' ZHEAD LOSS In Quick-Coupled

Aluminum Pipe

Used For Sprinkler Irrigation Systems

Asriculfure Handbook No. 147

UNITED STATES DEPARTMENT OF AGRICULTURE

in cooperation with the

Oklahoma Agricultural Experiment Station
ACKNOWLEDGMENTS

Such studies as the one reported here require the help

of many persons. The author wishes to acknowledge the

assistance received and to thank those who contributed.

These include:

R. A. Aldrich, College of Agriculture, State College

of Washington.

H. T. Barr, Louisiana State University and Agricultural and Mechanical College.

A. A. Bishop, Utah State University.

J. E. Christiansen, Utah State University.

T. W. Edminster, Agricultural Research Service,

United States Department of Agriculture.

J. E. Garton, Oklahoma State University.

H. E. Gray, New York State College of Agriculture,

Cornell University.

L. W. Hurlbut, College of Agriculture, University of

Nebraska.

M. C. Jensen, State College of Washington.

R. F. Johnson, Agricultural Experiment Station,

University of Idaho.

W. G. Knisel, Jr., Soil and Water Conservation Research Division, Agricultural Research Service,

United States Department of Agriculture.

V. I. Myers, College of Agriculture, University of

Idaho (now at University of Nevada).

H. M. Olson, North Dakota Agricultural Experiment

Station (now superintendent of the Williston, N.

Dak., Irrigation Substation).

C. H. Pair, Agricultural Research Service, United

States Department of Agriculture.

V. H. Scott, College of Agriculture, University of

California.

R. H. Shoemaker, Jr., Oregon State College.

W. C. Strong, Fresno State College, Fresno, Calif.

J. L, Wiersma, South Dakota State College of Agriculture and Mechanic Arts.

CONTENTS

Page

Definitions of symbols 1

Present design standards 2

Experiments on friction factor 3

Research by H. E. Gray, G. Levine, and M.

Bogema 3

Research by H. M. Olson 4

Research by L. S. Willardson 4

Research by A. Benami 8

Research by R. A. Aldrich 8

Experiments on coupler loss 9

Research by H. E. Gray, G. Levine, and M.

Bogema 9

Research by H. M. Olson 9

Research by L. S. Willardson 9

Research by D. A. Buhr 9

Research by A. Benami 11

Page

Discussion of pipe friction 12

New pipe 12

The Scobey formula 13

The Manning formula 13

The Hazen-Williams formula 13

Very good used pipe 14

Poor used pipe 15

Formula comparison 16

Discussion of coupler loss 16

Discussion of head-loss tables now in use 17

Head-loss tables calculated from available data 18

Flow in a line with multiple outlets 19

Conclusions and recommendations 20

Literature cited 20

U. S. GOVERNMENT PRINTING OFFICE: I9S9

For sale bv the Superintendent of Documents, U.S. Government Printing Office

AVashington 25, D.C. - Price 15 cents

Washingfon^ D.C Issyccl April 1959
HEAD LOSS in Quick-Coupled

Aluminum Pipe

Useci For Sprinkler Irrigation Systems

By W. O. REE, project supervisor^ Soil and Water Conservation

Research Division, Agricultural Research Service

This handbook presents a study of current

practices in estimating friction loss in portable

aluminum-pipe sprinkler irrigation systems. Literature by manufacturers of sprinkler irrigation

equipment has been reviewed by the author.

Reports of experiments to determine losses in

irrigation pipe and fittings have been studied,

as well as theses on the subject. Conclusions

reached by analyzing this material are presented

for the information and guidance of those engaged

in designing and selecting irrigation systems.

Field checks have disclosed that actual performance of sprinkler systems has not always

measured up to that which was predicted. Indications are that head loss, as a rule, has been

greater than calculated. When such differences

have been found, head loss resulting from pipe

friction has been regarded as the most probable

cause. Factors used in estimating head loss

have been based on the condition of the pipe

when new. It has been determined, however,

that under some circumstances aluminum pipe

corrodes while in use; also, that frequent moving

dents the pipe. This corroding and denting

increase the roughness of the pipe and thereby

increase friction loss. A point to be determined

in the investigation has been whether enough

increased friction has resulted to account for the

difference between actual and estimated head

loss. If so, more realistic values of the friction

factor should be used in designing irrigation

systems. Existing experimental evidence has

been examined, in an effort to find the solutions

to these problems.

Another source of head loss involved in the

problem studied is that caused by couplers.

Recently, data have been obtained on loss coefficients for the quick couplers used in aluminumpipe systems. These coefficients have a considerable range, depending on the design of the

coupler and the deflection angle between the pipes

joined at the coupler. Some of the coefficient

values included in these data are quite high.

This has raised a question as to whether pipefriction-loss tables in current use include coupler

loss; and if so, whether the values used are

reasonable. Manufacturers' literature and available bulletins and handbooks have not been

particularly helpful in settling these questions.

In fact, various sources have been contradictory.

Basic experimental data have therefore been

used in arriving at conclusions.

This study has disclosed that three formulas

expressing the relationship between rate of flow,

pipe size, and head loss were already in general

use. These were the Scobey formula, the Manning

formula, and the Hazen-Williams formula. Actually, none of these was employed in the study

of the experimental data. Instead, the DarcyWeisbach formula was used. Relationships were

then worked out to convert the Darcy-Weisbach

/ values to coefficients for the more common

formulas. These relationships also provide a

means for determining equivalent values for the

different types of coefficients. Diagrams showing

these relationships are included in this handbook.

DEFrNITIONS OF SYMBOLS

Definitions of symbols used in this handbook

are as follows:

a A constant, a function of boundary condition—^determined by the form of the

coupler.

Ci Coefficient in the Hazen-Wiiliams formula.

D Diameter oí pipe (feet).

d Diameter of pipe (inches).

F Tlie Christiansen F factor for estimating

head loss in a line vvith multiple outlets.

/ Darcy-Weisbach friction factor.

g Acceleration of gravity (32.2 feet per

second).

Hf Head loss due to pipe friction (feet).

he Head loss in the pipe coupler (feet).

K A constant in a general head-loss equation.

Kc Head-loss coefficient for pipe coupler.

Ks Coefficient in the Scobey formula.

L Length of pipe over v/liich head loss is

determined (feet).

1
m An exponent in a general head-loss equation.

n The Manning roughness coefficient.

n An exponent in a general head-loss equation.

0 Discharge rate (cubic feet per second).

R Ratio of diverted flow to the total flow

approaching a side outlet.

R Hydraulic radius (feet).

Re Reynolds number.

5 Slope of the pressure grade line.

V Flow velocity (feet per second).

Vi Velocity of flow approaching a side outlet

(feet per second).

Az Pressure rise at a side outlet (feet).

