80
YDRAUL CTABLES '
SHOWING THE L OSS OF HEAD DUE
THE FR ICTION OF WATER FLOWING IN
P IPES,AQUEDUCTS , SEWER S
,ETC.
AND
THE D ISCHAR GE.
OVER WEIR S
GAR D NE R S . WI LL IAM S , M . AM . S oc . C . E .
of Civil, S anitary and Hydraulic E ngineei"mg, University of Michigan
A ND
ALLE N HA!EN,M . A M . S OO . 0 . E .
Civil E ngineer
F I R S T E D I T I ON
FI R ST THOU SAND
NEW Y ORKJOHN WILE Y SONS
LONDON : CHAPMAN HALL ,L IMITED
1905
CONTENTS .
FORMULAINCREASING FRICTION WITH AG E
,HOW COM PUTED
, AND IND ICATED IN THETAB LESOB SERVATIONS O F FLOW IN CAST-IRONRIVETED S TEELWOODEN-STAVERECTANGULAR WO ODEN PIPE .CEMENTWROUGHT-IRONGALVAN I!ED-IRON PIPE .
B RASS PIPEL EADGLASSFIREOPENB RICK
F FL OW IN SMALL B RASSWROUGHT-IRONHO SE AND P IPES .
PIPES,4”
To 144
AQUEDUCTS , RELATIVE D ISCHARGING CAPACITY OF.TAB LE OF FLOWRS,TAB LE O F S LOPES REQUIRED TO PRO DUCE CERTAIN VELO CITIE S .SEWE R TAB LE .
B R ICKS E WE RREASE IN CARRY ING CAPACITY OF CAST-IRON PIPE WITH AGE .
N OF RESULTS WITH THO SE OF COFFIN AND WESTONPE TAB LE .
n o 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0
0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
kl
INTR ODUCTION.
THE following tables Show the fl ow of water in pipes and other passages,as computed by the Hazen—Williams hydraulic slide-rule , basedupon the formula
v
The most commonly used formula for determining the velocity of
flow of water in pipes and channels is the Chezy formula , namely,
where v is the velocity in feet per second , 3 is the hydraulic slope , andr the hydraulic radius in feet . 0 is a factor the value of which is anapproximat ion to a cons tant
,but depends upon the roughness of thepipe and upon the hydraulic radius and Slope . The variations in thevalue of c are considerable
,and make the general use of the formuladifficult .
Kutter ’s formula w as devised to compute the value of c in the Chezyformula . The value of c so computed depends upon an assumed coefficient of roughness , upon the slope , and upon the hydraulic radius . Withthe same degree of roughness the value of 0 increases with the hydraulicSlope and with the hydraulic radius . This is because the exponents usedfor these terms in the formula are below the true values . I f the exponents were increased to correspond more nearly with the facts
,the variations in the value of c would become less . I f exponents could be selected
agreeing perfectly with the facts,the value of c would depend upon the
roughness only , and for any given degree of roughness 0 would then be
however,
representing approximately average conditions,so that the value of cfor a given condit ion of surface will vary so little as to be practicallyconstant . Several such “exponential ” formulas have been suggested .These formulas are among the most satisfactory yet devised , but their
use has been limited by the difficulty in making computations by them .
2 INTRODUCTION.
This difficulty was eliminated by the us e of a slide-rule constructed forthat purpose .The exponents in the formula used were selected as represent ingas nearly as possible average conditions , as deduced from the best available records of experiments upon the fl ow of water in such pipes andchannels as most frequently occur in water-works practice . The lastterm,
-0-04,is a constant
,and is introduced simply to equalize thevalue of c with the value in the Chezy formula
,and other exponentialformulas which may be used , at a slope of instead of at a slope of l.The slide-rules were furnished by Mr . G . G . L edder
,9 Province
Court,Boston
,Mass
,the work being done in Germany . Suitable scaleswere laid out and the posit ionof each graduation w as computed tomillimeter . The drawings were then engraved upon steel and reproducedupon slide-rules of the general Size and appearance of the ordinary 10inch Mannheim rule . The graduat ion is very perfectly done
,and theaccuracy obtained is pract ically that which can be secured with the
ordinary Slide-rule of this size .All the computations of figures contained in this volume,except afew fundamental rat ios
,have been made with the slide-rule
,and onlysuch acc’uracy has been sought as can readily be obtained by thismethod of computation .This formula has been used by the authors for some t ime , and it ishoped that the tables will be useful to those not accustomed to the use
of the slide-rule , and also to those who use the slide—rule , as a referenceshowing velocit ies and velocity heads,and establishing beyond questionthe posit ion of the decimal point
,which is the most troublesome featurein the use of the sl ide-rule to beginners .These tables are not confined to a single value '
of the coefficient ofroughness,which is called 0 . Instead
,a series of values of c is given inthe various Columns
,and under each are placed the corresponding losses
of head . The headings also indicate in a general way the class of pipefor which the part icular coefficient should be used , but these indicationsare only general
,and it is the intention to leave the matter so that users
can select such values of c as in their judgment irepresent the part icularconditions upon which they are figuring .The gradual roughening of the interior of cast— iron pipe is one of themost familiar of water-works phenomena . It is also one of the mostdifficult to compute . I n a general way it may be said that in a seriesof years , which is not long compared with the total life of the pipe , theroughening of the surface and the reduction of the area through rustingand tuberculation reach such an extent that twice as much head isconsumed in sending a given volume of water through it as was the caseWhen the pipe w as new .
In a particular set of foreign tables , based on the Darcy formula,
INTR OD UCTHD I 3
the loss ~of head is given for new pipe , and in the second column,desig
nated old pipe , a figure twice as large is given . This has certain advantages over a table of factors to be applied to pipes of different ages,as
has been done in several American publicat ions , because it is less apt tobe forgotten;and while it is a crude pre '
cedure,it keeps in mind thefact that old pipe will pass very much less water than new pipe .
In this volum e effort has been made to put this subject in bettershape . It is a difficult matter to handle adequately , for no two piecesof iron pipe deteriorate at the same rate , and any figures given aretherefore at best only approximat ions to averages , which averages maybe very far from individual cases .The system used is to put certain figures surrounded by circles overthe columns . This mark was adopted because no words could be foundsufficiently concise and at the same t ime accurate . Over the columnfor c= 140 are placed tw o ze I OS in a circle :@ That indicates that thiscoefficient is obtained with the very best cast-iron pipe , laid perfectlystraight
,and when new . Over c= 130 Is placed one zero in a circle GI) ,and this is the value that can be fairly counted on for good new castiron pipe . Over the following columns are placed figures in circles .These figures Show the age in years at which
,on an average
,as nearlyas we know
,cast-iron pipe will reach the values given in the columnunderneath . It must be understood that these are necessarily ‘veryrough approximations, based on the best data available
,which are prin
cipally for soft and clear but unfiltered river-waters . Hard waters andlake waters will often attack the pipe less rapidly,and the figures mustthen be increased . Somet imes they must be mult iplied by two or more .
Other waters will corrode the pipes more rapidly than the average,and
for them the values will be reached more quickly than the figures indicate .The divergence with different castings and with different kinds ofwater is greatest in the smallest pipes,and no attempt is made to extendthe figures in the circles to the s izes below four inches in diameter .Steel pipes tuberculate and corrode in much the same manner ascast-iron pipes . On iaccount of the rivets and in—and-out joints theaverage value of c is lower than for cast-iron pipe . The data at handindicate a value of 110 for new pipe
,decreasing in the course of aboutten years to 100. For older pipes
,as far as the present data go , steelpipe of a given age will carry the same quantity of water as cast-ironpipe of the same size '
and ten years older .
