accurately measured. Next, the effect of a sloping bottom in
the bin would be studied. Finally, orifices of different sizes and
shapes would be used to test their effect on the flow rate of corn, the
grain selected for this investigation.

The necessary apparatus was constructed and was basically of two
parts: a stationary hopper with sides and bottom that could be easily
adjusted and a movable bin and scale. The hin.could be elevated so that
the corn could be dumped into the hopper. It could then be lowered to

receive the grain as it discharged through the various openings placed in

DALE JOHN EWALT

the stationary hopper. The flow rates of the corn were measured by
opening the orifice for a certain timed increment and then weighing the
discharged corn. An adjustable orifice was used so that an aperture of
any size up to six inches square could be Obtained. Round orifices
could be inserted for testing.

The initial portion of the investigation to test the effect that a
sloping bottom had on the flow rate of the corn indicated that the flow
rate of the corn increased slightly as the slope of the bottom increased.
This was true as long as funnel flow was present.

The remainder of the research endeavor involved the determination
of equations describing the flow of grain through horizontal and verti-
cal openings. Orifices were of different sizes and shapes. The corn
used in the experiments was shelled, yellow dent with a moisture content
ranging from 8.0% db to 12.72% db. The results indicated that the flow
rate of corn through a horizontal orifice was faster than that through a
vertical opening for a given size. From the data collected, equations
were developed to describe the flow of the shelled corn through the cir-
cular and the rectangular orifices placed in the bin bottom and side.
These equations had a maximum standard error of difference of i 3.2h%
when compared to the experimental data.

The head did not have an effect on the flow rate of the corn. It
was noted, however, that the flow rate of the corn decreased as the
moisture content of the corn increased. Thus, the moisture content of
the corn appeared to influence its flow rate.

Nb simple correlation could be found between the flow through the

horizontal and vertical openings. The contentiOn by Stahl that a certain

DALE JOHN EWALT

ratio existed between the flow through the two openings could not be
substantiated. In fact, the flow rate through the vertical openings
was found to vary from 30% to 50% of that through the horizontal open-
ings. The area of the orifice did not seem to directly determine the
flow characteristics for a rectangular opening. This result was also

in opposition to Stahl's findings.

FLOW OF SHELLED CORN'THROUGH
ORIFICES IN GRAIN BINS

by
DALE JOHN EWALT

A THESIS

Submitted to the Colleges of Agriculture and Engineering of
Ndchigan State University of Agriculture and
Applied Science in.partial fulfillment of
the requirements for the degree of‘

IMASTER OF SCIENCE

IN
AGRICULTURAL ENGINEERING

Department of Agricultural Engineering

é 5.0005
“7/7/(0‘1‘

ACKNOWLEIGMENTS

The author wishes to acknowledge gratefully the inspiring guidance
and many helpful suggestions contributed by Doctor F. H. Buelow, under
whose direction and constant supervision this research.was undertaken.

He also wishes to thank the other members of the guidance committee,
Doctor ll. 1.. Benny and Mr. D. J. Renwick, for their suggestions and guid-
ance in the preparation of this thesis.

The writer appreciates the efforts of Doctor A. W} Farrell, Head of
the Agricultural Engineering Department, for his interest in the investi-
gation and for obtaining financial support for the project. I

Grateful acknowledgment is due Doctor C.‘H. Hall for his guidance
during the investigations.

Sincere thanks go to.Mrs. Patricia Anderson for having typed this
manuscript and to the writer's wife, Mrs. Judith Envelt, for her patience,
assistance and encouragement.

The author also recognizes the contributions of the following: Fun
J. B. Cawood, mechanical technician, for his assistance in constructing
the test equipment; and all the other people who contributed of their

time and experience during the investigations.

TABLE OF CONTENTS

Page

INTRODUCTION......... ........ . ........... . ........... .............. 1
REVIEW OF LITERATURE. ................. .. ........................... 3
APPARATUS ................................... . ...................... 1h
METHOD OF PROCEDURE{ ......... . ..................... ... . . . . . l7
Sloping Bottom.. ......... ..................................... 1?
Horizontal Openings (openings in the bottom of a bin). ........ 19

Vertical Openings (openings in the side of the bin)........... 22
MYSIS w MTAOO0.00000..OOIOOOOOOOOOOOOOOOOO00.00000...000...... 2h

Results of Tests with Sloping Bin Bottoms....... .............. 2h
Results of Tests with Horizontal Openings in Bins............. 26
Romandsquare orificeBOOO0.00000000000000.0000...00000.0 26

Ream orificeBOOOOOOOOOO0.00.0..OOOOOOOOOOOOOOOOOOOOO 31
Results of Tests with vertical Openings in Bins............... 39

Round and square orifices ......... .....................:... 39

Rectangular orifices..... ...... ...................;........ Rh
WY...” ................................... ............ . 50
CONCLUSIONS ............. .......... ............. .... ..... .. ......... 53
RECWDATIONS FOR FURTHER STUDY .......... . ..... . .............. . . . 56
REFERENCES...... .................................. . ....... ... ...... 57
REFERENCES NOT CITED .................................. .... .. ...... S9
APPENDTXA .............. . ............ .. .................. 60

10.

11.

13.

1h.

15.

16.

LIST OF FIGURES

Page

An overall view of the apparatus showing the stationary

hopper above the movable bin......................... ........... 16

The movable bin in position to dump the corn into the hOpper.... 16

A view of the stationary hopper with the bottom at a 30°

angle with the horizontal.................... ..... . ............. 18

A view of the frame showing the four adJustable slats

forming a 3-inch long and 1-inch wide orifice.. ................. 20

The equipment in position prior to taking measurements on the

flow of corn through a horizontal opening....... ...... . ......... 23

The equipment in position prior to taking measurements on the

flow of corn through a vertical opening........ ..... ... ......... 23

weight discharged versus time for corn.flowing through an

orifice placed in a bin with a sloping bottom.. ................. 25
.-Flow'rate of corn through a round and a square orifice posi-

tioned horizontally and vertically in a hin........... .......... 27

Logarithmic plot of the flow of corn through a square and

round orifice positioned horizontally in a bin... ............... 29‘

Actual flow rate of corn compared to the flow equation for a

round orifice positioned horizontally in a bin... ........ . ...... 30

Flow of corn through a rectangular orifice of a given length

and varying width with the orifice positioned horizontally in

abinOQOOIOOOOOOOOOOOO0.00.00.00.00.........OOOOOIOO 000000000000 35

Actual flow rate of corn compared to the flow equation for a

rectangular orifice positioned horizontally in a bin ............ 36

Logarithmic plot of the flow of corn through a round and

square orifice positioned vertically in a bin.... ............... ho

Actual flow rate of corn compared to the flow equation for a

round orifice positioned vertically in a bin...... .............. A2

Flow of corn through a rectangular orifice of a given length
and varying width'with the orifice positioned vertically in

a bin........................................................... #5

Actual flow rate of corn compared to the flow equation for a
rectangular orifice positioned vertically in a bin....... ....... A7

II.

III.

VII.

VIII.

XI.

XII.

XIII.

XIV.

LIST OF TABLES

Page
Summary of previous investigations on granular flow............ 13

A comparison of the actual flow data to that determined using
the derived flow equation for a round orifice positioned
horizontallyOOOO0.0000.0..OOOOOOOOOOOOOOOOOOO00...00.000.000.00. 32

A comparison of the actual flow data to that determined using
the derived flow equation for a rectangular orifice positioned
horizontalmOOOOOOOooo00.000000....00000000000000.00000.0.0.... 37

A comparison of the actual flow data touthat determined using
the derived flow equation for a round orifice positioned ver-
tically000000.00.0.00000;0000000000000000000OOOOOOOOOOOOOOOOOOOO 1‘3

A comparison of the actual flow data to that determined using
the derived flow equation for a rectangular orifice positioned
mmmn-y‘p...OOOOOOOOOOOOOOOOOO0.000.0.0.00000000000000000000 “'8

Flow of corn through a bin.with a sloping bottom:.............. 61

Flow of corn through square apertures placed in the bottom of
a hopper...O0.0.0.000000000000000000000000000000000000IOOOOOOOO 62

Flow of corn through round apertures placed in the bottom of
a hopper.00000......0.00.0.........OOOOOOOOOOOOOOOOOOO0.6.0.00. 62

Flow of corn through rectangular apertures placed in the
bottom OfahopperOOOO0.000000000000000000000000000COOOOOOOOOOO 63

Flow of corn through square apertures placed in the bottom of
a hopper...I0.00.00.000.000.00000IOOOOOOOOOOOOOOIOOOOOOOOOO‘OOOO 61"

Flow of corn through rectangular apertures placed in the
bottom of a hopper............................... ..... . ........ 6h

Flow of corn through round apertures placed in the side of a
hopper.- 00000 .OOIOOOIOOOOOOOOOOOOOOO ...... 0000000000. 00000 0.00. 66

Flow of corn through square apertures placed in the side of a 66
binOOOOOOOOOOOOOOI0.00.0.0...I......... 00000000000000 000.00....

Flow of corn through a rectangular opening placed in the side
OfahopperOOOOOOOOOOOO 00000 0.0.0.0... ......... O ....... O ....... 67

INTRODUCTION

Many engineers today are concerned with the design of adequate
handling-systems for grain. The thousands of tons of cereal crops that
must be moved annually from fields through storage to final milling or
feeding operations present a huge problem. This handling must be mecha-
nized at all steps to make any system economical.