6 The absolute roughness height in the Colebrook-White equation. (The unit is the

same as for diameter, D,)

PRESENT DESIGN STANDARDS

A review of manufacturers' literature has

revealed that the basic reference usually presented

for the calculation of head-loss tables was a bulletin by Christiansen (1)} That part of this

bulletin which deals with pipe-friction factor will

therefore be discussed first. This bulletin, which

was written in 1942, does not mention alxmainum

pipe. However, friction loss in welded-steel pipe

of the type commonly used for main supply lines

for portable sprinkler systems is discussed. A

graph of friction loss in welded outside diameter

(O. D.) pipe is given (Í, p. 61), Accompanying

this diagram is the explanation: '^This graph is

based on Scobey's formula, with the coefficient

if5=0.32, which corresponds to new pipe in good

condition.'' In a discussion of friction loss in

sprinkler lines {p, 67), he states: *^Most portable

sprinkler pipe is made from lightweight O. D.

tubing." Here also he apparently means steel

pipe. A diagram (j?. 68) shows friction loss in

portable sprinkler pipe. This is based on the

Scobey formula

^^""1,000 Z)ii

Where

Hf is the total friction loss in a length of pipe

(feet)

L is the length of pipe (feet)

V is the mean velocity (feet per second)

D is the diameter of the pipe (feet)

Ks is the Scobey coefficient.

Values of Kg suggested by Christiansen are

given in table 1.

TABLE 1.—Values oj K^^ based on the Scobey

Jormvla

Suggested by Christiansen {!),

This statement is made by Christiansen {1,

p, 67): ^'According to tests on such pipe, higher

values of Ks may be expected of the smaller sizes,

and the values are influenced by the type of

coupling. The values given are believed conservative; most sprinkler pipe will have less

friction loss than is shown by the graph." The

foregoing statement implies that coupler loss is

included in the values of Ks*

Christiansen also developed an approximate

method for estimating friction loss in a pipe with

multiple outlets. The method involves calculating a head loss for the entire flow through the

entire length of pipe. A factor (F) is then applied

to this figure, to arrive at the head loss for the

actual flow condition. Factor F varies with the

exponent (m) in the foUowhig equation:

Hf:=^F KLQr

JJTm-^rn

1 Italic figures in parentheses refer to Literature Cited,

p. 20.

If m=2, factor JP will vary from 1.0 for 1 outlet

on the line to 0.359 for 20 outlets and 0.338 for 100

outlets. The approximation in this method is the

assumption that all outlets have equal discharge

rates. This is nearly true in a well-designed

sprinkler system.

The textbook of the Sprinkler Irrigation Association {6) is an important work in this field, for it

represents the industry generally. Pertinent statements on the subject of pipe friction in this

textbook are quoted or paraphrased in the following paragraphs.

^'Friction values now used throughout the

industry have been checked fairly close under field

conditions and are found to be on the conservative

side.''^ (See 6, p, 2Jf.7.) No corroborative material is given to support the statement.

Scobey^s formula is presented with the note that

it was developed for welded-steel and similar

Î)ipe. Christiansen's suggested values for K^ are

isted. It is then stated that when aluminum

pipe was introduced, designers continued to use

Scobey's formula and Christiansen's Ks values.

(See p, 263,)

The following statement is made on the subject

of couplers: ''To handle this problem [added

coupler loss] * * *, value of Kg in Scobey's

formula was increased for portable aluminum

main line [to] Ks=0.40. Most charts and slide

rules used by the industry are based on this value.''

(See p. 255.)
Reference is then made to the work of Gray and

coworkers (S) at Cornell University: '^Based on

this preliminary data, it would appear that charts

or tables based on Scobey's formula and Ks=0.40

are on the conservative side, at least for most

commonly used coupler types. Again, until data

is complete, the writers suggest using existing

material on the basis of the Scobey formula. It

should again be pointed out that aging and corrosion in some areas may make values, based on

the Scobey formula, nearly correct for the average

life of main lines.'' (See p, 255,)

Table X-5 of the cited textbook gives loss of

head in feet per 100 feet of plain aluminum pipe.

The table is based on the Scobey formula, with

Ks=^{).M for 2-inch pipe, 0.33 for 3-inch pipe, and

0.32 for other sizes. It is noted that the values

are for aluminum pipe without couplers. (See

p. 422.)

EXPERIMENTS ON FRICTION FACTOR

Experiments on friction factor for aluminum

tubing were located at several State universities.

These limited data, in most instances, were

incidental to the main objective of the experiment,

which usually involved measuring fitting losses.

Nevertheless, these data have proved useful and

valuable in this study.

Each experimenter has portrayed his results in

his own fashion. Most have chosen to present an

equation relating head loss to velocity and diameter. The equation would fit the data for the

particular experiment but would not be of great

usefulness for comparison with other experiments.

In one instance, the experimenter also calculated

the Darcy-Weisbach friction factors for the

individual runs. In two other experiments, no

head-loss equations or friction-factor values were

calculated, even though the data needed for doing

so were available.

A uniform method of analyzing and comparing

all the data had to be selected. The DarcyWeisbach formula

Hr ikYl

-^ D2g

was chosen for this purpose. The value of the

friction factor / and the corresponding Reynolds

number for the flow were calculated for each run.

The data were then plotted on log paper. A

separate plotting was made for each experiment.

It was noted that the data usually followed the

pattern found in the familiar pipe-friction-resistance diagram. An example of this diagram can

be found in King's Handbook (4, sect, 6jp, 8),

Experiments with fluid friction in pipes have

disclosed that the data for full turbulence usually

fit the Colebrook-White transition curves. These

are given by the equation

1_

V7^ ^"-''^Kri^+S)

When €, the absolute roughness height, becomes

zero, the equation reduces to the KarmanPrandtl expression for turbulent flow in smooth

pipes. It is

;~«2logñ,V7-0.8.

The foregoing equations are used as standards

for comparison in this publication. The KarmanPrandtl equation is shown on each plotting.

Where the pipe is not hydraulically smooth,

Colebrook-White curves with appropriate yj ratios

are added. These curves, when plotted with the

data, provide a quick way of evaluating hydraulic

properties of pipe and a means of comparing the

various experiments.

Each experiment studied is described separately

in subsequent sections.

Research by H. E. Gray, G. Levine, and

M. Bogema

Gray and coworkers (2) present the results of

friction-loss determinations on two 20-foot lengths

of 3-inch aluminum pipe. The pipe had been

used for 3 seasons in field irrigation. Two sets of

20 flow rates were used in the experiment with

Reynolds number, ranging from 4.82X10* to

1.36X10^. The results are given in the following

3 equations:

Upstream pipe Hf=0,30 1,0001)1-29

Downstream pipe Hf=0.30 ^ oon^^^^

Composite H/=0.30

.74 L F

1,000 Z?^-2ö

Gray's formula can be converted to a form

having the Darcy-Weisbach / and Reynolds

number as the variables. For a water temperature of 60° F., the equation becomes

/==0.3668 Re -0.26

The original data for the experiment were obtained from Professor Gray, and the DarcyWeisbach / values were calculated. These were

Elotted against the corresponding Reynolds numers (fig. 1). A comparison of the plotted points

with the calculated line derived from the KarmanPrandtl equation shows the pipe to be hydraulically smooth.

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REYNOLDS NUMBER, Rç

8

FIGURE 1.—Friction factor versus Reynolds number, for nearly new 3-inch-diameter aluminum tubing. (Experiment

by Gray, Levine, and Bogema (S).)

Research by H. M. Olson

As reported in his thesis, Olson ^ tested 40-foot

lengths of ALCOA 63S--T6 tubing. Pour pipes

were tested, including

3-inch diameter, new

4-incli diameter, new

4-inch diameter, used

5-inch diameter, new

Four couplers were also tested, but the newpipe tests will be discussed first. The values of

the friction factor (i) were plotted against Reynolds number (fig. 2). A comparison of these

points with the plot of the Karman-Prandtl

equation shows the three new pipes to be hydraulically smooth. The scattering of the small Reynolds numbers may have been due to increase in

experimental error.