On the Value of c .
-I n the E ngineering R ecord of March 28 , 1903,w as published by the authors a table of the values of c computed frompublished experiments upon the friction of water in pipes and conduitsof various kinds
,the results being selected as the most reliable availabledata . This table , with some addit ions , is as follows :
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8 INTRODUCTION.
In a general way it may be said that for cast-iron pipe,very straight
and smooth , c may be as high as 140,but for ordinary conditions 130
is a fair value for new pipe . As pipes rust and become dirty,the valueof 0 decreases
,as has been mentioned above . For ' new riveted steelpipe 0 is about 110.
In making estimates for pipe-lines where the carrying capacity aftera series of years,rather than the value of the new pipe
,is the controllingfactor
,a considerably lower value of 0 must be used
,depending upon
the amount of deterioration which is contemplated . A fair value forgeneral computation is c= 100 for cast-iron pipe and c= 95 for steel ?pipe,but for small iron pipes a somewhat lower value of c should
'
be
taken . In the pipe tables the column of slopes for-e= l00 is printedin heavier-faced type than the rest
,
‘
as these values are the oneswhich will probably be most often required . L ead,brass
,t in
,andglass
,and Other pipe presenting perfectly smooth surfaces
,and per
fectly straight,will give values of 0 up to 140. A very little falling
off in the smoothness will reduce the value of c to 130 and 120,oreven less . For smooth wooden pipe or wooden-stave pipe 120 seems afair value . For masonry . conduits of concrete or plastered
,with verysmooth surfaces , when clean , values of c= 140 may be observed . Gen
erally such surfaces become slime—covered , reducing the value of c to130 or less in a moderate length of time;and if the surfaces are only alittle less smooth
,say
.in such shape as ' is represented by ordinary goodwork
,the value of c is reduced to 120. A conservative value for general
use with fi rst-class masonry structures is about 120. For brick sewersmuch lower values may be used , and c= 100 seems safe . For vitrifiedpipe c= 110 may be used . It must be understood that these values depend entirely upon the smoothness and regularity of the surfaces , and ‘
are likely to vary in individual cases .This formula w as designed primarily for computing the flow of waterin pipes . It seems reasonably well adapted for computing the flow inopen channels,and the slide-rules have been made so as to allow t hisapplicat ion . A table has been prepared to show the applicat ion of thisformula to the most reliable experiments upon open channels . Fromthe data therein presented the investigator may determine for himselfthe probable accuracy to be obtained and the value of c which should beused in a given case .
4
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14 INTRODUCTION.
No tables to Show the application of these results, that is to say,tables corresponding to the pipe tables , have been made for Open channels . The variations in the conditions of depth , width , slope and character of bottom and sides are so enormously great that solution of eachparticular problem by the use of the slide-rule is the only practical wayof handling the subject .The slide-rule w ill also be found more closelyapplicable to actualconditions in pipes than any tables , because it gives at once values forconditions falling between the values w hich it is ‘ practicable to show inthe tables , and its use is therefore to be recommended in all cases whereclose computations are desirable.
SMA L L B R ASS PIPE S .
c 130.
Gallons Loss of Head in Fee t per 1000 fe e t of length .Dailyfor v 1
Ft . perSecond . v=0.5’
v= 1 .0’
v= 2 .0’
v=3.0’
v= 5 .0’
4700 7050 9400 1 1 700
2620 5250 6600
1680 2529 3370 4350
11 70 1 750 2340 3520
215 1930 2950
105
11 . O 40
36
34
31
2 . 23 29
27
26
1 . 85 6 7 24
1 .65 21
19
t’
(temperature) is taken as 50° F.
1 5
NominalSize ,
Inches .
2
1
ActualDiame te r ,Inches .
Discharge inPe t
allons .Per 24
Minute . Hours .
7-4 OCD
OO
Q
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mt-P
OO
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H
05
01
1-t
12
15
20
288
576
864
720
ELI GO
51880
51600
51880
42320
51760
73200
11 ,520
SMAL L PIPE .
Ve locity ,Fe e t perSecond.
mp
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. 16
. 70
. 05
. 10
. 16
. 21
. 26
.31
.37
42
. 47
52
7 .
9
2
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. 02
.03
WR OU GHT-I R ON-PIPE S I!E S .
Loss of Head in Fee t per 1000 fee t of length.SmoothNe wIron .
c= 120
44
158
335
570
860
250
56
200
425
730
1l00
46
167
OrdinaryIron .
c 100
62
220
470
1210
78
280
1030
1530
64
233
1360
OldIron .
c=80
94
335
710
1210
1830
118
4309 10
1550
2320
97
350
800
1220
2060
158
570
1210
2050
3100
200
730
1540
2600
4000
165
600.
1260
1370
2030
NominalSize ,Inches .
Actua lD iame te r ,Inches .
WROUGHT—IRON-PIPE S I!E S .
Discharge ina 0 118 .
Per Pe r 24Minute . Hours .3 <L32O
4 EL760
,5 73200
6
8
10
12
14
16
18
20
25
30
35
40
20
25
30
35
40
50
60
70
80 1
90
SMAL L PIPE .
Ve locity ,Fe e t p e rLoss of Head in Fee t per 1000 fee t of length.
Ve rySe cond . Smoo th
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. 86
. 23
. 98
. 72
. 46
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. 9 5
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. 36
. 43
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. 58
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30
anStraight .c= 140
6.
1 1 .
17 .
24 .
426
01
01
01
00
‘ 63
88
1 17
150
185
226
340
480
640
820
60
89
126
168
214
325
450
610
780
960
SmootheW
Iron .
c= 120
N
H
[0
00
01
0
CH
M
M
O
00
84
1 17
155
200
250
301
455
640
850
1090
79
1 19
169
223
285
432
610
8 10
1030
1280
OrdinaryI ron .
3-100
78
117
164
220
280
350
420
640
890
1520
111
166
235
312
850
1130
1450
1800
OldIron .
c=80
69
1 17
177
250
330
420
520
640
960
1350
2300
168
25 1
358
470
610
920
1290
1700
2200
2700
Ve ryRough.
c=60
32
55
84
117
200
300
420
560
720
890
1090
1640
2300
3080
3900
286
430
610
800
1030
1560
2200
2900
3700
4600
li-INCH VVR OU GHT-IRON PIPE .
(Actual D iamete r ,D ischarge in Gallons . Loss of Head in Fe e t per 10001 ee t of length
Ve e per ery Smoo th OrdinaryM ilrii
r
te . r
25
4Second . S l
él
t
o
rzt
ighifmNe w Iron . Iron . Iron .
c = 140 c = l20 c= 100 o=80 c=60
5
6
7 1 1 2
8
9
10 ‘
12
14
16 52
18 2 83 42,4 64
20 37 52 78
22 44 62 93
24 52 73 108
26 45 . 1 60 84 127
28 52
30 59
35 78
40 100
45 124
50 152. 202
5 5 181 240
60 212 28 1
65 246 328
70 1 1 . 02 282 376
75 1 1 . 80 321
80 361
85 405
90 450
9 5 498
100 15 74 5 50 730 1020 1540
1 10 650 870 1220 1840
120 770 1020 1430 2170
130 890 l 180 1660 2500
140 201 ,600 22 .04 1020 1360 1900 2880
Discharge inGallons .