Every design is based on calculations using equations and parameters
that describe the characteristics of various phases of a system. Tb-date,
little information is available which will describe the flow of grain
through an opening. The few equations that have been developed are not
satisfactory as they are either unreliable or not applicable for many
problems.

Shelled corn is one of the most widely-used grains in the world.
This crop was chosen to be used in this initial phase of the research.
Previous investigators had advanced opinions regarding the factors which
influenced the flow rate of grain. The variable most often mentioned was
the size and shape of the discharge orifice.

The objectives of the research then evolved into the following:
first, a method of testing and suitable equipment was to be developed to
test the flow characteristics of the corn; next, the effect of a sloping
bottom in the bin was to be studied; and finally, orifices of different
sizes and shape were to be used to test their effect on the flow rate of
the corn. Equations were to be developed to describe the flow rate and
were to be kept as simple as possible.

Once the data had been collected, comparisons could be made between

the information previously available and that determined through the

2

research. Such a process would aid in determining which lines of
endeavor seem to have the most promise toward eventually solving the

prdblem of how grain flows through orifices.

REVIEW OF LITERATURE

An increased interest has developed in the flow of semi-fluids in
the past few years. More investigators are attempting to determine the
primary factors affecting this type of flow. Such activity has produced
a number of relationships describing these controlling factors. All
provide a basis upon which to continue the investigation of semi-fluid
flow. Grain is classified as a semi-fluid: thus, this prior information
can be of considerable aid in determining relationships describing grain
flow.

Semi-fluids have flow characteristics which are difficult to pre-
di ct. Hinehley (1926) made the general comment that the peculiarity of
such materials was that their flow from an orifice was proportional to
the cube of the area of the orifice and was independent of the head.

As the following information'will indicate, there is one character-
istic upon which most investigators agree; that the flow is independent
of the head. This, in itself, distinguishes the flow of the semi-fluid
from that of the fluid.

Deming and Mehring (1929) studied the flow rate of a variety of
materials through an inverted truncated cone orifice. Their results indi-
cated that the flow rate varied.with a power of the orifice diameter and
was influenced by the size and apparent density of the particles, angle
of repose of the material, and the cone angle. Their equation was the
following:

M
Q . 2/ 1 E201 + (0.392+2.58 sin é.¢)( +0.130-0-151/U1]
Do 2'5 d “

Where:
= flow rate (hrs/ton)

tan G;'9 -;static angle of repose (degrees)
. orifice diameter (ft)
= particle diameter (ft)

a cone angle (degrees)

I density of the material (lbs/ft3)

This equation was found applicable for cone angles up to (77 -2cx),
where 0( was the angle of repose. As noted, the relationship contains no
reference to head. The equation was develOped for-various kinds of fer-
tilizer, lead shot, glass beads, and some varieties of seed.

Ketchum (1929) published a book on the design of bins. It was the
first comprehensive study devoted primarily to the design of grain stor-
age structures. He and Willis Whited had worked together in l9ll and had
shown that the flow of wheat was independent of head and varied as the
cube of the orifice diameter. Using glass-sided bins, he advanced the
theory that the flow of solids was actually somewhat intermittent. This
was caused by the formation and collapse of domes or bridges formed by
the mass of grain as it moved through the bin during discharge. With a
centrally located bottom orifice, grain from the center of the bin dis-
charged first while grain from the lowest part of the dome discharged
last.

work was also done by Ketchum on the pressures involved in storage

‘bins. thh variation was apparent depending upon different conditions.

In general, the ratio of lateral to vertical pressures varied from 0.3 to
0.6.

Takahasi (l93h) studied the flow rate of many types of sand, shot,
vegetable-seeds and other fine products. He developed an empirical rela-

tionship as follows:

t 1:2: 1.02.35 E912)+.(§§]

Where:
t = time for a certain flow (min/ft3)

a,b = constants depending on the system of units used
g = gravitational acceleration (ft/seca)

fﬁub)= Tan 0 3 0 - kinetic angle of repose (degrees)
Db = orifice diameter (inches)

Up = particle diameter (inches)

No comparisons with experimental data were cited.

During the next decade, little work was done on the exploration of
semi-fluid flow as it might relate to grain. newton, et a1. (l9hS), did
publish a general equation for semi-fluid flow which had been developed 1
for the flow of catalyst pellets. For pellets 0.1 to 0.2 inches in diam-
eter, the mathum flow rate through a horizontal orifice in a flat-bottomed

container was given as:

w = 8.50 D3'96 39'0“

Where:
w a flow rate (lbs/min)

H - ft (head)

D = orifice diameter (inches)

6

Newton felt the equation was valid as long as the diameter of the
orifice was greater than 6 times the particle diameter. Here again, the
flow was seen to be very nearly proportional to the cube of the orifice
diameter and little affected by head. It was the most simplified relay
tionship developed for semi-fluid flow apparent at the time.

Stahl (1950) develOped equations which applied exclusively to grain.
His relationships appeared to be based upon experimental data published ?l**
by Willis Whited in 1901 and subsequently printed in a technical bulletin

published by the American‘Society of Agricultural Engineers (l9h8). The r J

 

equations were for the flow of wheat through horizontal openings and.were

given as follows:

Circular Orifices: Q I 0.1753 D3

Rectangular Orifices: Q . 0.2232 W2L

Q 8 flow rate (bu/min)

D = diameter (inches)

w = width (inches)

L = length (inches) where L 2 W

The equation for flow through the rectangular orifice appears to be
based solely on the area ratio between a circular and square opening
where D = W. However, no experimental curves could be found to confirm
the rectangular relationship such as had been used to develop the equa-
tion for flow through the round orifice. Stahl also stated that the flow
through vertical openings was one-third the rate through horizontal aper-
tures. This statement seemed somewhat dubious as it appeared to be based
only on the premise that a ratio of approximately one-third exists be-

tween the ratio of lateral to vertical pressures in a bin.

luring the 1950's the work involving the theoretical explanation of
semi-fluid flow seemed to gain impetus. Jenike (1951; ), at the University
of Utah, began formulating a theory regarding the effect that the com-
paction of the grain had on its flow characteristics. He advanced the
following hypothesis: As a hopper opened, the material above the gate
began to discharge. Stresses within the grain were immediately redis-
tributed. An arching effect developed much like the dome effect de-
scribed by Ketchum. If the pressures in the arch were higher than the
strength the material had built up between the interlocking particles of
grain during filling and after settling, the arch would break down and
flow would continue. If the pressures in the arch were lower at some
levels, the material would not flow and an obstruction called "doming"
would result. Also, as flow occurred, more compact material would
appear. Occasionally, only the core would empty out and an obstruction‘
would develop. This phenomenon Jenike called "funnelling." Jenike
(1960) is still continuing his work on this theory of compaction.

Barre (1958) further described the process of emptying. The column
above the discharge opening leaves first and gradually widens as dis-
charge continues. All grain moves through the core described by Jenike
until the hopper has been emptied by literally turning itself inside
out. This Barre designated as "funnel flow." In hoppers with very steep
sides, the whole mess of grain.may flow simultaneously including other-
wise stationary material in the hopper. The flowing core increases in
diameter until it includes all the grain in the hopper. This is referred
to as "mass flow." This explanation by Barre regarding flow was also

substantiated by Anderson and Alcock (l9sh).

 

8

Franklin and Johanson (1955) derived a flow equation for a circular
orifice using glass beads, lead shot, cracking catalyst, and puffed rice
with particle sizes of 0.03 to 0.2 inches, product densities of 7.3 to
676 pounds per cubic foot and orifice diameters of 0.236 to 2.28 inches.
Their equation for a horizontal orifice was:

A 132-93
.W = Ps ,
T672091?- 23.16)Id +1.8897‘T- .9

 

Where:
flow rate (lbs/min)

I:
:0

Pa true density of the solid (lbs/ft3)

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

‘2

diameter of a circular orifice (inches)

U
0:

average screen size of particles (inches)

9.»
II

An accuracy of 127% was found by Franklin and thanson when the theoret-
ical and experimental data was correlated. A relation was also derived

for determining the flow rate of an inclined orifice:

 

W9 = W0 cosod +cos O
cosce,4-1
Where:
W9 I discharge rate through an inclined orifice (lbs/min)
0 = inclination of the orifice to the horizontal (degrees)

OK I kinetic angle of repose (degrees)

, The following factors were found by Franklin to influence the flow
rate:

1) A ratio of orifice diameter to particle diameter less than 5.

9

2) A ratio less than 6 to 3 between the diameter of the cylindrical
storage bin and the particle diameter.
3) A grain depth in the cylindrical bin less than one bin diameter.
Brown and Richards (1959) made a study of the flow of glass beads,
rounded yellow sand, and sharp grey sand through orifices and developed
the following equations for these materials having a specific gravity of

approximate 1y 2 .5 :

Rectangular Orifices: Q = 2.72 A 11%?

 

Circular Orifices: Q = 2.2h D25?
Where:

' Q = flow rate (grams/sec)

A = area of orifice (cm2)

H = perimetral diameter (’4 x area of orifice )cm

perimeter
LP = .21. (dimensionless unit) '
gHET
e . Q
V velocity of flow (cm/sec) W
g = acceleration of gravity (cm/sec)

' density of material (gr/cc)

{5/5

diameter of orifice (cm)

If (Pwas taken as 0.3, the accuracy for the equations was about
150%. The equations were limited to dry materials of a narrow range of
sizes and to values of D/P (D I diameter of a circular orifice in cm,

P - mean particle diameter in cm) of the order of 20 to 30.