The data from the tests on the used 4-inch pipe

are plotted (fig. 3). Comparison with the two

Colebrook-White curves shows this particular

piece of pipe to have a relative roughness of 0.0003.

In his conclusions (p. 20 of the thesis), Olson

states: ^It is the author's opinion that the roughness of the used tubing is not due entirely to the

formation of aluminum oxide tubercules and pitting of the pipe surface but also to many dents in

the pipe wall which occur in field handling."

In response to an inquiry, Olson wrote: ^'I do

definitely recall that there were some aluminum

oxide tubercules, but they were certainly not of the

2 OLSON, H. M. THE DETERMINATION OF THE FRICTION

FACTOR FOR NEW AND USED ALUMINUM TUBING AND HEAD

LOSS IN SPRINKLER-PIPE COUPLERS. 1950. [Unpublished

master's thesis. Copy on file in Library, Utah State

Univ., Logan.]

magnitude one would find on the inside of an

untreated steel tubing which had rusted. There

were also a number of small dents in the tubing

resulting no doubt from field handling." ^

The experiments on coupler loss will be discussed in the section of this report devoted to

that problem.

Research by L. S. Willardson

Tests conducted by Willardson ^ on couplers

involved measuring hydraulic grade lines in the two

20-foot lengths of ALCOA 63S-T6 tubing which

were joined by the coupler being tested. The

description of the pipe states (p. 17 of thesis):

"The pipes used for these tests had had little use

and should be classified as new pipe." From

these observations on both 3- and 4-inch-diameter

tubes, he concluded that head loss in the tubing

could be expressed by the equation

Hf=0.000246 —V-'^

This equation is the result of nearly 300 tests

made on 4 different lengths of 4-inch-diameter

tubing and 2 lengths of 3-inch-diameter tubing.

Rather than use this equation, however, the

Darcy-Weisbach friction factors and the corresponding Reynolds numbers were calculated for

each of the tests from the basic data. Plottings

of the results are illustrated (figs. 4-7).

3 In correspondence (Dec. 26, 1955).

* WILLARDSON, L. S. ENERGY LOSSES IN ALUMINUM

IRRIGATION PIPES DUE TO DEFLECTIONS IN THE COUPLERS.

1955. [Unpublished master's thesis. Copy on file in

Library, Utah State Univ., Logan.]
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REYNOLDS NUMBER, R^

FIGURE 2.—Friction factor versus Reynolds number for new aluminum tubing. (Experiment by H. M. Olson (see footnote 2).)

REYNOLDS NUMBER, R^

FIGURE 3.—Friction factor versus Reynolds number for dented and corroded 4-inch aluminum tubing.

by H. M. Olson (see footnote 2).)

DN-1243

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REYNOLDS NUMBER, R^

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,—Friction factor versus Reynolds number for nearly new 4-inch-diameter aluminum tubing, lengths 1 and 2.

(Experiment by L. S. Willardson (see footnote 4).)

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FIGURE 5.—Friction factor versus Reynolds number for nearly new 4-inch-diameter aluminum tubing. Flow in opposite

direction from that in experiment portrayed on figure 4. (Experiment by L. S. Willardson (see footnote 4).)
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REYNOLDS NUMBER, Rg

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FIGURE 6.—Friction factor versus Reynolds number for nearly new 4-inch-diameter aluminum tubing, lengths 3 and 4.

(Experiment by L. S. Wiliardson (see footnote 4).)

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REYNOLDS NUMBER, Rg

FIGURE 7.—Friction factor versus Reynolds number for nearly new 3-inch-diameter aluminum tubing. (Experiment by

L. S. Wiliardson (see footnote 4).)

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FIGURE 8.—Friction factor versus Reynolds number for aluminum tubing. (Experiment by A. Benami (see footnote 5)

and R. A. Aldrich (see footnote 6).)

A study of these diagrams shows that the pipes

api)ear to be nearly smooth. However, as the

majority of the points seem to lie a little above

the smooth-pipe curve, it should not be concluded

that the pipe is smooth. This is borne out by

results shown graphically (fig. 5).

In testing these two pipes, Willardson reached

higher values of Reynolds numbers than were

reached in all the other experiments. Almost at

the very point where the upper values of Reynolds

numbers previously reached were exceeded, the

resistance function left the smooth-pipe curve and

started to follow the Colebrook-White curve for a

pipe of relative roughness, j^ equal to 0.0002.

These few tests by Willardson, extending into the

higher Reynolds numbers, are very important.

They show the pipe to be hydraulically rough.

The absolute roughness height is small, however,

having an equivalent sand-grain roughness height

of only 0.0008 inch.

Data on coupler loss will be discussed in a subsequent section.

Research by A. Benami

In his study of couplers, Benami ^ measured the

hydraulic grade lines in the pipe above and below

the coupler. These data allowed the calculation

of the friction coefficient for the pipes. The pipes

were 3-inch aluminum. The Öarcy-Weisbach /

values were plotted against Reynolds number

(fig. 8). It is evident that the pipes are hydraulically smooth.

Research by R. A. Aldrich

Aldrich ^ used a 2-inch aluminum pipe in his

experiment. As length over which pressures

were measured was rather short, only two of his

tests were used to calculate friction factor. The

two points are plotted (see fig. 8) along with

Benami's data. Here also the points fall near

the smooth-pipe curve.

« BENAMI, A. EVALUATION OF LOSSES IN BRANCHINGFLOW SPRINKLER COUPLERS. 1954. [Unpublished master's thesis. Copy on file in Library, State Col. of Washington, Pullman.]

Ö ALDRICH, R. A. FLOW OF WATER IN PIPES WITH

MULTIPLE OUTLETS. 1952. [Unpublished master's thesis.

Copy on file in Library» State Col. of Washington, Pullman.]
EXPERIMENTS ON COUPLER LOSS

The experiments on couplers fall into two

classes—those without and those with flow

through the sprinkler outlet. The first class

yield data useful for main-line pipe design; the

other, for the sprinkler laterals.

Research by H. E. Gray/ G. Levine, and

M. Bosema ^

Gray and coworkers (S) tested 14 different 3-

inch quick couplers. Tests were made with the

couplers in alined position, then with 12° misalinement (except for 2), and then in offset position where possible. Coefficients K^ were determined for the equation

Where he is the head loss in the coupler

Type of coupler:

A, B, C, E_-

A, B, C, D>.

Diameter o,

pipe, inches

3

4

v.

2g is the velocity head.

The results of the coupler tests were effectively

portrayed by the use of detailed sketches showing

the coupler construction together with the loss

coefficients. The coefficient was found to vary

with the design of the coupler. For the couplers

in alined position, Kç varied from 0.15 to 0.70.

In the misalined position, the Ko values increased,

the range being 0.16 to 0.84.

Research by H. M. Olson

Olson ^ tested three different makes of couplers,

of the following types and sizes:

Diameter of

Type of coupler: pipe, inches

A 4

B 3,4,5

C 4

These tests were made with no flow through the

sprinkler outlet.

Olson observed that the coupler coefficient increased with the velocity. He also found that one

make of coupler had a different coefficient for each

pipe size. His results are portrayed graphically

, (fig. 9).