.
Pe rMinute .
10
12
14
16
18
20
25
30
35
40
45
50
55
60
65
70
75
80
90 .
100
1 10120
130
140
150
160
170
180
190
200
220
240
260
Pe r 24Hours .
144 000
Veloc:ity inFe e tperSecond .
7 15
7 66
9 19
10 21
1 1 23
12 25
13 28
14 30
15 32
16 34
17 36
18 38
2-INCH PIPE OR HOSE .
(Actual diameter , ins . )
. 04
. 05
. 06
. 10
. 15OOOOO
. 20
. 26
.33
. 40
. 490
0
0
0
0
. 58
.68
. 79
. 9 1
04H
O
O
O
O
. 31
.62
. 96
.33
. 73M
w
h—‘
l—li—K
. 17
.64
. 14
.67
. 2301
9
19-00
00
. 84
.46
. 82
.31
. 90O
QO
fl
Gb
Cfl
1
Ve rySm oo thandStraightBrass ,
Tin , etc .
14 .
20 .
27 .
35 .
53
64
74
86
99
1 13
127
158
192
230
271
312
360
407
460
520
570
630
690
830
980
1 130
Ordinary SmoothStraightBrass ,
Tin , etc .c= 140 c= l30
1 1 .
23
31
40 .
50
61
73
86
99
1 14
129
146
182
220
262
310
360
413
465
530
590
650
720
800
950
1 120
1290
CO
KI
.
CJ‘l
b-P
OO
N
H
OO
OD
H
O
N)
00
03
89
10
44
01
Ne w
Iron .
c= 120 c= 100
05
01
03
10
14
n
o
os
un
m
12 .
19 .
27 .
36.
46.
58
71
84
99
115
132
149
169
210
256
306
360
418
479
540
610
690
760
840
920
11 10
1300
15 10
00
01
d
63
27
38
139
161
184
209
237
294
358
429
500
580
670
760
860
960
1070
1180
1290
1540
1820
2110
Iron .
o=80
10 .
14 .
18 .
22 .
27 .
41 .
58
99
123
150
179
210
244
280
318
358
447
540
650
760
880
1020
1 140
1290
1460
1620
1780
1960
2340
2760
3190
to
xi
' cv
b
O
OT
Q
NJ
12 .
18
24
30.
38 .
46.
71
99
132
168
210
257
305
359
416
477
540
610
760
920
11 10
1300
15 10
1730
1950
2210
2480
2730
3030
3330
3990
4700
5400
Loss of Head in Fee t per 1000 fee t of length .
c=40
10 .
18
27
38
5 1
66
82
99
150
210
280
359
446
540
640
760
880
1010
1 150
1280
1610
1960
2330
2760
3190
3670
4180
4690
5300
5800
6400
7100
8400
9900
1 1500
01
15
i0
~1
Discharge inallons .
Per
Minute.
10
12
14
16
18
20
25
30
35
40.
50
60
70
80
90
100
120
140
160
180
200
220
240
260
320
340
360
380
400
420
440
460
Per 24Hours .
1
144,000
201 ,600
In
Velocit inFie tperSe cond
. 52
.65
. 78
. 92
.05H
O
O
O
O
. 18
.31
.63
. 96
. 29N
H
H
l—‘H
.61
. 27
. 92
. 58
. 2301
115
00
03
6)
5 88
. 76
. 07
. 38
.69
. 99
13
14
15
16
18
19
20
22
23.
.30
.61
. 92
. 22
53
2%-INCH PIPE OR HOSE .
(Actual diamete r, ins . )
Ve lceHead ,Feet .
. 00
. 01
01
01
. 02OOOOO
. 02
. 03
. 04
. 06
. 08OOOOO
. 1 1
. 17
. 24
. 33
. 43©0
0
0
0
54
66
95
. 30
70H
H
O
O
O
. 15
.66
. 22
. 82
. 4815
021
00
89
10
. 20
. 98
. 80
.68
.6000
x1
©01
01
Ve rySmootanStraight
B
hLoss of Head in Fee t. per 1000 fee t of lengthOrdinary SmoothStraight Ne w
Iron .
OrdinaryIron .
c= 140.
c= 130 c= 120 c= 100
0
11 .
17 .
24 .
33.
42 .
53
64
90
120
156
1 9 1
232
277
330
378
432
493
560
620
690
780
840
920
1000
11 10
. 9
O‘I
M
CO
OO
OO
318
1150
1260
12 .
15
23.
33.
44 .
254
l 1201220
1330
1460
w
moo
ki
357
431
520
610
700
810
920
1030
1710
2050
O ldIron .
c=80
own-oo
to-H
N
fl
ob
c'b
xl
13.
19 .
26.0
01
0
10
01
33
5 1
70'
94
120
149
182
254
339
440
540
660
780
920
1070
1220
1390
1570
1750
1940
2160
2370
2590
2810
3100
Very .
R ough .
o=60
10 .
12 .
15:
23.
57
86
120
1601
204
254
309
433
580
750
920
1120
1330
1570
1810
2080
2370
2670
2980
3310
3670
4020
4400
4800
5300
culated.
C=40
H
H
w
q
w
co
c»
N
A
QD
NJ
H
N)
50
70
94
120
182
254
338
433
540
660
920
1220
1570
1940
2370
2820
3340
3860
4400
5000
5700
6400
7100
7800
8600
9300
10200
11200
D ischarge in.
Per
Mmute .
20
25
30
35
40
50
60
70
80
90
100
120
140
160
180
450
500
5 50
600
650
700
750
800
850
900
OD S
Veloc1ty mFe e t
Pe r 24Hours .
H
O
O
O
O
M
M
P—‘H
H
10
144
00
00
10
1 1
12
14
15
16
17
19
20
21
22
perSecond5 1
64
77
89
02
28
53
79
04
30
55
06
57
08
60
49
77
04
32
59
87
15
42
70
98
OOOOO
OOOOO
0
0
0
0
5
04
00
10
10
WQ
O
CR
D-P
00
01
01
01
02
03
04
05
06
. 08
15
20
26
33
05
53
06
65
28
4-INCH PIPE .
107
153
181
209
240
272
308
343
382
Loss of Head in Fee t per 1000 fee t of length.
(9 69c= 120 c= l00
[0
q
ua
o
q
40
0
01
01
122
148
177
207
240
276
312
352
395
439
l—‘I—‘O
O
O 38
. 58
81
07
.38
. 08
. 9 1
H
H
O
O
O
x1
01
19~
00
w
16
20
25
141
172
205
240
279
320
362
410
458
510
. 44
.67
. 94
24
. 59
41
38
50
8
2
CO
CO
NJ
ND
OO
0 62
0 94
1 32
l 74
23
39
72
3
1
0
i-a
i-Voo
i-a'm
198
240
287
337
390
449
510
570
640
710
c=80 o=60
299
362
433
5 10
590
680
770
870
970
1080
OO
N
NJ
H
O
15
03
0
15
0
M
M
CN
NJ
H
00
C”
(N
th-CO
NJ
H
16
20
25
31
44
59
75
93
5 10
620
740
870
1010
1 160
1310
1480
1650
1840
00
01
0-15
05
(O
OO
QD
ND
OO
c=40
H[OQON
CH
M
Q
M
H
34A
44
55
66
93
124
159
198
1080
1320
1570
1840
2130
2450
2790
3120
35 10
5-INCH PIPE .