Contrary to Jenike's theory, their experiments indicated that the
flow rate was independent of the tightness of the initial packing.

Flow from narrow vessels was influenced not only by friction at the

10

walls but by the interlocking of particles owing to the proximity of the
walls. Other comments made were:

1) Fine particles discharged more rapidly than coarse particles.

2) Spherical particles flowed more quickly than angular particles
(larger spheres discharged at about the same rate as the smaller
angular particles).

3) For orifices of the same area, a rectangular orifice discharged
at about the same rate as an elliptical orifice but both were
appreciabky slower than the flow from a circular orifice.

Fowler and Glastonbury (1959) used dimensional analysis to produce

the following equation for the flow of sand, rape seed, rice, wheat, and

sugar through orifices:

Where:

= shape factor

5:
It

weight discharged per unit time (lbs/sec)

(is

bulk density of packing (lbs/ft3)

g = gravitational constant (ft/sec?)
Dh = hydraulic or perimetral diameter (inches)
= “x2222
perimeter of orifice
d3 = mean particle size (inches)

Their accuracy was 110%. They further found the following to be true:
1) The influence of the head was small and could be ignored.

2) There was a slight variation of flow rate with bulk density.

 

ll

3) Bridging and erratic flow occurred with ratios of Dh/ds approach-
ing A to 6.

h) In large vessels, the influence of the container dimensions was
negligible (ratio of diameter of container to spherical diameter
of particles).

Dimensional analysis was used again by Rose and Tanaka (1959).

Their equation was very complicated and will only be mentioned as exist- ‘
ing here. They also produced a curve which could be used to compute
discharge rates for openings other than those that were circular. Some
soil mechanics theory was utilized in their analysis. Their results
indicated 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 of the materials and proportional to DB-S (D = the ori—
‘fice diameter). Flow was also independent of the nature of material,
provided the particle shapes were substantially similar. Their experi-
ments involved steel balls, silica sand, steel disks, and some ferti-
lizers. Bridging was noted when the minimum dimension of the opening
was approximately equal to 3 particle diameters.

Further work on the formation of the flow lines was advanced by
O'Callaghan (1960). He contended that the rupture line between the
stationary and moving grain in a bin could be represented by a logarith-
mic spiral. Inclining the hopper sides at the approach to the discharge
orifice did not alter the general shape of the rupture line from that
which developed in a flat-bottomed container.

Welschof (1961) also developed some equations for the flow of cats,
wheat,granular fertilizer, and sand through circular and rectangular

orifices. The accuracy of these relationships was dependent on whether

12

the physical properties of the material being measured remained con-
stant. Results were again good except when the ratio of the orifice
diameter to the grain diameter became small. In his equation, welschof
used the coefficient of discharge, angle of internal friction, bulk den-
sity, and a constant which took into consideration the constriction of
the orifice caused by grainstuff passing through. He advanced a set of
equations, each of which was dependent upon the shape of the opening.

These equations were hard to use,as they required the measurement of

 

physical properties which, in themselves, would be difficult to obtain.

Although the literature review produced some equations for semi-
fluid flow, there was considerable discrepancy between the relation-
ships. Many of the references indicated that the flow rate was a func-
tion of the diameter of the orifice. .Most equations were considered
valid only above a certain minimum ratio of D/dk (D I orifice diameter,
dk = particle diameter).

Basically, the flow equations determined by various investigators
are of the form Q = K Dn'where K is dependent upon the physical proper-
ties of the material being tested. The values of n and the limiting
values of D/dk as suggested by these researchers are sunnnarized in Table
I. The materials used in each investigator's work are also listed. As
noted, no general agreement exists between investigators regarding the

effect of the orifice on the flow rate or the limiting ratio of D/dk.

13

TABLE I

Summary of previous investigations

on granular flow.

 

 

 

n(Power
Investigator Materials of D) D/dk
Deming, Mchring (1929) Fertilizer, lead shot , 2.50 .-
glass beads, seed
Takahasi (193%) Sand, shot, and vegetable 2.50 -
seeds
Newton, et a1. (1915) Catalyst pellets 2.96 6
Rausch (l9h9) ------------------------ 2.80 -
Stahl (1950) wheat 3.00 -
Franklin, Johanson (1955) Glass beads, lead shot, 2.93 5
cracking catalyst, puffed
rice
Brown, Richards (1959) Glass beads, sand 2.50 -
Rose, Tanaka (1959) Steel balls, sand, fertilizer 2.50 3
Fowler, Glastonbury (1959) Sand, rape seed, rice wheat, ---- h-6
sugar
Oats, wheat, fertilizer, sand ---- h

twelschof (1961)

 

 

APPARATUS

In constructing the equipment to be used in the experimental
studies on grain flow, the primary concern was flexability. Different
variables were to be used in the testing, primarily different opening
sizes. The apparatus wOuld be most effective by making it as portable
and adjustable as possible. With these conditions in mind the equip-
ment in Figure l was designed. It was constructed principally for mea-
suring the flow rates of grain through orifices.

The apparatus was composed of two major parts: the stationary
hopper in which the grain was retained until the testing was accomplished
and a movable bin. The hopper was fastened together with bolts to facil-
itate making changes. The bottom of the hopper was held in place by
clamps and had a hinged door attached to one end. It was possible to
elevate one end of this bottom board to provide a certain slope. The
hopper was composed of é-inch,p1ywood; its frame was made of 2ux hustock.
The hopper had the following interior dimensions: h8 inches high, 12
inches wide, and 2h inches deep.

Tb facilitate taking weight measurements, the apparatus was con-
structed so that the hopper was 5 feet off the floor. This allowed a set
of scales to stand beneath the hopper. Balance beam Toledo scales
mounted on a movable platform and with a capacity of 200 pounds were used
in the tests. With these scales, it was possible to read weights to the
nearest 1/8 pound.

The height of the hopper also allowed the addition of the movable
bin. Arms were attached to the main frame of the equipment and pivoted

(an the frame at a point 9h inches above the floor. The arms were

15

connected to a winch. powered by a g horsepower lhster gearhead electric
motor. This provided a mechanical means of elevating the bin above the
War as shown in Figure ,2, dumping the corn, and then lowering the bin
back to the scales. A double-pole, triple throw switch was used to con-
trol the motor for raising and lowering the bin.

,The hopper held approximately 200 pounds of corn, while the bin held
Just less than 200 pounds. ’

Battles were placed in the corners of the front of the movable bin
so that more complete emptying of the bin would occur. A latch on the
bin door was operated from the floor by a cord. The moisture content of
the corn used in the tests was determined initially by using a Steinlite
capacitance type moisture meter. Later, an air oven was used for more
accurate moisture content measurements. The orifice was opened and

closed mnually. All runs were measured with a stop watch.

 

16

 

Fig. l - An overall view of the apparatus
showing the stationary hopper above
the movable bin.

 

Fig. 2 - The movable bin in position to
dump the corn into the hopper.

METHOD OF PROCEDURE

Cbrn used in the testing was secured from the university farms.
The corn had been harvested by a picker-sheller and was a yellow dent
variety of moisture content ranging from 8.h% db (dry basis) to 12.72%
db. The larger pieces of cob and other foreign material were removed
by screening. The corn was quite free of dirt and other foreign mate-
rials. Complete cleaning was not accomplished, as it was felt that this
would eliminate the essence of actual grain conditions from the testing.

Approximately 100 pounds of the corn was used at a time. It was

 

placed in the moveable bin and elevated above the hopper. The corn was
released at this point and allowed to flow into the hopper. The bin was
lowered back into position on the scales so that weight measurements
could be taken.‘ The elevating arms were disconnected from the bin so
that the bin could be weighed on the scales.
Slopigg Bottom

The first tests were to find what effects a sloping bottom had on
the flow rate of the grain. The bottom of the stationary hopper was not
nailed in place for these measurements. It was secured in position by
first tightening the bolts on one end of the frame bottom. Different
angles were then achieved by moving one end of the bottom up or down and
holding it in place with clamps. Figure 3 shows a sketch of the bin
with a 30o slope to the bottom. '

While testing, the level of the discharge end in the bottom of the
hopper was kept in the same position relative to the side of the hopper.
While changing the slope of the bottom, this end was not allowed to move

up or down. A carpenter's level, graduated so that it would indicate

18

 

 

 

 

 

-—-—- —-—-—-_ -——_-———-

      

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig. 3 - A view of the stationary hopper with the bottom at
a 300 angle with the horizontal.

19

degrees from the horizontal, was used each time the position or slope of
the bottom was changed. The level was set at the prescribed angle and
the bottom board moved until the bubble on the level was centered. Flow
rates were taken at 20°, 30°, hop, and 52.50.

The orifice was opened or closed by rapidly dropping or lifting the
swinging door. The corn was allowed to empty into the bin and the time
for discharge noted for each loepound interval up to 75 pounds. This
data of weight versus time was plotted for various bottom slopes. All
measurements‘were made with the orifice running full.