Research by L. S. Willardson

Willardson * tested five different couplers of the

following types and sizes:

These tests were made with no flow through the

riser outlets. The couplers were tested with

straight alinement and then with full deflection.

Three of the couplers were also tested with flow

direction reversed. The results of the experiment

are given in the following equation and in table 2.

Coupler coefficient Kc in expression hc=Kc y

TABLE 2.—Results of coupler tests with no dejlection

{straight alinement) and with full deflection, in

direct and reversed position

Deflection

angle of

coupler

Position of pipeline

Size of pipe and

type of coupler

Direct Reversed

Nodeflection

Full deflection

Nodeflection

Full deflection

3-inch:

A

Degrees

¿5

8.1

7.6

9.7

5.4

8.4

13.8

0.108

. 169

.062

.506

. 110

.098

.016

.318

0.059

.172

. 105

.538

.064

. 106

"fois"

B

C

E

4-inch:

A

B

C

D

0.064

.064

.027

0.017

.089

.029

Research by D. A. Buhr

Buhr® tested 5 different couplers. His tests

were conducted with flow through the riser. He

evaluated the pressure rise across the coupler due

to flow out of the outlet. He also measured

energy loss between the sprinkler line and riser

outlet.

Five couplers of the following types and sizes

were tested:

Diameter

of pipe,

Type of coupler: mches

A 4

B 3,4,5

C .--- 4

Analysis has predicted and experiment has verified the rise of pressure that takes place in a pipe

when flow passes from upstream of a side outlet

to a downstream position. Buhr used the following equation, developed by J. S. McKnown and

reported by Soucek and Zelnick (5), to predict

this pressure rise :

f See footnote 2.

8 See footnote 4.

• BUHR, D. A. A STUDY OP HYDRAULIC LOSSES IN

SPRINKLER IRRIGATION COUPLERS. 1950. [Unpublished

master's thesis. Copy on file in Library, Utah State

Univ., Logan.]
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VELOCITY - FEET PER SECOND

FIGURE 9.—Coupler loss coeflScients versus velocity for no discharge through riser outlet.

(Experiment by H. M. Olson (see footnote2).)

DN-1249

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Where As is the pressure rise in feet

-—- is the velocity head of the approaching

^^ stream

R is the ratio of the diverted flow to the

approaching stream

hf is the turbulence loss at the junction.

Barton ^^ further modified this expression to

read ;

10 BARTON, J. R. A STUDY OF DIVERGING FLOW IN

PIPE LINES. 1946. [Unpublished master's thesis. Copy

on file in Library, State Univ. of Iowa, Iowa City.]

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>

UJ

UJ

(XL

(/) œUJ

Q:

a.

Uo

<

/ &>-.

-

A

^

^B

-

r

í

7

1f\ 1 1

"^•'O .2 .4 .6

RATIO OF DISCHARGE THROUGH RISER

TO DISCHARGE IN APPROACH LINE, R

DN-1250

FIGURE 10.^—Pressure rise across a sprinkler outlet when

flow passes from the upstream to the downstream pipe.

(Experiment by D. A. Buhr (see footnote 9).)

Where a is a function of the boundary conditions

and is determined by the form of the

coupler.

Buhr's results are portrayed graphically (fig.

10).

Research by A. Benami

Tests byBenami" were made with flow through

the riser outlet. In his findings he separated

turbulence loss from the theoretical pressure rise.

In this respect he differed from Buhr, who presented the net pressure gain only. The results

are shown graphically for two of the couplers

(figs. 11 and 12). The turbulence losses were not

large.

" See footnote 5.

.8

o

UJ

o

Lu

O

O

en

<n

o

-j

ce

LU

-J

Û.

O

O

.6 \\

\ M

\ M- FLOW IN APPROACH LINE

)\\ IN GALLONS PER MINUTE

^\ y

-\ \

\

o\\ \

\

\

1 1 1

.2 —

0 8 16 24

FLOW IN RISER OUTLET - G. P. M.

FIGURE 11.—Head-loss coefficients for irrigation-pipe couplers with flow through the riser by coupler No. 1. (Experiment by A. Benami (see footnote 5).)

11
0.15

8 16 24

FLOW IN RISER OUTLET - G. R M.

FIGURE 12.—Head-loss coefficients for irrigation-pipe

couplers with flow through the riser by coupler No. 2.

(Experiment by A. Benami (see footnote 6).)

DISCUSSION OF PIPE FRICTION

At this point in the discussion, an important

question should be considered. That is, were the

various pipes (except the corroded and dented one)

alike? All were described as new or nearly new.

In the absence of precise physical measurements

of the interior surfaces of tne pipes, the only test

of similarity lies in the measurements of the friction

factors.

The flow tests indicated that differences did

exist. Most of the new or nearly new pipes were

found to be hydraulically smooth (at least to a

Reynolds number of 4X10^). Yet some of the

pipes answering the same description were hydraulically rough. For the purpose of this study, it

will be concluded that the new or nearly new pipes

tested included both smooth pipe and hydraulically

rough pipe.

Adding the corroded and dented pipe gives three

categories of pipe to be discussed. These are new

pipe, very good used pipe, and poor used pipe.

Each kind will be discussed separately in the

following sections.

New Pipe

The experiments by Olson, Benami, and Aldrich,

discussed previously, showed new aluminum

tubing to be hydraulically smooth. This means

that the relationship between the Darcy-Weisbach

friction factor / and the Reynolds number Re is

best expressed by the Karman-Prandtl equation

i-21og., Ä.V7-0.8

This equation can be used to calculate properties

of turbulent flow in smooth pipes. However, it

has not found general acceptance among hydraulic

engineers because most are accustomed to using

simpler empirical formulas such as Scobey's,

Hazen-WüHams', and Manning's. Thus, there is

a reluctance to change to a more cumbersome

formula even though it might be more exact. As

the formulas just mentioned will continue to be

used, coefficients for use in these formulas have

been calculated for smooth pipe.

The first step in this calculation was to replace

the Karman-Prandtl equation by a simple power

function. This operation was limited to a narrow

range of Reynolds numbers, extending from 10*

to 10 ^ Most flows in portable sprinkler pipe fall

in this range, with but few exceeding 4X10^.

Furthermore, a straight line will not deviate far

from the curved line of the Karman-Prandtl equation over this range. The equation of the straight

line was obtained by calculating the regression

equation for the logarithms of selected pairs of

/ and Re values. The relation obtained was

^=0.2074 Är'-2"2 -- 2

1^2
By choosing a water temperature (60° F., in

this instance), the kinematic viscosity term in

Reynolds number reduces to a constant and the

equation can be converted to the form

íí/=0.295

1.79 L F

1,000 Z^i-21

In this form, the expressed relationship is very

similar to Scobey's equation. By the use of this

equation, the coefficients were calculated for several of the more common formulas. These will be

discussed in turn.

The Scobey Formula

Scobey's formula for metal pipes is

•^""1,000 D''^ *

By a simultaneous solution of this formula and

equation 3, the following expression for Kg was

obtained:

Ks=0.295 (FZ?)-«-ii 4

If the diameter is expressed in inches, D==-^f then

equation 4 becomes

¿r,=0.388(Fd)-«-" 5

Equation 5 has been plotted (fig. 13, the Scobey

formula).