Discharge in Gallons . Lo ss of He ad in Fe e t per 1000 fee t of length .Ve lc e Veloc1ty 1n
155356,
ce t. 0c= 120 c=80 c=60 c=40
“
30 0 49 0 00 1
40 0 65 0 01 54 1
50 0 82 0 01 8 1 13 2
60 0 98 0 02 13 59 4
70 1 14 0 02 1 52 2 5
80 0 03 1 94
90 1 47 0 03 1 2 41
100 1 63 0 04 2 94
120 0 06 4 1 1
140 5 5
160 9 8 25 54
180 2 94 0 13 2 2 31 67
200 3 27 0 17 4 8 38 . 81
220 3 59 0 20 17 7 45 96
240 3 92 0 24 20 8 54 113
260 4 25 0 28 24 1 36 62 132
280 4 58 0 33 27 7 41 72 152
300 4 90 0 37 31 4 47 81 172
320 0 42 35 4 54 9 1 193
350 5 72 0 5 1 41 9 63 108 229 1
400 6 54 0 66 28 54 81 138 292
450 7 35 0 84 35 67 101 172 364
500 8 17 1 04 43 49 81 122 209 442
550 8 99 1 26 52 60 96 146 249 530
600 9 80 1 49 61 70 113 172 292 620
650 0 62 1 75 71 81 132 199 339 720
700 1 44 2 03 81 93 108 151 229 388 820'
750 2 34 92 06 172 260 442 940
800 13 07 2 66 104 194 292 499 1060
8 50 13 89 2 99 117 217 328 560 1 180
900 14 71 3 36 129 240 362 620 1320
9 50 15 52 3 74 143 267 402 690
1000 16 34 4 15 157 292 443 750
1 100 17 97 5 00 187 249 349 530 900 19 10
1200 19 61 5 96 220 620 480 2240
75
joc é M i AJl-c f c
J7 7. 3
4 79 6/
D ischarge in6-INCH PIPE .
Loss of Head in Fe e t per 1000 fee t of length .
8—INCH PIPE .
Discharge Ln Loss of He ad in Fee t per 1000 fee t of length.
Velocit inFis tGallons Cubic per
<5)er 24 Fee t per Second.
ours . Second .
c= 140 c= 130 c= 120
0 5 8
5 37 0 44
5 76 0 52
6 20 0 60
000 6 65 0 69
7 09 0 78 25 5
7 98 0 99 1 6
8 86 1 22 08 79 75 1 47 34
,
9 462 54
10 64 1 76 41 0 47 55 644
.
1 1 52 2 06 47 5 55 63 74"
12 41 2 39 55 62 73 85
13 30 2 74 62 71 83 97
14 18 3 12 70 80 93 09
Discharge inGallonser 24
ours . CubicSecond .
464
495
526
5 57
588OOOOO.619
.696
. 774
. 85 1
. 928OOOOO006
. 083
160
238
392H
H
H
H
t—a
547
702
857
M
NJ
H
H
J—t
. 166
.321
476
785
. 094
404WOO
M
M
N
. 713
. 023
.332
.642
. 95 1bh
hb-rlk
rh
w
26
57
88
19
9603
01
01
01
01
Velocity inFe e tperFee t per Second
HHHHH
M
M
M
l—‘H
03
01
01
1t
QD
OO
N
Q
Q
10
10
11
H
I—‘O
O
O
OO
CJO
OJ
CO
M
. 85
9 1
96
. 02
08
. 13
. 28
. 42
. 56
. 70
. 84
. 99
. 13
. 27
. 55
84
. 12
. 40
.69
. 97
. 26
. 54
. 1 1
.67
. 24
. 81
.38
. 94
. 5 1
. 08
.65
21
78
.35
12 . 77
H
H
O
O
O
OOOOO
OOOOO
OOOOO
M
M
H
HJ—l
. 10-INCH PIPE .
04
05
06
07
08
10
12
15
18
21
24
28
32
41
50
60
72
84
98
12
28
44
62
80
00
52
M
H
H
H
H
O‘K
A
OO
OO
M
16.
18 .
20
26.
29 .
32
35
44 .
©0
0
0
0
H
O
O
O
O
H
co
oo
ou
01
xl
co
h-lcfl
oo
01
00
w
o
' xi
. 29
. 33.
. 37
. 41
45
50
.62
76
90
. 06
. 23
41
60
81
24
73
25
82
44
1
00
01
m
Loss of Head in Fe e t per 1000 fee t of length .
69c= 140 c= 130 c= 120 c= 1 10
l—‘I—‘OOO
1 1 .
13.
- 15
18
21
23
27
30 .
33
37
40
5 1
OOOOO
01
01
1-5
00
03
[C
lo
t—“H
id
bkOO
O'I
o
oo
o
in-kr
34
38
. 42
47
57
71
87
03
21
. 41
62
. 84
. 08
. 58
. 13
. 72
. 40
1
. 8
WM
CJI
N)
w
w
NJ
P—‘H
H
H
i—‘O
O
OOOOO
03
01
01
t
10 .
13.
15 .
18 .
21
24 .
27 .
31 .
35
38
43
47
59
471
?q
69
9
00
00
00
. 39
. 44
. 49
. 55
.60
.66
. 83
. 01
. 20
. 41
.64
. 88
. 14
. 41
. 00
.63
. 32
. 1
. 9
. 8
OO
H
QO
O
OO
M
M
NJ
H
b—ll—‘r—‘O
O
OO
Q
O'D
O‘I
‘
Hk
12
15
18
21
25
28
32
36
41
45
51
56
69
OOOOO
©40
w
. 46
. 52
. 58
64
. 71
. 78
. 97
18
41
.65
. 92
21
50
83
. 50
7
OO
CJI
Q
O
FD
-q
GI
N)
c= 100
H
H
H
H
C
Cc
hfi-H
15
09
00
10
10
20
00
x1
05
0:
mH
I—i
25 5
34 0
38 6
43 8
49
60
66
83
moo
r-40:
oo
HB
CD
O
UI
tP-OO
c=80
38
45
5 1
59
66
74
92
00
H
H
H
O
O
CO
NJ
M
H
I—l
00
33
01
0:
. 83
. 93
. 04
16
. 28
40
75
. 13
. 55
.00
6
A
CR
OO
N
NI
O
q
c=60
M
H
H
H
H
100
113
127
140
156
171
213
. 41
. 59
. 78
. 98
. 19
40
Gallons Cubic perer 24 Fe e t per Second .
ours . Second .
0 20
0 59
0 619 0 . 79
0 . 774 0 99
0 . 928 1 . 18
1 . 083
1 . 238 1 . 58
(1 392 1 77
1 547 1 97
1 . 702
1 . 857
1 2 166
2 321 2 96
2 476 3 15
2 785 3 55
2 . 940
3 094
3 404
3 713 4 73
4 . 023
4 642 5 9 1
8 87
7 74
8 5 1
1 1 82
12 38
13.9 2 17 . 73
15 47
12-INCH PIPE .