Horizontal gpeningg (openings in the bottom of the bin)

Once the initial tests involving the sloping bottoms were completed,
the bottom board was removed. A hole, slightly more than 6 inches square,
was cut in the center of the board. A frame was constructed of ﬁ-inch
plywood and bolted over the opening. Four slats made of the same mate-
rial were placed between.the frame and the bottom. Two slats were used
to regulate the width and two were to adJust the length. Wing nuts were
used on the bolts fastening the frame to the bottom to facilitate loosen-
ing the frame to change the aperture size. Two cross members of plywood
were placed on the frame to hold the sliding gate. A sketch of the
adjustable frame is shown in.Figure h. 'The gate was constructed of k-inch
plywood and.was moved manually. The bottom board was placed back into
position in the hopper and a carpenter's level used to assure that the
bottom was horizontal.

The following method was used to find the flow rate for the horizon-
tal openings. The elevation of the bin, filling of the hopper, and lower-

ing of the bin were accomplished as before. The bin was placed on the

2O

 

Fig. it - A view of the frame showing the four adjustable slats
forming a 3-inch long and l-inch wide orifice.

—‘

21

scales and pushed under the hopper. The bin was then weighed. Figure 5
shows theequipment as it appeared prior to taking tests on flow of corn
through a horizontal opening.

The sliding gate was opened for a certain increment of time and
the weight of the discharged corn recorded. The time intervals varied
from 25 seconds to 60 seconds. The runs were conducted so that flows
were measured at various corn depths. An average of 8 runs was made for
each opening size. The average weight recorded in these runs was used in
the calculations.

At some opening sizes, it was noted that a very small error in time
determination would result in a considerable weight error. It was de-
cided to take these runs for longer time periods to reduce this possible
error in time measurement. This procedure materially increased the appar-
ent accuracy of the data.

Runs were made on round, square and rectangular openings. The round
orifices were constructed from §~inch plywood and were of 8 diameter
sizes. The 1%, 2, 2%, 3, and 3% inch openings were made by using a hole
saw. The remaining h, h%, and 5 inch diameter holes were cut using an
expansion bit on an upright power drill.

The-square and rectangular orifices were produced by adjusting the
four slats in the frame and then clamping them in place. Runs were made
on square holes in sizes differing in é-inch increments and ranging from
1% inches up to 5 inches on a side.

Tests were made on the rectangular openings for lengths of 6, 5, h,
and 3 inches. The width was changed in g-inch increments from a value

equal to the length down to 1 inch. The width was always equal to or

22

less than the length. Measurements of the dimensions were made twice to
assure accuracy.
vertical gpenipgg (openings in the side of the bin)

In testing the vertical openings, a 6-inch square was cut in the
end of one side board. This made one side of the opening flush with the
bottom of the hopper. The same sliding gate arrangement was bolted to
the side with a slight modification made to the lower part of the frame
to allow for tightening the gate. This outlet side was fixed in position
using a carpenter's level to assure a vertical orientation.

Flow rates for vertical openings were determined using the same test
procedure and orifice sizes as were described for the horizontal open-
ings. The one exception was that the scales were not moved beneath the
hopper, but remained forward under the side opening. Figure 6 shows the

equipment prior to taking tests on the flow of corn through a vertical

QPeninS-

.;;_;3""

 

A
J
J

 

g. 5 - The equipment in position prior
to taking measurements on the flow of

corn through a horizontal Opening.

 

Fig. 6 - The equipment in position prior
to taking measurements on the flow of
corn through a vertical opening.

ANALYSIS W DATA

Results of Tests with SlopingﬁBin Bottoms

Tests were run to determine the effect a sloping bin bottom would
have on an orifice of a given size. Sielled, yellow dent corn of mois-
ttu'e content 11.5% db (dry basis) to 9.2% db was used. The flow meas-
urements were made using a l" x 12" orifice with a bottom slope of
20°, 30°, #00, and 52.50 from the horizontal. All tests were made with
the entire bottom sloping toward an opening in the bottom side of the
bin.

These tests indicated that the flow rate of the corn increased
slightly with an increase in the slope of the bottom. This was true as
long as the flow was funnel, flow. At 52.50 the corn movement was mass

flow and, as shown in Figure 7, the rate was slightly below the flow

-. rate for hOO.

An additional series of tests were made to determine the effect of
head on flow rate. The same size orifice as before and a bottom slope
of 30° were used. The corn was first dumped into the. stationary hop-
per. It was raked back manually on the top so that the depth of grain
above the opening was a minimum. The corn was then in funnel flow posi-
tion. The orifice was opened and flow measurements taken at lO-pound
intervals up to a total of 70 pounds. Next , the corn was dumped into
the stationary hopper and allowed to remain as it fell. The depth of
grain above the opening was greater in the second case than in the
first. The orifice‘was opened and flow measurements were taken at 10-
pound intervals up to a total of 70 pounds. An average of 3 tests was

taken for each lO-pound interval in both cases.

WEIGHT DISCHARGED (LBS)

9O

80

70

6o

50

#0

3O

2O

10

25

 

boo
” 525°
/3o°
,/ 20°
' M.C. = 11.5% db - 9.2% db //
- /
/
/
’ /
/
~ /
- ‘/
/

 

2 h 6 8 10 12 1h 16
TIME (sscorms)

Fig. 7 - Weight discharged versus time for corn
flowing through an orifice placed in a bin with
a leping bottom.

26

Upon comparing the flow measurements for the two situations, no
difference was found between the emptying rates. These results sub-
stantiate the finding of other researchers that head has no effect on
the flow rate of grain.

From the results of this investigation of bins with sloping bottoms,
it appeared that the flow rate of corn was slightly larger at greater
bottom slopes. Thus, the slope of the bottom of a bin had a slight

effect on the discharge rate of corn.
Results of Tests with Rbrizontal Openings in Bins

The high flow rates of the corn through the horizontal openings
affected the accuracy and consistency of the test data. Small errors in
either the measurement of time or size of opening caused a large varia-
tion in the determination of the corn flow rate through the orifice.

All of the available information on work comparable to the tests
conducted indicated that a logarithmic relationship would describe the
flow of a semi-fluid through an orifice. The flow also was found to be
proportional to some power of the diameter. Since grain is a semi-
fluid, these results should have some validity.

The raw data used for deriving the equations for flow through a
horizontal opening are found in Tables VII-XI, Appendix A.

Round and Square Orifices

Runs were first made on square and round openings. The data were
then plotted on rectangular coordinate paper as shown in Figure 8. Pre-
vious investigators had found that a logarithmic relationship would

describe the flow of grain through an orifice. Therefore, the data were

Q (bu/min)

2’4.

22

2O

18

16

1h

10

27

X/ Horizontal Orifices
M.C. = 12.1% db
. .1
- x

0 Circular Orifices
x Square Orifices
e
'-
/ / Vertical Orifices
' X
e / 14.0. = 12.72% db
/ /

 

 

- o
/ /
K /@
_ / /
/xf/°
Q / O
' /
I ’f’ 1 I l I
1 2 3 h 5 6

DIAMETER 0R more cs SIDE (moses)

Fig. 8 - Flow rate of corn through a round and a square
orifice positioned horizontally and vertically in a bin.

28

next plotted on log-log paper and a straight line resulted, as shown in
Figure 9.
The equations, therefore, were of the following form:

For a square orifice:

q - K‘Wn

Where:
Q

W'

flow rate of corn (bu/min)

width of orifice (inches)

K, n8 constants

For a round orifice:

KDn

D
I:

Where : -
diameter of orifice (inches)

U
II

The unknowns K and n were determined by simultaneously solving two equa-
tions. The resulting equation for the flow of shelled, yellow dent corn
of moisture content 8.h$ db through a square orifice in the bottom of a

bin is:
Q - 0.1755 w3°°1

The flow of the same corn through a circular orifice was found similarly

to be:
Q = 0.1196 DB-lo

A comparison of the actual data to that determined using the derived

flow equation was made for the round orifice. As shown in.Figure 1o,

Q (bu/min)

100

80
7o
60

50
ho

30

20

4:" U'I QQCDWO

29

 

 

 

I
‘ ILC. =
‘MLC. 8
F- e Square Orifice /n.c. -
3: Round drifice
0/
,.. G
/
s /
c9/
/
1 2 3 h 5 #6 '7 8 910

DIAMETER on mom or SID! (In)

Fig. 9 - Logarithmic.plot of the flow of corn
through a square and round orifice positioned
horizontally in a bin.

8.h% db
12.10% db
8.15 db

 

3O

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no 36 n 6.2 -
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SI CD \0
(aw/not) t

S!

 

31

the equation proved quite accurate. Table II shows that the maximum
difference between the equation and the data is h.06%‘with a standard
deviation of difference of t 2.75%. The equation for the square opening
is discussed as part of the development of an equation for the flow of
corn through a rectangular orifice.

.ﬁggtgggular Orifices

The relationship describing the flow through a rectangular orifice

 

was determined by making runs using orifices of lengths 6, 5, h, and 3
inches. The width of the orifice was varied by é-inch increments from
1 inch up to a value equal to the length. .A plot of these data on rec-
tangular coordinate paper indicated a possible logarithmic relationship.
However, in presenting the information on log-log paper by plotting the
flow rate versus the width, slightly curved lines resulted.

Several methods were attempted in order to describe the curved lines
mathematically. All lacked reasonable accuracy and it appeared that a
new approach to a solution was required. It was observed that for rec-
tangular openings with a constant ratio of W/L, the flow rate varied
approximately as W3. According to this relationship, the flow rate then
varied as Al'5 where A is the area of the orifice (ing). Therefore, the
data were plotted on a graph using Q/A1°S as the ordinate and W/L as the
abscissa. The first representation of the data in this fashion gave very
inconsistent results. Runs were made on the vertical openings to provide
some clue regarding the rectangular relationship. (vertical openings
will be discussed later.) The data for the vertical openings produced a
definite family of curves with each curve representing a different orifice

length. Since the initial tests on the rectangular orifices positioned

32

TABLE II

A comparison of the actual flow data to that determined
using the derived flow equation for a round orifice
positioned horizontally.