From the foregoing equations, it is seen that Kg

varies with the velocity as well as the diameter.

Consider 15-inch-diameter pipe: Kg will vary from

0.37 to 0.23, depending on the velocity. If the

mean value of 0.30 is used for Kgj the error in the

estimate of the head loss will be ±23 percent at

the extremes of the velocities shown on the diagram.

The Manning Formula

Manning's formula for channels is usually written in the form

n

For pipe flow it can be rearranged to

Hf==2.88n'L^, 6

A simultaneous solution of equations 3 and 6

yields the following expression for n:

72,=0.0101 yo.i

If the diameter is expressed in inches, D=j^f then

equation 7 becomes

n=0.00870 yo.: 8

Equation 8 is plotted (fig. 13, the Manning

formula).

Again, it is found that the coefficient varies with

the velocity as well as the diameter. Using the

15-inch-diameter pipe for illustration, the maximum error introduced by a single value choice for

Manning's r^, is ±48 percent. One reason for the

large error is that the head loss varies as n^. (See

equation 6.)

The Hazen-Williams Formula

The Hazen-Wüliams formula is

17'=í7jA».63 5.0.64 0.001-004.

10

8

i 4

«0

I 2

, I

>0.8

I .6

O

>

V s, ' \ S V-ft. —1—

\\\ \ ^fS"".' '

\'\^\. \

s, \ ^.

1

V

\^^^

>

\\

\

t

\^

s

\

^^N \

\

\

- .X s \ S.ÍJNP s, ^ S s

- MSvV

^

<^ \ \\

\"v"^\

\

s

- ^:

%^

s

\^^

\

ks

K.-C

1 ">

).388(Vdr^"

1 1 1 1 1

\

.1, \^

\

V

2 4 6 * 10 20 40

PIPE DIAMETER - d - inches

SCOBEY'S K^

2 4 6 10 20 40

PIPE DIAMETER - d - inches

MANNING'S n

2 4 6 10 20 40 IOÓ

PIPE DIAMETER - d - inches

HAZEN-WILLIAMS C,

DN-1253

FiGURB 13.—Coefficient values for the pipe-flow formulas by Scobey, by Manning, and by Hazen-Williams for new smooth

aluminum tubing for a water temperature of 60° F.

13
This can be rewritten as

1 yi.s5i

Hf=0.04: ^ j g5i L 2^1 166 9

Solving equations 3 and 9 simultaneously yields

an expression for Ci in terms of V and D, It is

(7i=148 FÖ-032 2^0.022 10

For diameter expressed in inches, equation 10

becomes

C^^l^ç)yo.mjo.m n

Equation 11 is plotted (fig. 13, the Hazen-Williams

formula).

Thus it is found that Hazen-Williams C also

varies with both velocity and diameter. A single

average value of C chosen for the 15-inch-diameter

pipe will produce an error in the head-loss estimate

of about lb 13 percent. This is over the velocity

range of 0.1 to 10.0 feet per second.

Similar derivations could be made to determine

coefficients for other formulas for the condition

of turbulent flow in smooth pipes. The method is

straightforward and proceeds on the basis that

the Karman-Prandtl equation correctly expresses

the hydraulic characteristics of the pipe.

Very Good Used Pipe

The tests by Willardson^^ showed that some

of the nearly new pipe tested appeared to be

12 See footnote 4.

hydraulically rough. The few tests on two lengths

at higher Reynolds number values indicated

strongly that these pipes were rough with a

relative roughness, -5^, of 0.0002. To study further

the departure of friction-factor values from the

smooth-pipe curve, all the data for all tests

reported here were plotted on one diagram (fig.

14). The Colebrook-White transition curve

shown appears to be a fairly good fit for the

maximum friction-factor values (excluding the

scattered values in the low Reynolds-number

range). It is assumed, therefore, that very good

used pipe is hydraulically rough with -^ equal to

0.0002. This assumption permits an analysis

similar to that made for smooth pipe.

The first step in this analysis is to fit a straight

line to the Colebrook-White curve for D' =0.0002.

In this instance, the fit is limited to a Reynolds

number range of 3X10* to 7X10^, which is the

range of the data. The equation of the straight

line is

/=0.107 Ar'-'"'.

If a water temperature is chosen, this expression

can be rewritten into the head-loss form. For

water at 60° F., it becomes

£r^=0.000309L

•^1.852

^148 12

Solving equation 12 simultaneously with Scobey's yields an expression for Scobey's Ks for

REYNOLDS NUMBER, R^

DN-1254

FIGURE 14.-

14

-A composite plotting of friction factor versus Reynolds number for aluminum tubing. (Experiments by

Aldrich, Benami, Gray, Olson, and Willardson.)
turbulent flow in hydraulically rough pipes

C^=0M02\ It is

0.309 (FJ9)-o.o5 13

For diameter expressed in inches, this equation

becomes

0.350 (W)-ö-os 14

Equation 14 is plotted (fig. 15, the Scobey formula).

A similar solution has been made for Manning's n. The equation is

7^=0.0104

and for diameter in inches

0.075

71=0.00829

15

16

Equation 16 is plotted (fig. 15, the Manning

formula).

The solution of equation 12 to obtain an expression for Hazen-Williams G for turbulent flow in

rough Í-^=0.0002) pipe yields an interesting

result. The value of the coefficient is independent

of velocity and varies only slightly with diameter.

The equations are

(7i=143.6 Z>-<^-oo972 ___ 17

and (for diameter in inches)

(7i=147.1 d-o-oow2 .^ 18

Equation 18 is plotted (fig. 15, the Hazen-Williams

formula).

It is evident that the Hazen-Williams formula

very closely defines the hydraulic characteristics

of nearly new aluminum tubing in the Reynoldsnumber range extending from 3X10* to 7X10^.

A value for d of 145 would be satisfactory for

very good used irrigation pipe.

Poor Used Pipe

The only data located on aluminum pipe that

has had considerable use was in the thesis of

Olson.^^ These showed that the relationship

between / and Be followed the Colebrook-White

transition equation for rough pipe. The ^ value

turned out to be 0.0003 for the particidar piece

of pipe tested. Since this was a 4-inch-diameter

pipe, the absolute roughness value, e, woidd then

be 0.0012 inch. Therefore, the friction factor for

any other diameter of pipe having an interior

surface similar to the one tested could be estimated

by substituting this value of e and the pipe

diameter in the Colebrook-Wliite equation.

A study to determine the values of coefficients

for other formulas similar to the study on new

pipe was not attempted. It could be done for

selected values of e, the absolute roughness height,

if it were assumed that the Colebrook-White equation applies. The evidence indicates that it does

apply. However, in the absence of data relating e

to measurable or definable physical characteristics

of the interior pipe surface, the effort expended in

such a study would not seem justified. When

additional d^ta become available, such a study

could be made.

If research is undertaken to evaluate j^ for used

pipe, the value of € should be deternained ai^d

related to an adequate physical description of the

pipe. These tests could be made satisfactorily on

13 See footnote 2.

o

o

-\ \ \

s^i, 1

- N. \

S

k ^Oo7

\^ '

\^\^.

s

k

S X

" \x^ S

[sN

NXÓ

^^^

^^\ s

\

NX

X

- '^¿x^\ V \, \, \

- <:S\&X \, ^s

-

'•!

0!