Loss of Head in Fee t per 1000 fee t of length.
c= 140 c= 130 c= 120 c= 1 10 c= 100
N
M
H
H
H
HR
OJ
OO
OO
N)
.42.
11 .
14 .
18 .
22 .
26.
31 .
41 .
0
0
0 .
0
0
H
O
O
O
.02
.06
12
. 20
.31
. 58
74
. 92
12
.34
. 58
. 83
. 10
.39
69
00
33
70
.06
. 85
01
0
0
t
OOOOO
[c
ro
tc
h-ma
H
H
O
O
O
l-lk
t-P
OO
OO
OJ
ba
n-403
03
10
. 02
.07
. 14
. 24‘
.36
. 50
66
. 85
. 06
. 29
. 54
. 81
10
40
. 73
10
14
CO
M
M
NJ
H
O't
flk
hlk
hlk
w
ya
p-4
19 .
24
29 .
35 .
55
71
87
107
0
0
0
0
0
I—ll—‘OOO
I—‘O
OO
KI
Q
01
H
00
0>
01
14
10
5
00
0:
. 02
.08
. 16
27
.41
58
. 77
. 99
. 23
. 50
. 79
. 10
. 43
. 79
. 17
. 58
. 00
. 43
. 92
. 4
©0
0
0
0
10 .
1 1
13.
17
22
28
34
41 .
48 .
65
83
OU
O'I
CJi
l-h
v-lk
OO
OO
NJ
N
NJ
H
H
H
~O
O
OI
QD
OO
QD
O)
16
00
69
01
40
.02
. 09
. 19
.32
.48
68
. 9 1
. 15
. 45
. 76
. 10
47
85
. 26
71
. 20
.69
2
. 8
. 4
122
150
(0
1—41-40
44
19-00
00
.
10
12
15
17
19 .
26.
33.
41 .
50 .
121
148
0
0
0
0
0
15
10
05
00
10
04
. 13
. 27
. 47
. 71
. 99
.32
.68
. 10
.04
. 58
. 14
. 76
ONN
O
OD
N
N
H
l—l
0
0
0
0
0
M
O
00
(0
JP
CO
U‘
PP
FP
O'I
C?
O)
OI
GB
O
Q
Discharge in
fl
CD
Gb
cfl
i-lk
H
QO
OO
OO
xl
H
13
14
15
16
99
54
09
65
20
76
31
86
97
08
19
30
40
5 1
62
OOOOO
H
H
l—‘H
O
A
CAD
OO
JO
M
16-INCH PIPE .
39 4
48 5
58 6
69 7
81 8
93 10
08 1 1
22 13
54 16
90 19
30 23
74 27
22 32
73 36
29 41
00
03
1-403
10
(O
NI
O
N
(G
ib
b-“WC?
Los s of Head in Fee t per 1000 fee t of length.
27
31
36
42
48
05
03
w
[0
00
01
09
10
O
M
OO
OO
O
H
O
OO
NI
O
H
p—fi
15
17
21
26
31
36
42
49
56
[O
NI
i-P
i-F-O‘J
OO
M
N
OJ
O
O/OO
QO
NJ
10
12
13
15
18
20
25
30
36
43
50
58
66
(COM
O-10
CO
N
CJO
l—‘QO
c=90 c=80
24-INCH PIPE .
D ischarge in Loss o f Head in Fee t per 1000 fee t of length.
G 11 c b'
Fe et Head 2
a ons u 10 perper 24 Fe e t per Second.
Fe et .Hours . Second .
c= 140 c=~ 130 c= 120 c= 1 10 c= 1 00 c=90 c=80—o
0 774 0 00 0 014 0 020
1 547 0 49 0 05 1 0 060
0 152
3 094 0 218 0 259
3 868 0 390 02 59
0 459 0 55
0 61 0 73
0 78 0 93
0 98 1 16
1 18 1 41
1 42 1 68
1 66 1 97
1 93 2 29
2 21 2 63
2 5 1 2 98
2 83 3 38
3 16 3 77
3 52 4 20
3 89 4 62
4 28 5 1.92 .
-5 1 6 1 . 7 14
5 . 1f
6 0 ~ 7 1 o
6 9 . 8 3
.8 0 9 5
7 7 9 1 10 8
10 2 12 2
1 1 4 13 6
12 7 15 2
14 0 16 7
15 4 18 3
18 4 21 9
21 7 25 9
25 0 29 9
28 8 34 2 52
32 8 39 0 59
Discharge inGallons
8
9
10
10
1 1
12
13
13
15
17
18
20
21
23
24
26
27
29
30
34
5 1
28
06
83
60
38
15
'
92
47
02
57
1 1
66
21
76
30
85
40
94
04
37 13
.25"
40 23
28 43
46
54
61
32
42
1
9
ba
ht
ht
ht
ht
l0
l0
l0
10
H
01
01
15
44
19
“
OO
OO
OJ
N
N
10
26
42
58
73
. 89
. 05
. 21
. 36
. 52
.68
. 84
. 15
47
. 78
10
41
73
04
36
30-INCH PIPE .
Loss of Head in Fe e t per 1000 fee t of length .
0 6) f.c=140
'
c=130 c= 120
OOOO
O
OOOOO
OOOOO
h‘
h‘
C’
Cflo
N>
w
1~
r~
hd
. 013
. 028
. 047
. 071
. 099
. 132
. 168
. 210
. 256
.304
.357
. 414
. 474
. 54
.61
.68
. 76
92
. 09
. 28
. 50
72
. 95
. 20
46
O
O
O
'
O
O
C>
C>
C>
CHO
l0
l0
10
F-‘H
OOOOO
015
.032
. 054
. 081
. 1 13
15 1
194
. 241
. 292
.349
. 410
. 475
. 55
.62
. 70
. 78
. 87
. 06
. 26
. 47
. 72
. 97
. 24
. 52
. 82
-OOOOO
OOOOO
h‘
hl
h‘
HWD
1
2
OOOOO
. 017
. 037
. 062
. 094
. 132
. 176
. 225
279
340
405
475
55
64
72
8 1
9 1
01
23
46
72
98
28
2 60
2
3
93
28
c
'
= 1 10
OOOOO
dbd
hfl
h4
C>
CH3
OO
OO
OO
M
N
OOO
OO
. 020
. 044
. 073
. 1 1 1
. 155
CO
N
N
[0
03
0
(Q
t
.399
. 476
.65
. 74
. 84
. 95
.07
. 18
. 44
72
02
.34
.69
. 06
45
85
N
N
H
H
H
H
u
c
c
c
Q
Q
C
Q
Q
Q
Q
Q
91
15
00
03
10
Hai
r—to
o
O
O
O
Q
O
01
0
19-00
00
OOOOO
l0
l0
l0
l—‘l
029
.062
106
160
225
. 298
.382
. 476
58
69
. 81
. 94
. 08
. 22
.38
. 54
. 72
. 09
. 49
. 92
.40
. 89
. 43
. 99
.6
OOOOO
OJ
CJO
M
NJ
H
«1
01
01
114
14:
. 037
.078
. 132
. 199
. 280
.372
.477
59
72
. 01
. 17
.34
. 53
. 72
Discharge inM illionGallonsp
_
er 24
h ours .
15
01
00
10
10
(D
OO
RI
GD
OI
10
12
13
14
1 5
16
17
18
19
20
22
24
26
28
30
32
34
36
38
40
45
50
5 5
60
CubicFe e t per Second .Second .