 

 

 

 

Diameter Q (From Equation) Q (Actual) Per Cent
[inches ) (btdmin) (buLm_in_) Difference
1.5 0.h2 0.12. +3.22
2.0 1.03 0.99 - h.06
2.5 2.06 2.02 I - 1.98
3.0 3.58 3.73 + h.02
3.5 5.80 5.90 + 1.70
14.0 8.78 8.95 +-l.90
h.5 12.68 12.1w — 2.26
5.0 17.15 17.20 - 1.1.5

 

33

horizontally did not give shmilar results, the tests were re-run. Also,
the flow rates were high during the first tests and the timed intervals
had been necessarily small, many being only 2.5 seconds in duration. An
error of only 0.2 seconds here would result in an 8% error in time meas-
urement. To alleviate this discrepancy during the second tests, some
runs were taken over longer periods of time. This new technique greatly
improved the accuracy of the data.

In.plotting the second set of data (Table XI, Appendix A) using
Q/Al'5 versus W/L, a smooth family of curves resulted. This indicated
that both the width and the length had some non-linear effect upon the
flow rate.

As the square is simply a special case of the rectangle, it was evi-
dent that any equation describing the flow through a rectangular orifice
would also have to be valid for the square orifice. The square aperture
had already been described by a logarithmic relationship. Thus, the

equation for the rectangular orifices seemed likely to be of the form:

Q = xzwm Ln

Where:
Q = flow rate of corn (bu/min)
‘W = width of the orifice (inches)
L a length of the orifice (inches)
K,m,n = constants
‘W SE L

Furthermore, when the width equalled the length, as in the square, m.tn
would have to be equal to the coefficient of W'as determined for the
square orifice. This was necessary, as the equation for rectangular

orifices must be valid for the square orifices.

31+

Since a new set of data had been obtained from corn of different
moisture content, a new relationship was first obtained for the square
orifices. The data were plotted as before on log-log paper, as shown in
Figure 9. Points were selected and the necessary mathematics carried
out to solve for K, m and n. The resulting equations for shelled, yellow
dent corn of moisture content 12.1% db flowing through a square orifice

placed in the bottom of a bin follows:
Q = 0.15h1 w3'01

Three sets of points were next chosen from the data plotted in
Figure 11. The sets of data selected were those falling on the curves
representing various orifice lengths. The points yielded three equations
in three unknowns. These equations were solved simultaneously and the
following relationship resulted for rectangular orifices in the bottom

of a bin for shelled, yellow dent corn.of moisture content 12.1% db:

The constant K was found to be nearly equal to that for the square
orifices and m-rn was approximately equal to 3.01. Thus, this relation-
ship can be used to describe the flow through the square openings.

A comparison of the actual data to that determined using the derived
flow equation was made for the rectangular orifices. As shown in.Figure
12, the equation is quite accurate. Table III shows that the maximum
difference between the equation and the data is h.39$ with a standard
deviation of difference of't 1.83% for all widths greater than 1.5

inches.

 

Q (bu/min)

2O

18

16

in

10

35

r- L ... 6" ’L . 5"
x1

M.C. = 12.1% db

K\
°\\",\

 

l l l l I

2 3 h 5 6
WIDTH (INCHES)

Fig. 11 - Flow of corn through a rectangular orifice
of a given length and varying width with the orifice
positioned horizontally in a bin.

 

a (bu/min)

2O

18

16

1h

10

36

 

0.15311 "1.62Ll.h0

12.1% db

?‘
'5’
ll

 

 

  

L 1 n l i i I
20 ho 60 80 100 120 11.0

w1°62L1'l‘° (w a. L mm IN ments)

Fig. 12 - Actual flow rate of corn compared to the flow
equation for a rectangular orifice positioned horizontally
in a bin.

37

TABLE III

A comparison of the actual flow data to that determined
using the derived flow equation for a rectangular orifice
positioned horizontally.

 

k _

Size

 

1. x w Q (Flow Equation) 2 (Actual) Per Cent
(inches ) (by min ) ' (bu/ min ) Difference
6 x 1.0 1.88 1.31 - h3.30
1.5 3.6a 3.22 .+ 12.30
2.0 5.80 5.7h - 1.05
2.5 8.3% 8.56 .+ 2.57
3.0 11.20 11.72 + h.39
3.5 1h.3h 1h.8h .. 3.36
h.0 17.81 18.61 +. h.29
5 x 1.0 1.h6 1.01 - h5.oo
1.5 2.82 2.h6 - 1h.62
2.0 u.ue u.h3 - 1.13
2.5 6.h5 6.61 + 2.h2
3.0 8.66 8.87 -+ 2.36
3.5 11.11 ‘11.22 -+ 0.98
h.0 13.80 1h.1h + 2.h0
h.5 16.70 16.75 + 0.30
5.0 19.80 19.61 - 0.97
h x 1.0 1.06 0.80 - 32.50
1 o 5 2 o m l 0 9+ " 6 .20
2.0 3.28 3.23 - 1.55
2.5 h.72 h.76 + 0.8a
3.0 6.35 6.37 1 0.31
3.5 8.11 8.1h -+ 0.37
h.0 10.08 10.00 - 0.80
3 x 1.0 0.71 0.58 - 21.60
1.5 1.38 1.h0 -+ 1.h3
2.0 2.19 2.18 - 0.h6
2.5 3.17 3.13 - 1.27
3.0 h.22 n.2o - 0.u8

 

38

The accuracy found using the computed equations describing the flow
of corn through round and rectangular orifices seems very good, consider-
ing the equipment used. Also, the runs were made over a period of days.
Daring this time, temperatures fluctuated, the moisture content of the corn
varied, and the relative humidity of the ambient air changed. All these
factors could conceivably have an effect on the flow rate of the corn.

An indication of the effect the moisture content of the corn can have
is seen in the comparison of the two equations developed for the square

orifices . They were as follows:

4; 4' 0.1755 w3-01 11.0. - 8.1.; db
q . 0.15111 w3°°1 14.0. - 12.15 db

The moisture contents were computed using the air-oven procedure of dry-
ing. Figure 9 indicates that a change in moisture content will not affect
the slope of the flow equation, but will simply displace the relationship
8 by changing the constant. In this case, an increase in the moisture con-
tent of the corn of approximately 11% decreased the flow rate by 12%.

In another comparison of the effect a change in moisture content
has on flow, runs were made using an opening of 3/h" x. 12" and a bottom
slope of 20°. The moisture contents of the corn samples tested were
7.07% and 9.63% as measured on a Steinlite moisture meter. Here, the
decrease in flow rate was 8.7% for an increase in corn moisture content
of approximately 2.56%. These two comparisons indicated an approximate
decrease in flow rate of 3% for every 1% increase in moisture content.

It could not be definitely concluded that a ‘1inear relationship existed

 

39

between the decrease in product moisture content and the corresponding
increase in flow rate, however.

The achieved accuracy was quoted for widths greater than 1.5 inches.
An accuracy of 1.h3%'was obtained for an opening 3" x 1.5". This might
indicate that a certain ratio of W/L is actually a more proper limiting

value for the derived equations.
Results of Tests with vertical Openings in Bins

The same opening sizes and shapes as used for the horizontal open-
ings were used in testing orifices placed in the side of the bin. The
length of the orifice was made parallel to the bottom of the hopper.

The hopper bottom was flat throughout the testing.

Little information was available regarding the flow of corn through
vertical openings. Stahl (1950) did state that the flow of wheat through
a vertical opening was 1/3 the flow through a horizontal opening. Other
than this one individual, few investigators mentioned vertical orifices.
Square and Round Orifices

Runs were made initially on the square and round orifices. The
resulting data are shown on rectangular coordinate paper in Figure 8 com-
paring the flow rate versus the diameter and the length of a side. As
in the case of the horizontal openings, a logarithmic relationship was
assumed to describe the data. upon.plotting the information on log-log
paper, a straight line resulted for both shapes as shown in Figure 13.

The equations were of the following form:

Q (bu/min)

ho

0 Square Orifice
1: Round Orifice /
M.C. = 12.72% db

/.
2.0~ Q/
X

 

 

1.0

0.9-

0.8r

0.7-

0.6'

0.5+ 0

0.11%

0.3-

0.2- o

0.1 l I l l l l I l I
1 2 3 h 5 6 7 8 910

pm 0R LENGTH OF SIDE (IN’)

Fig. 13 - Logarithmic plot of the flow of corn
through a round and square orifice positioned
vertically in a bin.

111

For a square orifice:

Kw”

Q

Where:
flow rate of corn (bu/min)

Q
w - width of orifice (inches)

K, n8 constants
For a circular orifice:

Q = K D“
Where: 7
D = diameter of orifice (inches)
Two sets of points were chosen from each line and the equations
solved simultaneously for K and n. The following equation resulted for
the flow of shelled, yellow dent corn of moisture content 12.72% db

through a square orifice placed vertically in a bin:
Q 8 0.0523 W3'26

The equation developed for the same corn flowing through a circular ori-

fice positioned vertically was:
Q = 0.0351 D3'3O

A comparison was made between the actual flow rates of the corn and
the rates determined using the derived equation for flow through a circu-
lar orifice. As shown in Figure 1h, the relationship was found quite
valid. Thble IV shows that the maximum difference between the equation
and the data is h.h0% with a standard deviation of difference of r 2.31%-

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43

TABLE IV

A comparison of the actual flow data to that determined using

the derived flow equation for a round orifice

positioned vertically .