Ç^. \^\,

\

\

- ^^X^ \

\

Ks 0.350

1

(Vd

1 ^

>

X

\

>

- ^/ z /

^\ 1

- QV' /

/

/^%. -

f ^f. 1/ y' /a.

>f

/

/

/ >v *

,>k.

r

^

1

-

^1/V.Y\ \ A.'sO> /// /

- ^TW /./ /

-

. 1*M4VV/

/'

-

3.0S

3.0-

-<

f -

^

f

\ i

/

/

n « (D.0082

1

9-i

V

1 1

I 2 4 6 10 20 40

PIPE DIAMETER - d - Inches

SCOBEY'S K2

PIPE

4 6 10

DIAMETER

20 40

d ^ Inches

2 4 6 10 20

PIPE DIAMETER - d -

MANNING'S n

40

inches

100

HAZEN-WILLIAMS C,

FIGURE 15.- -Coefficient values for pipe-flow formiilas by Scobey, by Manning, and by Hazen-Williams for

aluminum tubing with a relative roughness of 0,0002 and for a water temperature of 60° F.

DN-12S6

very good used

15
single 40-foot or even 30-foot lengths of pipe when

tests are made with precise measurements under

laboratory conditions. In any such experiments,

Keynolds number should reach at least 5X10^ in

order to get a good determination of €.

Formula Comparison

Should the need arise to compare coefficients for

different formulas, the diagrams (figs. 13 and 15)

would be helpful. The only way such a comparison

could be made is on the basis of like velocity and

like diameter. A study of these diagrams will

confirm this.

The question is sometimes asked: Which of the

pipe-flow formulas is best? All of the empirical

formulas are equally good. The accuracy of the

estimate—of head loss, for instance—will depend

on the ability to choose the correct coefficient.

The study of the three most common formulas has

indicated that the Hazen-Williams formula is less

sensitive to errors in coefficient selection and may

therefore be somewhat superior to the others.

Although the Hazen-Williams formula seems to

fit the data a little more accurately, the Scobey

formula is used more frequently. Therefore the

results of this study are summarized in a few

suggested values for Scobey's Ks (table 3).

TABLE 3.—Suggested values jor Scohey^s Kg for

aluminum tubing used in irrigation {without

couplers)

Diameter of pipe New pipe, Very good

smooth used pipe

Inches

8 0.30

.29

0. 31

4___ .31

6___ .28 .30

8--- .27 .30

10__ .26 .29

12__ .26 .29

The question is sometimes raised as to what

diameter should be used when calculating head

loss by use of formulas. Should it be the nominal

diameter or the actual inside diameter? The

diameter used in the determination of the coefficient should be employed in subsequent calculations which use the coefficient. The studies

reported here all used the true inside diameter of

the pipe in the coefficient determinations.

DISCUSSION OF COUPLER LOSS

The coupler head-loss coefficient was found to

vary considerably with the form of the coupler.

Gray's tests showed that the coefficient ranged

from 0.15 to 0.70 for 14 different makes, all of the

same size. The tests by Olson ^* showed that size

of coupler also affected the coefficient. One type

of coupler, designated as 5 in this report, at a flow

velocity oí 5 feet per second (f. p. s.) showed the

following loss coefficients:

Diameter of pipe, inches:

3

4

5

Loss coefficient

Ke

0. 11

. 15

.05

Willardson's tests ^^ also showed size to be a

factor. The coefficients for 2 sizes of 3 different

types of couplers are shown (table 4).

.TABLE 4.—Effect of size on the coupler coefficientfor

S different types of couplers

Type of coupler

Coefficient when diameter of

pipe was—

4-inch 3-inch

A. _ __ __ 0. 11

. 10

.016

0. 11

B . 17

C .062

Olson also found that the coefficient varied

with the velocity. The 4-inch coupler-loss coefficient ranged from 0.12 at 3 f. p. s. to 0.19 at 16

f. p. s. The results obtained by Gray {2) and

by Olson cannot be compared, since a common

type and size of coupler was not tested by each.

Once a coupler head-loss coefficient has been

selected, the next problem is to introduce it into

the calculations. One suggested method is to

add an amount to the pipe friction factor so that

coupler head loss will be included in the friction

head-loss estimate. Equivalent values of Scobey's

Ks for the coupler loss can be determined by

using the following equations:

Head loss for 1 coupler is

Total head loss for couplers on a line of length L

and a spacing S is

Therefore, the equivalence sought is

y2 L F-

^^ See footnote 2.

1^ See footnote 4.

S^' 2g ^'IflOOD'-'

By using algebra and by assuming a water

temperature of 60° F., this is reduced to

16
Thus, the equivalent value of Scobey^s Ks depends

not only on the coupler coefl&cient but also on the

coupler spacing and the pipe diameter.

Values of equivalent Ks have been calculated

for a Reynolds number of 10^ and are presented

(table 5).

TABLE 5.—Equivalent values oj Scobey^s K^ for

coupler-loss coefficients K^

Spacing Diameter

of pipe

Equivalent Ks

(feet)

When When

Zc=0.2

When

Kc=O.S

20

30

40

20

30

40

20

30

40-_

Inches

3

3

3

6

6

6

12

12

12

0.02

.01

.01

.04

.03

.02

.08

.05

.04

0. 04

.03

.02

.08

.05

.04

. 16

. 11

.08

0.06

.04

.03

. 12

.08

.06

.24

. 16

. 12

A comparison of these values with Scobey's Kg

for pipe friction loss will indicate the relative

importance of coupler head loss in the flow.

Also, this table shows the special need for hydraulically efficient couplers in the larger diameter

pipe lines.

The tests of Gray, Olson, and Willardson were

all made without flow through the coupler sprinkler

outlet. The results therefore are limited to direct

application to mains or other lines without side

outlets. The experiments by Benami ^^^ and

Buhr ^^ were conducted with flow through the side

outlet. Buhr presented his results in the form

of pressure rises across the outlets. Benami

separated the turbulence loss from the pressure

rise due to velocity-head change and thus derived

the coupler-loss coefficients. Benami's work was

especially interesting, because he showed that the

coupler-loss coefficient varied with the flow, and

with the ratio of the flow diverted at the outlet

to the flow of the approaching stream.

The research on couplers to date has been of

great help in estimating coupler losses, as it has

provided data where none were available heretofore.

At the same time, however, such research has

indicated that a number of variables affect the

coupler-loss coefficient, thus introducing new

problems and questions. More data are needed;

and simpler methods of applying the data already

obtained to design problems in the field are

required.

ï5a See footnote 5.

Iß See footnote 9.

DISCUSSION OF HEAD-LOSS TABLES NOW IN USE

The literature of the irrigation industry ^^ has

been examined. Head-loss tables in these

publications have been compared. Comparative

values for 1 pipe size—4-inch-diameter—are given

in a composite table (table 6).

A study of the following table shows the

various sources to be in fair agreement. The

comparison, however, raises questions. The first

question concerns the discrepancies in the descriptive material provided for column 1 of the

table. None of the four sources using the identical

table agree exactly on the conditions or kind of

coefficient. A check calculation showed that

the values in this column were calculated by use

of Scobey^s formula with Ks=0.32 and an inside

diameter of 0.323 feet (this is 4-inch O. D. tubing

with a wall thickness of 0.063 inch).