OU
O‘l
Hk
OJ
10
12
15
17
18
20 .
.6621
23.
. 76
.30
. 85
. 40
24
26
27
29
30
34
40
43.
46.
49 .
52 .
55 .
58 .
61 .
69 .
77 .
85 .
92 .
. 868
.642
.41
19
. 74
. 28
. 83
. 38
13. 92
. 47
. 02
. 57
1 1
21
. 94
. 04
37 .
. 23
13
32
p—i
WN
GD
CR
OO
H
MA
O
QO
Velocity inFe e tper
. 44
. 55
.66
. 77
. 88
. 41
.63
. 85
. 0600l0l0
l
0
. 50
. 72
. 94
. 16115
00
00
00
.38
. 82
. 25
.69
. 13
57
.44
. 88
.32oo
q
q
-qc»
. 76
Veloc
Head ,Fe e t .. 00
. 01
. 01
01OOOOO. 02
03
. 04
. 05
. 06OOOOO
.07
. 09
. 13
. 15OOOOO
. 17
. 19
. 22
. 24
. 270
0
0
0
0
0 .30
. 50
. 58O
.67
. 76
. 86
. 96
.07‘
H
O
O
O
O
19
. 50
. 86
. 25
M
N
H
H
H
1 1.
. 36'
Loss of Head in Fe e t per 1000 feet of length .
36—INCH PIPE .
0 0 0 ec= 140
OOOOO
ro
mp-ward
OOOOO
H
H
i—‘O
O
. 019
. 029
. 041
. 054
070
. 105
. 147
. 196
. 250
.31 1
.379
. 45 1
. 53
62
. 71
. 80
90
. 02
. 12
. 24
.37
.63
. 92
. 22
. 55
c= 130 c = 120 c = 1 10 c= 100 c= 90 c= 80
0
0
0
0
0
1—1
1—1
1—11—40
OOOOO
81
10
01
118
01
00
81
01
01
81
. 044
. 066
. 092
. 123
157
238
333
444
57
. 71
. 86
.02
. 21
.39
.60
. 82
. 05
. 30
. 56
. 81
. 10
.69
.35
1
. 8
l—‘P—li—‘i—‘H
O
O
O
C
O
OOOOO
03
00
10
10
10
10:
1 1
12
13.
17 .
21 .
25 .
29 .
“03
01
144
00
kr
iu
w
' w
io
. 054
. 082
. 1 15 .
. 153,
. 297
. 415
. 55
. 71
. 88
.07
. 28
. 50
. 74
. 98
. 27
. 56
. 86
. 18
. 5 1
. 86
.60
fl
t-‘H
rb
to
Discharge inM illionGallonser 24ours .
00
01
01
15
00
CubicVelocity inFe e tper
Fe e t per SecondSecond .
42-INCH.PIPE .
C :
i—‘H
i—‘
l—‘O
OOOOO
OOOOO
-“
l“-l
OOOOO
111-04
00
00
10
OO
NI
O>
01
14>~
Loss of Head in Fe e t per 1000 fe e t o f length .
c = 1 10 e = l00 c= 90O
140
. 019
. 033
. 050
070
092
. 1 18
. 147
. 178
. 213
. 25 1
.333
. 428
. 53
.64
. 77
. 90
. 05
. 21
.37
. 54
. 73
. 92
. 12
.33
. 56
. 78
c= 130 c= 120
111-15
00
00
09
l0l0l0
10
l~4
HHHHH
0
0
0
0
0
©0
0
0
0
OOOOO
CO
OO
Q
O
O‘I
. 022
038
057
080
106
136
168
207
245
288
382
490
61
74
88
04
21
38
57
77
98
20
43
68
92
19
48
76
05
82
G
OD
Q
O
Q
pa
p—4
oo’
ooo
01
0-141-15
00
03
00
l0
l0
10
t0
l r
-*l'
-41
-*r—'L
H
O
O
O
O
OOOOO
H
O
OO
Q
CD
. 026
. 044
. 066
092
. 123
. 158
. 196
238
284
333
57
71
86
03
21
39
61
83
06
29
56
82
10
40
70
02
36
N
O
OO
Q
O)
OOOOO
OOOOO
00
00
00
0J
t0
(0
10
1-‘l-‘H
-lk
1-1k
10 .
1 1 .
13.
l-‘l—‘OOO
. 030
. 052
. 078
. 108
145
. 185
. 230
. 280
. 334
. 392
. 52
.67
. 83
02
. 21
. 42
.64
. 88
. 14
.41
. 70
. 00
.31
.64
99
36
71
1
5
6
l0
\1
00
0
\l
0 1 72
0 220
0 273
0 332
62
80
99
21
44H
H
Q
O
C
1 68
1 96
2 25
2 56
2 88
21
OOOOO
OOOOO
H
I—‘i—‘O
O
. 044
074
. 1 13
. 210
268
333
406
. 483
57
. 76
. 97
21
.47
. 74
. 05
38
. 74
. 10
. 50
9 1
35
80
00
03
mo
m-00
00
H
QO
QD
O
N)
KI
Q
OB
CR
FF
PP
OQ
OQ
M
M
H
O
G
OO
NI
OO
O
N
CR
OO
Discharge inM illion
100
Cubic
34 .
37 .
40 .
43.
46.
49 .
52 .
55 .
58
61 .
65 .
68 .
71 .
74
77
85 .
92
100 .
108 .
1 16.
123.
131 .
139 .
147 .
154 .
ib-
éfi
M
b—‘O
0
00
03
00
1-4
fl
O
l0
01
00
1 1 .
1 1 .
12 .
03
01
01
01
01
EP
PP
I-P
l-P
OO
00
03
00
l0
l0
l0
l0
l—‘M
M
H
O
O
O
O
CO
OO
OO
KI
Q
48-INCH PIPE .
VelocityHead ,Fe e t .
. 00
. 01
01
. 01
. 02OOOOO03
.05
. 06
08
. 09©0
0
0
0
. 1 1
14
16
. 18
. 21OOOOO
. 24
. 27
. 31
34
.38OOOOO
. 41
. 45
. 50
54
. 59OOOOO
. 71
. 85
. 99
. 15
. 32I—‘i—‘OOO
. 5 1
. 70
. 9 1
. 12
. 35M
N
H
H
t—fi
Loss of Head in Fe e t per 1000 fe e t of length .
GDc= 130 c = 120 c= 1 10 c = 100c = 140
0 017
026
036
062
0940
0
0
0
131
. 174
. 222
277
338OOOOO401
472
55
63
72OOOOO80
90
00
1 1
22I—Jt—‘
I—‘O
O
. 33
. 45
. 58
. 71
. 84I—‘
I—l
l—li—‘H
19
58
99
43
9000
03
63
10
10
40
9 2
5
0
7O
OD
CJT
HA
LF
0
0
0
0
0
OOOO
O
mu
H
I—H—t
OOOOO
l—‘I—li—l
I—lo
$
03
03
l0
l0
N
‘Q
GD
CR
O‘
. 020
.030
042
.071
-107
. 150
199
. 256
. 319
.387
460
54
63
72
82
92
. 03
. 15
. 27
.39
. 53
.67
. 81
. 96
. 12
. 52
97
. 43
. 94
.48
l0
l0
l0
l—‘H
i—‘
l—‘
l—‘H
H
OOOOO
OOOO
O
OOOOO
01
10
03
00
10
OO
OO
Q
O‘J
OI
OO
O
0O
CD
CD
. 023
. 035
.048
.082
124
174
. 232
298
369
449
. 54
.63
. 73
. 84
. 95
. 07
. 19
.33
. 48
.62
. 77
. 93
. 09
. 28
.46
92
44
98
58
2
H
M
C
C
OO
I—fil—‘i—‘
I—l
l—l
0
0
0
0
0
9
01
15
110
00
l0l0l0
l
0
l
0
O
QD
OO
\1
03
0 .