 

 

 

Diameter Q (Flow Equation) Q (Actual) Per Cent

(inches ) (b11131!) ) (bu/min) Difference
1.5 Bridging Occurred
2.0 0.35 0.3h - 0.87
2.5 0.72 0.72 + 0.00
3.0 1.32 1.31 - 0.76
3.5 2.18 2.11!- - 1.83
11.0 3.111 3.56 «141.110
1&5 5&2 11.91 - 2.19
5.0 7.05 7.26 + 2.98

 

 

uh

The equation for the square opening is discussed as part of the develop-

ment of an equation for the flow of corn through a rectangular orifice.

Begtaggular Orifices
The same procedure used in testing the flow rate through the hori-

 

zontally positioned rectangular orifices was used for testing the verti-
cal openings. All sizes were identical to those used in prior tests.

The information obtained produced a family of curves as shown in Figure
15. These curves were similar in appearance to those found for the ori-

fices positioned horizontally and were, therefore, of the form:

Q = x1wm LP

Where:
Q = flow rate of corn (bu/min)
W I width of orifice (inches)
L I length of orifice (inches)

K,m, n= constants

W S. IL

Three sets of points were chosen from the curves of Figure 15. The
resulting three equations were solved simultaneously for the unknowns K,
m and n. The final equation developed for the flow of yellow dent corn
of moisture content 12.72% db to 12.h% db through a rectangular orifice

placed in the side of a bin is then:

Q = 0.0528 w1'75LF'50

Q (bu/min)

1h

13

11

10

1*5

L=6"

r

11.0.: 12.72% db - 12.11% db

T I
X

 

 

.O‘l'

 

Fig. 15 - Flow of corn through a rectangular orifice
of a given length and varying width with the orifice
positioned vertically in a bin.

1+6

The constant is nearly equal to that found for the equation for square
orifices and m+n is approximately equal to 3.26. Thus, the equation is
applicable to square openings.

A comparison.was made between the actual flow rates of the corn and
those determined using the derived equation for the rectangular orifices.
As shown in Figure 16, the equation was quite valid. Table V'shows that
the maximum difference between the equation and the data is h.92%'with a
standard deviation of difference of f 3.2h% for all widths above 1.5
inches with the exception of two cases. These two sizes were both found
to be outside the best curves determined by plotting the original data.
Thus, it would seem that the experimental data for these two cases could
be in error.

In the derived equations for flow through vertical openings, the
powers of the width of the square orifice and the diameter of the circu-
lar orifice were quite similar. There was not much difference between
these same exponents for the relationships developed for the horizontal
openings. This would indicate a possibility that, for a ratio of W/L
equal to 1, the flow rate was dependent upon area. However, when a
ratio of areas was taken for a circle and square with the diameter of the
'circle equal to the side of the square, the following results were

obtained: .
Ratio of 8‘12”“? area - “2 - 1.272
circular area TT h

The ratio of the constants for the derived equations representing the

round and square orifices was.8;8§§% 3 l.h90. Thus, it appeared that a

factor other than area determined the flow characteristics_of the opening.

1+7

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Li
5:

an aim.” - as $8.8

cm. a me». 4: 3.8.0

 

 

OH

NH

1:

(um/M) a

48

MMEV

A comparison of the actual flow data to that determined
using the derived flow equation for a rectangular orifice

positibned vertically. .

 

 

Per Cent

Difference

Q (Actual)
(bu/min

(bu/min)

Q (Flow Equation)

Size
1.x W
<(inches)

 

more. who resume .

”Pug:— thtu. 52
...++++++

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012356803
11

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1.1223th5
1

6

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. . . .+.+. .

home room more

0012.45689

$m%%m%Wm%

.........

0112h5689

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112233.“..u5

x
5

2161.30
273198

001223.”

2 20 88
.u.%.h.1 77:

0.01223.“

11.2233.“

.....

 

l+9

Stahl (1950) stated that a ratio of l/3 existed between the flow
through a vertical orifice to that through a horizontal opening. It was
apparent from the relationships determined during these tests that no
similar ratio exists for corn. There is no direct correlation between
the powers describing the effect the length and width of the opening
have on the flow rates through the vertical and horizontal openings.
Thus, a ratio cannot be given which would allow the equation for the
horizontal openings to be used to calculate flow through the vertical
openings. Indeed, when the flow rates were compared for specifically
sized orifices, the ratio of vertical to horizontal flow ranged from
approximately 0.3 to 0.5.

The equations derived for the vertical openings were found for ori-
fices whose length was parallel to the bottom of the bin. Tbsts were
not made on the possible effect on flow that would result from making
the length perpendicular to the bottom of the hopper.

no definite tests were conducted to determine the ratio of the ori-
fice diameter to the mean particle diameter that would cause bridging.
It was noted, however, that bridging would occur when the minimum dimen-
sion of the orifice being tested was smaller than approximately 3 par-
ticle diameters. Since corn is not spherical, an actual dimension can-

not be given.

SUMMARY

The design of materials handling systems could be greatly improved
if more data were available to accurately describe the flow of grain
through an opening. This would allow the design of bins that could be
placed into a system and be expected to operate independently and as
desired. Such systems would be a definite aid in grain storage.

A review of literature revealed that some work had been done in the
area of semi-fluid flow pertaining to grain. Stahl (1950) produced some
equations based on work by Willis Whited indicating that flow was propor-
tional to the cube of the diameter of an opening and independent of the
head. He also indicated that the flow from a vertical orifice was one-
third that from a horizontal opening. Other investigators agreed that a
logarithmic relationship would describe grain flow and that flow was pro-
portional to the diameter of the discharge orifice. These derived equa-
tions for semi-fluid flow were very general in nature and required for
their solution a knowledge of certain physical properties difficult to
evaluate for grain.

The purpose of this work was to attempt to determine the relation-
ship between the flow rate of grain and the orifice size. The resulting
equations were to be of a simplified nature that would facilitate their
use. The findings of other investigators, principally Stahl, would be
evaluated as to their applicability to corn. The effect of a sloping
bottom on the flow rate was also studied.

Apparatus was used that had been constructed principally for this
work. The equipment was basically of two parts: a stationary hopper

with sides and bottom that could be easily adjusted and a movable bin.

51

The bin elevated the corn so that it could be dumped into the hopper.
It was then lowered to receive the grain as it discharged through the
various openings placed in the-stationary hopper. The flow rates of
grain were measured by opening the orifice for a certain timed increment
and weighing the discharged corn. An adjustable aperture was used so
that an orifice of any size up to six inches square could be obtained.
Round openings could also be inserted.

The effect of a sloping bottom on the flow rate was investigated
initially. The results indicated that the flow rate .of- the corn
increased slightly as the slope of the bottom increased. This was true
as long as funnel flow was present.

The majority of the work involved the determination of equations
describing the flow of grain through horizontal and vertical openings.
Orifices were of different sizes and shapes. The corn used in the exper-
iments was shelled,yellow dent with a moisture content ranging from
12.72% db to 8.0% db.

The results indicated that the flow rate through a horizontal ori-
fice was faster than that through a vertical opening for a given size.
Equations were developed to describe the flow of shelled corn through
circular and rectangular orifices in bin bottoms and sides.

These equations had a maximum standard error of difference of
£3.2hﬁlwhen compared to the experimental data. The head did not have an
effect on the flow rate of the grain. It was noted, however, that the
flow rate of the corn decreased as the corn moisture content increased.

Thus, the moisture content of the corn appeared to influence its flow

rate.

 

52

No correlation could be made between the flow through the horizontal
and vertical openings. Thus, the contention by Stahl that a certain
ratio existed between the flow through the two openings could not be sub-
stantiated. In fact, the flow rate through the vertical openings was
found to vary from 30% to 50% of that through the horizontal openings.
The area of the orifice did not seem to affect the flow characteristics
for a rectangular opening. This result was also in opposition to a find-
ing of Stahl's.

CONCLUSIONS

The results of this work have produced some equations that are
unique for corn. The derived relationships have been found to have a
maximum standard deviation of difference of t 3.2h$ when compared with
experimental measurements for widths greater than 1.5 inches. The
equations formulated for yellow dent, shelled corn of the moisture con-
tent listed follow:

Horizontal Openings:

Round Orifices: q=o.ll96 203-10; n.c.= 8.14 db
Rectangular Q=0.153l w1-52L1°"°; M.c.=12.l$ db
Orifices:

vertical Openings:

Round Orifices: Q-0.0351 133-30; M.C.-l2.72$ db
Rectangular Q90.0573 W1°75Ll°5O;JM.C.-12.72$ db-l2.h$ db
Orifices:

Since none of the equations have exponents of the same power, a
fixed ratio cannot be determined so that the calculation of flow through
vertical openings can be accomplished by using the equations for horizon-
tal orifices. Thus, the contention by Stahl (1950) that this can be done
does not appear valid for corn. In fact, actual comparisons of flow
rates for horizontal and vertical orifices revealed a ratio of 0.3 to
0.5 between the two. This ratio was found to increase as the ratio of
the width to the length (w/L) increased.