Another question raised is whether a Scobey's

K of 0.32 includes pipe coupler loss. If the pipe

is hydraulically smooth, coupler loss must be

included to bring head loss up to the tabular

values. If the pipe is rough (relative roughness

0.0003), a small coupler loss must be added. This

is discussed further in the next section.

17 The mention in this publication of a trade product or

its manufacturer does not imply its endorsement by the

U. S. Department of Agriculture over similar products or

manufacturers not named.

TABLE 6.—A comparison of values of head loss (in

feet per 100 feet of pipe) for portable sprinkler

pipe for Jf.-'inch 0, D, aluminum tubing

Rate of Loss reported according to source reference i

flow (gallons per

minute) (1) (2) (3) (4) (5)

Feet per Feet per Feet per Feet per Feet per

hundred hundred hundred hundred hundred

feet feet feet feet feet

20 0.04 0.03 a 04 0.04

30 .08 .07 .08 .08

40 . 13 . 11 . 13 . 13

50 .20 . 18 .20 . 19

60 .28 .25 .3 .27

70 .38 .34 . 4 .37

80 .49 .44 .5 .48

90 .60 .54 . 6 .58

100 .74 .66 .7 .72 Ö. 92

120 1.06 . 95 1.0 1.03

140 1. 41 1.27 1.4 1.37

160 1. 82 1. 64 1.8 1.77

180 2.27 2.04 2.2 2.20

200 2. 78 2. 50 2. 7 2. 70 3.00

220 3. 31 2. 98 3. 2 3. 21

240 3.91 3.52 3.8 3.79

260 4.56 4. 10 4.4 4. 42

280 5.26 4. 74 5. 1 5. 10

300 5. 98 5. 38 5. 8 5.80 6.24

See footnote at end of table.

17
TABLE 6.—A comparison of values of head loss (in

feet per 100 feet of pipe) for portable sprinkler

pipe for 4'ii^ch 0, D, aluminum tubing—Con.

Rate of

flow (galLoss reported according to source reference *

lons per

minute) (1) (2) (3) (4) (5)

350

400

450

500

550

600

650 _

Feet per

hundred

feet

8.03

10. 36

12.90

15.73

19. 12

22.46

26.10

Feet per

hundred

feet

7.23

9.35

Feet per

hundred

feet

7.8

10.0

12.5

15.3

18.6

21.8

25.3

Feet per

hundred

feet

7. 79

10.5

12.51

15.26

18.55

21.79

25.32

Feet per

hundred

feet

8.32

10.40

13. 17

15.94

22.64

25.87

^ISources are as follows (the data in each instance are

accompanied by the explanatory material given) :

Column 1.—The data in this column are from the

following four sources:

Buckner Manufacturing Co., Inc,

Pipe with couplers. Hazen-Williams formula with

C=120.

National Rain Bird Sales & Engineering Corp,

Pipe with couplers. Wall thickness, 0.063 inch.

Scobey formula with iir,=0.32 inch.

Irrigation Equipment Co, ISteelume]

Pipe with couplers.

Sprinkler Irrigation Association

Pipe without couplers. Scobey formula with

ir.=0.32 inch.

(Note that the three sprinkler companies state that

the table is for pipe with couplers, whereas the

Sprinkler Irrigation Association specifies the same

values for pipe without couplers.)

Column 2.—Food Machinery and Chemical Corp., John

Bean Division [Shur-Rane Manual]

Pipe with couplers. Wall thickness, 0.050 inch.

Column 3.—Irrigation Equipment Co., Inc.

Pipe with couplers. Scobey formula with Ks—0.Z2

inch.

Column 4.—Miller and Boston Mfg. Co.

Pipe with A-M coupler. Wall thickness, 0.063 inch.

Scobey formula with JK'S=0.32 inch.

Column 5.—Olin Mathieson Chemical Corp,

Table values were given in pounds per square inch.

These have been converted to feet for this tabulation. The corporation advises that the figures do

not in any way reflect the friction loss of Olin

Mathieson pipe with couplers, but are presented

purely as a guide to cover pipe with couplers in

general.

HEAD-LOSS TABLES CALCULATED FROM AVAILABLE DATA

By using the data from the experiments described in the preceding section, head-loss values

were calculated for 4-inch aluminum tubing

(table 7). Extreme variations were used in

these calculations in order to arrive at an estimate

of what could happen. All calculations in this

table are based on an inside pipe diameter of

0.323 feet. This is 4-inch tubing with a 0.063-

inch wall thickness.

A study of table 7 shows that calculations

based on present industry usage (column 7) are

conservative when compared with estimated

minimum loss (column 5). When compared with

a condition approaching a maximum coupler loss,

however, values from present tables fall appreciably below actual loss. For a flow rate of 200

gallons per minute (g. p. m.),^^ the low and high

conditions of head loss range from 2.54^0 4.53 feet

per hundred feet, when compared with industryusage calculation of 2.78 feet per hundred feet.

The high head-loss condition assumes that couplers

are located at 20-foot intervals, with a 12° deflection

at each joint. Such crooked alinement seems

absurd, but it is included to show what is possible.

18 This is a velocity of 5.4 feet per second (f. p. s.) in a

4-inch tube, which is an upper limit for good design.

Velocities of 10 f. p. s., however, are sometimes used.

It may account for some of the difliculties experienced in the field. Even with a straight alinement, however, the coupler chosen would give a

total head loss of 4.21 feet, which is still considerably higher than the industry standard.

If the minimum coupler loss were added to the

rough-pipe loss, the resulting total head loss would

be nearly equal to the industry standard. These

figures, however, are not included in this comparison.

Inasmuch as no great difference in head loss exists

between the smooth pipe and the rough pipe up to

flows of 200 g. p. m., it seems that pipe condition

may not be the most important factor contributing to errors in head-loss estimates. Instead, it

appears that the inaccuracies occur largely in

estimates of coupler loss. Further study on the

subject of coupler loss could be undertaken

profitably.

One determination of friction loss in a used pipe

is an inadequate basis for general conclusions.

Additional work should be done to determine the

pipe friction characteristics of corroded and dented

pipe and to correlate pipe condition with friction

factor. A study relating degree of pipe deterioration to time and conditions of usage would also be

helpful.

18
TABLE 7.—Calculated head loss (in feet per 100 feet of pipe) for various pipes, couplersj and combinations

for ^'inch 0. D, aluminum tubing ^

Rate of flow

(1)

Smooth pipe,

no coupler

(2)

Rough pipe,

no coupler

(3)

Minimum

coupler loss

(4)

Maximum

coupler loss

(5)

Smooth pipe

plus minimum

coupler loss

(6)

Rough pipe

plus maximum

coupler loss

(7)

Present industry usage

Gallons per minute

20._._

30

40

50

60

70 ..