O0
057
. 097
146
204
272
349
433
53
.63
. 74.
. 86
. 98
. 12
. 26
. 41
. 57
. 73
. 90
08
28
. 47
.67
. 88
.43
.04
68
.4
. 1
1&
01
CD
'Q
CO
0 048
0 068
o=go
15
03
03
03
00
l0
l0
l0
l0
l—i
H
H
H
H
O
OOOOO
OOOOO
OO
N'I
O‘J
CJ'I
blk
OO
OO
OO
QD
CD
10
12 .
13.
15 .
039059
. 082
140
212
297
. 395
5 1
63
76
. 9 1
. 07
. 24
. 43
.62
. 83
.03
. 28
. 5 1
. 77
.02
. 29
. 58
88
18
7
r—axua-w
o
c=80
N
H
F—‘
I—‘H
OOOOO
OOOOO
03
03
00
10
l0
l0
01
H
13.
15 .
17 .
18 .
H
QO
OO
KI
GD
o
qw
co
r-415
00
11;
.048
. 073
. 102
. 174
. 263
.369
. 490
63
78
95
. 13
. 33
. 54
. 77
.02
. 27
. 54
. 82
. 12
. 44
. 76
. 10
. 81
2
54-INCH PIPE .
Discharge in Loss of Head in Fe e t per 1000 fe e t of length .
ity in'Million Fee t.
(331133
81153
5
321 S e‘éfifid .
oursecond
c= 140 c= 120 c = 1 10 c= 1 00 c=90 o= 80
6
8
10
12
14 0 153
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44 82
46
48
50
55
60
65
70
75 4 99
80 5 6
85 6 3
90 3 08 5 8 7 0
95 3 41 64 7 8
100 7 0 8 5
1 10 . 4 48 8 4 10 2
120 5 3 11 9
Discharge inM illionGallonsper 24Hours .
24
26
28
30
32
‘
34
f 36
38
40
45
Cubic
12
15
18 .
21
24 .
. 85
. 94
.04
27
30
34
37
40
. 19
. 28
.38
. 47
57
.66
76
. 13
. 23
43.
46.
49 .
O
l0
01
00
0
qw
q
perFe e t per SeconSecond .
Q
Q
O
OU
OI
01
01
h5>
hl>~
03
00
00
10
83
10
l0
l0
10
l0
H
I—‘l—‘b—‘i—AH
OOOOO
H
O
QO
OO
N
ha
y-4
Velocity inFe e t
. 32
. 47
.63
. 79
. 95
10
. 26
. 42
. 58
. 73
. 89
. 05
21
. 36
52
68
84
. 99
. 15
. 55
. 94
. 33
. 73
. 12
. 52
9 1
.30
. 70
.09
. 49
. 88
.67
. 46
. 24
.03
OOOOO
OOOOO
OOOOO
OOOOO
OOOOO
OOOOO
H
M
I—‘l—‘O
Velocityead ,d .
Fe e t .. 00
00
. 01
. 01
. 01
. 02
. 02
03
. 04
. 05
. 06
. 07
. 08
. 09
. 10
. 1 1
. 12
. 14
. 15
. 19
. 24
. 29
.35
.41
. 47
. 54
.62
. 70
. 78
. 87
. 97
. 17
. 39
.63
. 89
l0
F-‘
l—‘P-‘H
F—‘
l—‘OOO
9
0
0
0
0
0
0
0
0
0
©0
0
0
0
OOOOO
101
00
00
10
10
. 006
. 012
. 021
. 032
. 044
059
075
. 094
. 1 13
. 136
. 159
. 185
. 212
. 241
. 271
. 303
. 338
. 372
. 410
. 5 1
.62
. 74
. 87
02
. 16
. 32
;48
.66
. 84
.03
. 24
68
. 13
.63
. 18
l0
l0
I-4
l—‘I—l
H
H
H
O
O
OOOOO
OOOOO
O
O
O.
O
O
hFs
i-P
QD
OO
N
. 007
. 014
. 024
. 036
. 05 1
. 068
. 086
. 107
. 131
. 156
. 183
. 212
. 243
. 277
310
349
388
428
. 470
59
. 71
. 85
. 00
. 16
.33
. 51
. 70
. 90
. 12
.34
. 57
. 07
.60
. 79
l0l
0
l
0
1—‘H
H
H
H
O
O
OOOOO
OOOOO
OOOOO
OOOOO
01
rb»
it
60-INCH PIPE .
. 008
. 016
. 028
. 042
. 059
078
. 100
. 124
. 152
. 181
j212
. 247
. 282
.320
.361
. 404
. 449
496
55
68
83
98
16
34
54
75
97
21
47
71
98
57
18
84
6
0O
t0
l0
10
10
l—‘i-‘i-‘H-O
OOOOO
OOOOO
OOOOO
OOOOO
05
01
1-5
41
00
. 009
. 019
. 033
. 049
. 069
. 092
. 1 17
. 146
. 178
. 212
. 249
289
331
377
425
474
53
58
64
80
. 97
. 16
.36
. 58
. 81
06
31
59
. 89
. 19
5 1
. 18
. 90
. 7
.6
c= 1 10 c = 100
Q
G
C
Q
C
co
n
-amen
01
®
©00
Q
H
H
H
Q
M
M
[0 HK]
00
00
mmfi
c
fl
fi
C
03
00
01
10
0
00
00
10
00
20
«1
01
01
10
30
oo
po
w
co
n-s
OOOOO
OOOOO
C
O
C
O
[0
OO
Q
G
CJ!
OI
GO
H
O
H
Loss of Head in Fee t per 1000 fee t of length .
. 69c = 140 c = 130 c = 120 c = 90
. 013
. 028
. 047
. 072
. 100
. 133
. 171
. 212
. 258
. 308
. 361
. 419
. 480
. 55
62
69
. 76
85
93
16
41
68
98
29
62
98
37
75
19
61
H
H
e = 80
. 016
. 035
. 059
. 089
. 124OOOOO
. 166
. 212
. 263
.320
.381©0
0
0
0
. 449
52
60
68
76OOOOO. 86
. 95
.05
. 16
.44H
H
H
O
O
.75
. 09
.462
OO
M
NJ
M
H
28
c.
OO
N
OD
l—‘KI
OO
CO
O
01
01
1-5
9
03
H
O
OO
Q
OO
00
01
09
01
11:
D ischarge inMillionGallonsper 24Hours .
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
45
50
55
60
65
70
75
80
90
100
110
120
130
140
150
160
170
180
CubicFe e t per Second .Second.12 .
15 .
18 .
.6621
24 .
27 .
. 9430
34 .
37 .
. 2340
43
46.
. 5 1
52 .
55 .