Stahl's equations also indicated that area had an effect on the flow
rate. If his equations are used to calculate the flow of wheat through
a square and a circular opening with the diameter of the circle equal to

the length of the side of the square, the ratio betweenxflow'rates is

51+

exactly the ratio between the areas. This can be shown by the following:
as determined previously, the ratio of areas of the aforementioned square
and circle is 1.272. The ratio of the constants for Stahl's equations
with D3 - w2L is o.2232/o.1753 which is equal to 1.272. The contention
that the area affects the flow rate appears invalid in the light of the
results found in this research. The effect of both the width and length
seems more important.

An increase in the slope of the bottom of the hopper increased the
flow rate of the grain slightly. This was true as long as the flow
remained funnel flow. At 52.50 mass flow occurred and the flow rate
decreased below that recorded at hos. This result may not occur for all
opening sizes. With a larger discharge area, there may be no effect on
the flow rate. 0

The moisture content appeared to have a bearing upon the flow rate
of the grain. As the moisture content increased, the flow rate tended
to decrease. This may have resulted from the fact that as the moisture
content of the corn increased, the friction coefficient of corn on corn
increased. Thus, the flow rate of the corn decreased.

Two tests were conducted to evaluate the effect of head on the flow
of grain. In both instances, flow rates were measured at different
depths in the bin for given openings. Little, if any, variation occurred
in the flow rate at the different grain depths. Thus, the head clearly
had no effect.

Nb definite tests were conducted to determine the ratio of the ori-
fice diameter to the mean particle size that would cause bridging. It
was noted, however, that bridging occurred when the minimum dimension of

the orifice was less than approximately 3 particle diameters.

While the results appeared good regarding correlation between
theoretical determinations and experimental data, it was evident that
many factors affected the flow rate. Continued investigation is required
to develop more adequate equations that will cover grains under different

conditions.

RECOMMENDATIONS FOR FURTHER STUDY

Tests should be’conducted under conditions that maintain a constant
moisture content for the grain so that the effect of this variable
on flow rate through orifices can be evaluated.

The effect that an increase in fine material has on the flow rate
should be examined.

The effect of the temperature and relative humidity of the ambient
conditions upon flow rate should be studied.

Different construction materials should be used in the hoppers so
that the effect of a change in the coefficient of friction between
the grain and the hopper can be measured.

A study should be made of the effects on the flow rate that the
presence of foreign matter, insect droppings, etc., produces.
Further work should be done on the effect a sloping bin bottom has

on the flow rate of grain.

RWERENCES

Anderson, J. A., and A. W. Alcock (195%). Storage of Cereal Grains
m Their Products. Jones Press Inc., Minneapolis, Minn. 515 pp.

ASAE (19h8). Engineering data on grain storage. Agr. Eng. Data 1:1-11.

Barre, H. J. (1958). Flow of bulk granular materials. A. E. Journal.
V- 39. pp. S3h-‘536. 539.

Brown, R. L., and J. c. Richards (1959). Exploration study of the flow
of granules through apertures. Trans. Instn. of Chem. Engrs.,
London. V. 37, pp. 108-119.

Deming, w. E., and A. L. Mehring (1929). The gravitational flow of
fertilizers and other cominuted solids. Industr. and Engng. Chem.
V. 21, PP. 661‘6650

Fowler, R. T., and J. R. Glastonbury (1959). 1118 flow of granular
solids through orifices. Chem. Engng. Sci. V. 10, pp. 150-156.

Franklin, F. C. , and L. N. Johanson (1955). Flow of granular material
through a circular orifice. Chem. Eng. Sci. V. ’4, pp. 119-129.

Hinchley, J. X8 (1926). EnqLclopedia Britannica. Chemical Engineering
V. 5, p. 3 .

Jenike, A. w., P. J. Elsey and R. H. Woolley (1960). Flow properties
of bulk solids. Paper - Amer. Soc. for Testing Engrs. June. 1h pp.

Jenike, A. w. (1951+). Better design for bulk handling. Chem. Eng.
‘ V. 61, part 2. Dec. pp. 175-180.

Ketchum, M. S. (1929). _T'h_e Design _o_i:_ Walls, Bins and Grain Elevators.
3rd ed. McGraw-Hill Book Co., New York. 556 pp.

Newton, R. H., G. S. Duncan and T. R. Simpson (1916). Trans. of Amer.
Inst. Chem. Engng. V. 1+1, p. 218.

O'Callaghan, J. R. (1960). Internal flow in moving bins of granular
material. Jour. of Ag. Dig. Res. (JAE'R) v. 5, pp. 200-217.

Rausch, J. M. (19.9). Gravity flow of solid beds in vertical towers.
Ph. D. Thesis. Princeton University.

Rose, H. E., and T. Tanaka (1959). Rate of discharge of granular
materials from bins and hoppers. Engineer, Lond. V. 208 (#5h13 ),
pp. 165-1469.

58

Stahl, B. (1950). Grain storage design. USDA Ciro. 835 (Based on data
in Eng. mta on'Grain Storage, Agr. Eng. mta lzl-ll, 19h8). 23 pp.

Takahasi, K. (1931+). Inst. of Phys. and Chem. Research, Tokyo.
Scientific papers. V. 26, pp. llff, No. 5&0.

Welschof, G. (1961). Beitrag zur Messung der Ausflugdmengen k6rniger
cuter mit Blenden und D'lsen (translated) Institut fiir Tandtechnik,
Stuttgart " HOhenheim. PP. 138'1’4’10 '

REFERENCES NOT CITED

Brown, R. L., and P.G.W. mwksley (191w). The internal flow of
granular masses. Fuel, V. 26, p. 159.

Gunderson, J. M. (1953). B. s. Thesis in Chem. Eng. Univ. of Wash.

Lorenzen, R. T. (1959). Mbisture effect on granular friction of
small grain. ASAE Paper, 59-hl6.

Rudd, Jé x. (1951;). Flow of solids in bins. Sugar, v. 1.9, No. 6,
p. 3 .

APPENDIX A

EXPERIMENTAL RESULTS

a

TAELE VI”

Flow of corn through a bin with a

sloping bottom.

 

 

Time of

Average
Discharge
(seconds)

Discharge Time
(seconds)

weight
Discharged
mgmﬂ

a.
+0
mm
m:

0
...m
mm
)

8
want
nicx
eSn
m an

 

71690719

Funnel

l x 12

emanates
135791 3h.
1.1.1.

86 5
J.qo o/
“Ono/o/o/o/o/o/o

Jesosneo
1357913h.
111

00000005
1231456717..

3&

Funnel

vuvuéwcuomo.nwnw
1.qo:/7.o/1.Q¥4
1.1.1.

soernde
135791314
111

"MKN:UhnomomﬁKﬁ
135791 3
1. 1.

Jtﬂoaeoo
135791314
1.1.1.

00000005
123.“..5677.

uﬁ

Funnel

J75h2335
12357.91 3h...
111

Jﬁﬁﬁﬁﬁﬁé
aloha/7.011.234
1.1.1.

detonate
1357191314
111

rm/mhﬁn¢n¢hmn¢n¢
1.:oczqtn7slashw
1.1.1.

00000005
1.?.RHh.cJéuquvl

$5°

Mass

 

62

TABLE VII

Flow of corn through square apertures
placed in the bottom of a hopper.

 

 

 

Average
Side Time of Weight
Dimension Discharge Discharged
(inches) (seconds) Weight Discharged (pounds) (pounds)
1.0 10.0 B r i d g i n g 0 c c u r r e d
1.5 10.0 532 5.1 5.3 5.0 5.0 5.1 5.2 5.1
2.0 10.0 12.h 12.6 12.h 12.6 l2.h 12.5
2.5 5.0 12.8 12.8 12.7 13.0 12.7 12.8
3.0 5.0 21.5 21.9 2l.h 22.6
3.5 2.5 18.2 18.5 18.5 18.8 18.5
h.0 2.5 27.1 27.1 27.5 26.0 27.2
h.5 2.5 36.8 37.0 38.1 38.0 .37.5
5.0 2.5 5h.1 51.0 51.6 52.2
TABLE VIII

Flow of corn through round apertures
placed in the bottom of a hopper.

 

 

 

Average
Time of Weight
Diameter Idscharge ~ - Discharged
(inches) (seconds) Weight Discharged (pounds) (pounds)
1.5 10.0 h.0 h.2 h.l 3.9 h.0 h.h h.2 h.06
u.0 h.0 h.1 k.0 h.l 3.9 h.o

2.0 10.0 9.1 9.2 9.1 9.3 9.20
2.5 5.0 9.5 9.“ 9-h 9.3 9-2 9-3 ' 9.35
3.0 2.5 8.9 8.9 8.5 8.7 8.8 8.6 8.70
3.5 2.5 13.5 13.7 13.9 13.6 1h.o 13.7h
h.o 2.5 21.2 21.3 21.5 21.1 21.30
11.5 2.5 29.9 29.7 29.0 29.0 29.2 29.6 29.110
5.0 2.5 11.1.1 111.3 hl.l 111.20

 

63

TABLE IX

Flow of corn through rectangular apertures
placed in the bottom of a hopper.

 

 

e)
are
Mn
e 0
CC
......
who
. )
Mae mnw
muax
no n
MW ...L
(

Average
Wéight
(pounds)

Discharged

weight Discharged (pounds)

 

6576071308

20140141996
11212231“.