80 .__

90

100

120

140

160

180

200._ _

220

240

260

280

300

350.._

400

450

500

550

600

650

Feet per

hundred feet

0.04

.08

. 13

.20

.27

.36

.46

.57

.68

.95

1.25

1.59

1.96

2.37

2.82

3.29

3.79

4.31

4.88

6.47

8.26

10.21

12.36

14.68

17.23

19.93

Feet per

hundred feet

0.04

.08

.13

.20

.28

.37

.48

.59

.71

1.00

1.33

1.72

2. 14

2.61

3. 13

3.68

4.27

4.92

5.62

7.51

9.73

12. 15

14.85

17.68

20.80

24.30

Feet per

hundred feet

0.01

.01

.02

.02

.03

.04

.04

.06

.08

. 11

. 14

. 17

.21

.25

.29

.34

.39

.53

.69

.87

1.08

1.30

1.54

1.81

Feet per

hundred feet

0.02

.04

.08

. 12

.17

.24

.31

.40

.48

.69

.94

1.23

1.56

1.92

2.33

2.77

3.25

3.77

4.33

5.88

7.71

9.74

12.05

14.52

17.30

20.32

Feet per

hundred feet

0.04

.08

. 14

.21

.29

• .38

.49

.61

.72

1.01

1.33

1.70

2. 10

2.54

3.03

3.54

4.08

4.65

5.27

7.00

8.95

11.08

13.44

15.98

18.77

21.74

Feet per

hundred feet

0.06

. 12

.21

.32

.45

.61

.79

.99

1. 19

1.69

2.27

2.95

3.70

4. 53

5.46

6.45

7.52

8.69

9.95

13.39

17.44

21.89

26. 90

32.20

38. 10

44.62

Feet per

hundred feet

0.04

.08

.13

.20

.28

.38

.49

.60

.74

1.06

1.41

1.82

2.27

2.78

3.31

3.91

4.56

5.26

5.98

8.03

10.36

12.90

15.73

19. 12

22.46

26. 10

1 Column 1 gives the head loss in feet per 100 feet of new

or nearly new pipe. The value of friction factor was taken

from the smooth-pipe curve. The evidence indicates that

the smooth-pipe curve is the appropriate one to use for

this condition.

Column 2 gives the head loss in a used pipe similar to

the one tested by Olson (p. 5). This pipe was indicated

to be corroded and dented.

Column 3 gives the head loss in feet per 100 feet of pipe

contributed by the couplers for a probable minimum

condition. This is 1 coupler every 40 feet, with no

deflection at the joint and with the loss coefficient assumed

to be 0.15, the minimum found by Gray (p. 9).

Column 4 gives the coupler loss per 100 feet of pipe for

a maximum loss condition. This calls for 1 coupler every

20 feet, with 12° deflection at the joint, and with the loss

coefficient assumed to be 0.84, the maximum found by

Gray (p. 9).

Column 5 gives the sum of columns 1 and 3. This is the

estimated minimum head loss in feet per 100 feet of quickcoupled 4-inch aluminum tubing.

Column 6 gives the sum of columns 2 and 4. This is an

estimate of a possible high head loss in feet per 100 feet of

quick-coupled 4-inch aluminum tubing. This is not

necessarily a maximum.

Column 7 is identical with column 1 of table 6 and is

included for comparison.

FLOW IN A LINE WITH MULTIPLE OUTLETS

Another possible source of error in estimating

flow in a sprinkler system is the use of approximate

solutions for estimating head loss in a line with

multiple outlets. The method most used is the

one devised by Christiansen and involves the use

of an F factor. This method has been described

in a previous section (p. 2). To test this possibility, a pressure grade line was calculated in an

assumed line by using more exact methods. The

line chosen was a 4-inch aluminum line with risers

located every 30 feet for a total of 20 risers. The

coupler losses were assumed to be what Benami^s

test indicated. The calculation showed the friction loss to be 4.12 feet. This compares with 4.25

feet estimated by the use of Christiansen's F

factor. This close agreement is not surprising

since the sprinkler discharge varied only 2 percent

from the downstream to the upstream riser.

Under average conditions, therefore, the approximate method is sufficiently precise for determining head loss in a line with multiple outlets. It

was also found that the sum of the theoretical

pressure rises across the sprinkler outlets equaled

the approach velocity head.

19
CONCLUSIONS AND RECOMMENDATIONS

A study of available information on head loss

in quick-coupled aluminum pipe in sprinkler

irrigation systems has resulted in the following

conclusions.

1. New aluminum tubing is smooth pipe.

The relationship between the Darcy-Weisbach

friction factor, /, and Reynolds number, Re, is

given by the Karman-Prandtl equation

-^=2 1ogioÄ.V7-0.8.

Between Reynolds number of 10* and 10*^ and for

a water temperature of 60^ F., this equation can

be^satisfactorily approximated by the equation

T7-1.79

^^=0.0002951: ^î:^-

2. Very good used aluminum tubing is hydraulically rough, but of a low order of roughness.

The relative value of -^ in the Colebrook-White

equation is 0.0002. The head loss in this kind

of tubing between Reynolds numbers 3x10*

and 7x10^ is approximately

iZ"^=0.000309L V

n

3. By using the equations given in items 1 and

2, the values of the coefficients for the commonly

used pipe-flow formulas can be calculated. Diagrams giving the values for the Scobey, Manning,

and Hazen-Williams formulas are provided in

this report.

4. Suggested values of Scobey's Ks for new pipe

and very good used pipe are given (see table 3).

5. A 40-foot length of used 4-inch aluminum

tubing described as corroded and dented had a

relative roughness of 0.0003. This is the ratio

y^ in the Colebrook-White equation.

6. The tests on quick couplers show loss coefficient values ranging from a low of 0.02 to a

high of 0.84. The values depend on the make of

the coupler, the size of the pipe, the alinement of

the pipes joined at the coupler, and the velocity

of the flow.

7. Coupler loss in a pipeline can be expressed

in terms of an equivalent Scobey K^, Values

are given in table 5.

Recomendations for future testing of irrigation

pipe and fittings are as follows;

(1) Tests should be directed first toward

evaluating coupler losses and losses in

other fittings. The errors in estimating

such losses will likely be greater than the

errors in estimating pipe friction losses.

(2) Used pipe should be tested. These tests

can be made on 30- or 40-foot lengths.

Reynolds numbers of at least 5x10^

should be reached, to get a good determination of the roughness characteristic,

€. This roughness characteristic should

then be carefully correlated with the

physical condition of * the pipe.

(3) Consideration should be given to making

careful measurements of a few irrigation

systems in the field.

LITERATURE CITED

(1) CHRISTIANSEN, J. E.

1942. IRRIGATION BY SPRINKLING. Calif. Agr,

Expt. Sta. Bui. 670, 124 pp., illus.

(2) GRAY, H. E., LEVINE, G., and BOGEMA, M.

1954. FRICTION LOSS IN ALUMINUM PIPE. Agr.

Engin. 35: 715-716, illus.

(3) LEVINE, G., and BOGEMA, M.

1954. HEAD LOSS IN IRRIGATION-LINE QUICK COUPLERS. Agr. Engin. 35: 804-807, illus.

(4) KING, H. W.

1954. TURBULENT FLOW IN PIPES. In his Handbook of Hydraulics for the Solution of

Hydraulic Problems, ed. 4, revised by

E. F. Brater, sect. 6, pp. 8-12, illus.

(5) SoucEK, E., and ZELNICK, E. W.

1946. LOCK MANIFOLD EXPERIMENTS. Amer. Soc.

Civ. Engin. Trans. (1945) 110: 1357-1400,

illus. (Includes discussion from p. 1377.)

(6) SPRINKLER IRRIGATION ASSOCIATION.

1955. SPRINKLER IRRIGATION. Comp. and ed. by

A. W. McCullock and J. F. Schrunk.

466 pp., illus. Washington, D. C. [Processed.]

o

20