3 n 1
14 h. 9
1 1 2
rt AN Adeont
m“ R, aéalnu
1 123
czcvn071n7éuc/Ruc/
0.4031896
112122314
sooooinno
0140“

.........

men/5522229..

mawpmwmwm
1111223314
x

6

0 17318
1E11233

oucv
o/w1
nwéw cunwiw
on 317
1. 9.241.

02201428

0 17.317
1 11233

36 52 597.

0 17309
1 11233

0 171 O

.......

052222
1 2

mwmwmmm
112233“
I

5

......

914 91“».

5319
11

 

6h

TABLE X

Flow of corn through square apertures
placed in the bottom of a hopper.

 

 

 

 

 

Time Average
Major of Weight
Dimen. Disch. Discharged
ﬁn.) (sec.) Weight Discharged (pounds) (pounds)
2.0 10.0 11.75 11.50 11.50 11.50 11.50 11.50 11.50 11.50
2.5 5.0 12.00 11.75 11.50 11.50 11.50 11.75 11.25 11.61
3.0 10.0 39.38 39.25 39.31
h.o 7.5 70.00 70.00 70.00
5.0 2.5 h6.oo h5.75 h6.75 Ah.75 h7.25 uh.oo h5.75
TABLE XI
Flow of corn through rectangular apertures
placed in the bottom of a hopper.
Tine Average
Size of Weight
(in. ) Disch. Discharged
L x W Jaec.) Weight DischarJgd (pounds) (pounds)
6xl.0 5.0 6.63 6.00 6.13 6.13 5.88 6.13 6.13 6.11
6.00 6.00 6.00 6.00 6.25
1.5 2.5 7.88 7.63 7.38 7.38 7.25 7.75 7-63 7.53
7.63 7.25 7.50
2.0 2.5 13.75 13.50 12.50 12.88 13.88 13.25 1h.oo 13.ho
13.50 13.38 13.00 13.13 13.75
2.5 2.5 20.25 19.50 19.80 2o.h0 19.50 20.00 20.00 19.98
19.30 20.25 20.90 20.00
3.0 2.5 27.50 27.00 27.30 27.50 27.00 27.80 27.35
3.5 2.5 35.00 3h.50 3h.38 3h.88 2h.63
h.0 2.5 h3.oo h1.1o h2.80 h3.20 hh.70 h6.oo h2.80 h3.lo
h2.80 hl.50
5x1.0 10.0 g.gg 9.75 9.25 9.25 9.25 9.50 9.50 9.hh
1.5 5.0 11.50 11.50 11.50 11.50 11.50 11.50
2.0 2.5 10.00 10.50 10.25 10.50 10.50 10.25 10.38 10.3h
2.5 2.5 16.00 15.25 15.25 15.63 15.75 15.00 15.88 15.h2
15.00

 

65

TABLE XI (cont . )

Flow of corn through rectangular apertures
placed in the bottom of a hopper.

 

 

 

Time Average
Size of Weight
(in . ) Disch. Discharged
L x W _(sec.) Weight Discharged (pounds) (pounds)
5x3.0 2.5 20.50 21.50 21.25 21.00 20.50 20.00 20.00 20.69
20.75
3.5 2.5 26.50 26.50 25.25 27.25 25.50 26.00 26.17
h.0 2.5 33.00 33.00 33.50 33.50 32.75 33.10
h.5 2.5 10.25 38.50 38.25 39.25 38.50 3h.75 39.08
5.0 2.5 h6.oo h5.75 h6.75 hh.75 h7.25 hh.oo h5.75
uxl.o 10.0 7.63 7.63 7.25 7.50 7.63 7.00 7.50 7.50
7.50 7.50 7.88
1.5 5.0 3.35 8.75 9.00 8.75 9.13 9.13 9.00 9.03
- 5
2.0 2.5 $.gg 7.50 7.50 7.50 7.50 7.50 7.38 7.53
2.5 2.5 11:50 11.00 10.75 10.75 11.75 11.00 11.00 11.11
3.0 10.0 59.75 59.75 59.00 59.50
3-5 7.5 56-75 57-25 57.00
h.o 7.5 70.00 70.00 70.00
3xl.0 10.0 5.50 5.50 5.75 5.25 5.25 5.25 5.50 5.h3
5.50 5.50 5.25
1.5 5.0 6.50 6.50 6.50 6.75 6.75 6.50 6.25 6.53
6.50 6.50 6.50
2.0 15.0 30.75 30.50 30.63
2.5 10.0 29.50 29.00 29.25
3.0 10.0 39.38 39.25 39.32

 

66

TABLE XII

Flow of corn through round apertures
placed in the side o£_a hopper.

 

 

 

 

 

 

 

 

Average
Time of Weight
Diameter Discharge Discharged
(inches) (seconds) Weight Discharged (pounds ) (pounds 1
1.5 60.0 Bridging occurred periodically
2.0 20.0 6.2 6.5 . 6.3 6.h 6.2 6.h0
6.3 6.5
2.5 10.0 6.7 6.9 6.8 6.6 6.7 6.8 6.75
6.7 6.8 6.7
3.0 5.0 6.0 6.h 6.1 6.1 6.1 6.0 6.13
6.1 6.1 6.0 6.2
3.5 5.0 10.1 9.9 9.9 10.1 9.8 10.2 10.00
10.0
h.0 2.5 8.3 8.5 8.2 8.5 8.2 7.9 8.32
8.h 8.3 8.h
h.5 2.5 11.8 11.0 11.5 11.h 11.5 11.5 11.hh
5.0 2.5 17.6 16.9 17.0 16.9 16.8 16.0 16.90
17.0
TABLE XIII
Flow of corn through square apertures
placed in the side of a bin.
Average
Major Time of weight
Dimen. Discharge Discharged
(inches) (geconds) Weight Discharged (pounds) (pounds )
1.5 60.0 10.h 10.5 10.h 10.h3
2.0 20.0 9.5 9.7 9.5 9.3 9.2 9.3 9.6 9.h5
2.5 10.0 10.0 10.0 10.0 10.0 10.2 9.8 10.00
3.0 5.0 3.2 9.2 8.8 8.9 8.9 8.9 8.9 8.90
3.5 2.5 7.5‘ 7.6 7.6 7.9 7.6 7.3 7.1 7.h6
7.1 7.h ,
h.0 2.5 11.1 11.1 11.2 11 0 11.1 11.10
h.5 2.5 16.2 16.8 15.6 15 h 15.8 16.0 16.0 16.01
16.h 15.9 '
5.0 2.5 23.3 23.0 22.8 23 O 22.9 23.1 23.0

m

TABLE XIV

placed in the side of a hopper.

Flow of corn through a rectangular opening

 

 

Mame
Weight

Discharged

Opening

L

@wﬁs

WﬁﬁtManﬁjmwﬂ)

unnue
(seconds)

ﬂmof

LxW

mu

 

(inches)

5 A

3 9

s s

3 9

3 ”—9 1613
2233

5
3.619 E7L&L&
12233

335mg amuse»

1481911712555.

............

335u99muawnn

n nn5 555555
E 552 2&2222
D 5&5 £5£5£5
1.122 3$hh55
x
6

2m

9m
8.6 8.50
66 6

9

12

23.00

2.7
up m
18.6 19

901

209
8h
6
9
3
6
8

26

83 86 SJ 9D
83
6
9
6
9

3£

23
86 85
9
h
h
8
5

09117h0655023

o o n 55555 5
o 0 5

1.— 1.. 22222 2
n 5 o 5550.5 0
1 1.. 2 233M...“ 5
X

5

6
9
n
6
9
23.0 22.8 23.0 22.9 23.1

27086000

8 53760 0.4

1.1..mmm

nnnn

ﬂ
0005 5
211

ﬂéﬂ
112
x

1“.

25

68 6%

6.9 6.9 6.9 6.6 7.1

3£

5£
314

 

68

TABLE XIV (cont. )

Flow of corn through a rectangular Opening
placed in the side of a hopper.

 

 

 

Opening Average
Size Time or ‘ Weight
(inches ) Discharge Discharged
L x W (seconds) Weight Discgged (pounds) (pounds)
h x 3.0 2.5 6.6 6.9 6.9 6.9 6.6 7.1 6.8 6.85

7.0

3.5 2.5 8.9 8.7 8.1 8.9 9.2 8.9 9.2 8.89

1L.O 2.5 11.3 10.8 10.8 11.0 11.2 11.0 11.0 11.00
10.5 11.3

3xl.O 30.0 Bridging Occurs

1.5 20.0 3.; 9.0 9.1+ 9.h 9.5 9.5 9.6 9.1+2

2.0 10.0 3.2 8.5 8.1+ 8.5 8.1+ 8.6 8.5 8.50

2.5 5.0 6.6 6.6 6.7 6.5 6.8 6.5 6.8 6.69
6.9 6.9 6.6

3.0 5.0 8.9 8.7 8.8 8.9 9.2 8.9 9.0 9.00
9.1!- 9.0

 

GLOSSARY

Apparent particle density - the nu per unit mm» of a latex-161
dependent upon the physical for: and heterogenity of the size of
the particle coqosing the use.

061nm ¢ -theanglefmedhythesidesofahopper.

Muffler-the lengthoftinerequiredforacertainalountof
asterial to discharge through an orifice. .

Staticangleofrepose -thenximangulardeviationfrouthe
horizontal of the surface of a static pile of granular material.

Kinetic angleefrepose - the slopeofacontinnouslyloviusur-
face of a pile of granular naterial.