49
58 .
61 .
69 .
77 .
81 .
92 .
100 .
108
1 16
123
139 .
154 .
170 .
185 .
201 .
216.
232 .
247 .
263
278 .
60
° 0
6
o
38
47
57
76
85
04
13
.32
42
01
9
9
9
00
r—txl
w
xl
w
01
9
9
1
per
H
H
l—‘I—‘O
b—lt—‘r—‘l—‘H
fl
9
9
01
>4>~
9
9
9
9
9
“k
l
9
9
00
00
. 44
55
.66
. 77
. 88
. 98
. 09
. 20
. 31
. 42
. 53
. 64
. 75
. 86
. 97
. 08
19
46
74
. 01
. 28
56
. 83
. 10
.38
. 92
. 47
. 02
. 57
. 1 1
72-INCH PIPE .
Loss of Head in Fe e t per 1000 fee t of length.
trem elySmoo thandStraight
c= 140
H
b—‘
l
ooooo
ooooo
ooooo
ooooo
ooooo
M
NJ
N
P-‘H
. 009
. 013
. 018
. 024
. 031
. 038
. 047
. 056
. 066
. 076
. 087
. 099
. 1 12
. 125
. 138
. 153
. 169
. 210
. 255
. 304
. 358
. 414
. 476
. 54
.61
. 76
. 92
. 10
. 28
. 50
. 72
. 95
. 20
. 46
. 73
Ve rySmoothc= 130
I—ll—‘l—‘l—‘O
OOOOO
OOOOO
w
w
w
w
w
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
. 010
015
. 021
. 028
.035
044
054
. 064
. 075
. 087
. 100
. 1 13
128
. 143
159
. 176
. 193
. 241
. 292
. 349
. 410
. 475
. 55
. 62
. 70
. 87
. 07
. 27
. 48
. 72
97
24
52
82
13
GoodasomryAqueducts .
c = 120
.01 1
017
. 024
. 032
.0419
9
9
9
9
. 05 1
. 062
. 074
087
1029
9
9
9
9
. 1 16
. 132
. 148
. 166
. 1859
9
9
9
9
204
225
280
340
. 4059
9
9
9
9
476
. 55
.64
. 72
819
9
9
9
9
. 01
. 23
. 47
. 72
. 99H
H
P—‘i—‘H
. 29
.60
. 92
. 28
.639
9
l0
t0
10
Rive tedSte e lPipe ,
New .
c = 1 10
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
M
N
P—‘H
b—l
9
9
9
9
9
l-P
9
9
9
M
. 013_
. 020
. 028
. 038
. 043
. 060
. 073
. 087
. 103
. 1 18
. 136
. 155
. 174
. 195
. 217
240
263
329
399
476
56
65
74
84
96
. 18
. 44
. 72
.01
.34
.69
05
. 43
. 85
. 29
Ste e lO ld ,BrickSe w e rs .
c 1 00
0 142
162
185
208
232
2599
9
9
9
9
287
.315
. 391
. 4779
9
9
9
67
. 78
. 88
. 01
. 14H
H
9
9
9
y—L
. 42
. 721—1
. 20
.62
. 10
. 59$
93
9
9
9
l\3
l\D
l\D
b
I—‘l—‘
l
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9 . 087
. 106
. 126
. 148
. 172
. 197
. 225
. 252
. 282
.315
348
.382
477
58
69
. 81
. 94
. 08
. 23
. 38
. 72.
. 10
. 49
. 92
. 40
. 90
. 41
. 99
l—‘P—‘
l—Jl—‘H
9
9
9
9
9
9
9
9
9
9
A
9
9
M
M
fl
o
or
»
O
N
CJI
OO
. 108
. 132
. 157
. 185
. 215
. 246
. 279
315
. 35 1
. 391
. 432
. 476
59
. 72
. 86
. 02
. 17
. 34
. 53
. 72
. 14
.60
10
64
78-INCH PIPE .
Discharge inGood
a
sonryAque ~ducts .c= 120
9
9
9
9
9
H
H
P—‘P—‘O
9
9
9
9
9
9
9
9
9
9
9
b3
m
9
9
9
9
9
9
9
9
9
9
. 005
. 011
. 019
. 028
. 040
053
.068
;084
102
122
144
. 167
. 190
. 217
. 246
. 272
304
337
.369
. 440
. 52
. 60
.69
. 78
. 88
. 99
. 09
. 22
.33
. 59
. 87
. 17
.49
. 82
. 19
R ive te d PiStee lPipe ,New .
c= 1 10
9
9
9
9
9
9
9
9
9
9
H
H
P—ll—iH
9
9
N>
N
N>
9
9
9
9
9
9
9
9
9
9
H
O
O
O
O
006
. 013
. 022
. 033
. 047
062
080
. 099
. 120
. 144
169
196
. 223
253
. 288
321
.358
.396
432
52
61
71
. 81
. 92
.03
. 16
. 28
. 43
. 57
. 87
. 20
. 54
. 92
.31
. 74
Stee lOld ,BrickSe w e rs .
c 1 00
0 382
0 426
0 471
0 52
0 62
p e 10Ye arsLoss of Head in Fee t per 1000 fee t of length .
R ough .
c=90
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
H
H
H
H
O
N
N
N
l—‘H
9
9
9
9
9
009
. 019
. 032
. 048
. 068
. 090
. 1 16
. 144
. 174
. 208
. 245
284
. 325
.369
. 419
. 467
. 52
. 57
.63
. 75'
. 88
. 02
. 17
.33
. 50
.68
. 87
. 07
. 27
. 70
. 19
.69
23
. 80
. 4
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
w
w
w
w
w
HHHHH
OOOOO
9
9
01
9
9
. 011
. 023
. 040
. 060
. 084
. 1 12
. 144
178
. 218
. 259
304
354
. 404
. 459
52
. 58
64
72
. 78
. 94
.09
. 27 .
Discharge inCubicFe e tperSe cond .
10
15
20
25
30
35
40
45
50
55
60
65
70
80
90
100
1 10
120
130
140
150
160
170
180
190
200
220
240
260
280
300
320
340
360
380
MillionGallonsper 24Hours .
19
22 .
. 85
. 08
.32
25
29
32
35 .
38 .
42 .
45 .
5 1 .
58 .
64 .
71 .
77 .
84 .
90 .
96
103
109
116
122 .
129 .
142 .
155 .
168 .
181 .
193.
206.
219 .
232 .
245 .
oo
' oo
' ao
lpfco
. 46
. 69
12 .
16.
. 39
93
16
62
55
78
01
24
O1
9
CJI
H
9’
9
9
H
M
9
Velocity inFe e tperSe condVelocityHe adFe e t .
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
H
H
H
H
O
. 00
. 00
. 00
. 01
. 01
01
. 02
. 02
. 03
. 03
. 04
. 04
. 05
. 07
. 09
. 11
. 13
. 18
. 21
. 24
. 27
. 30
34
.38
. 42
5 1
.60
. 71
. 82
. 94
. 08
. 21
36
. 52
84-INCH PIPE .
E xtremelySmoo thandStraight
c = 140
. 003
. 006
. 010
. 015
. 0219
9
9
9
9
. 028
. 036
. 044
. 054
. 0649
9
9
9
9
. 075
. 087
. 100
. 128
. 1599
9
9
9
9
. 193
. 231
. 272
. 314
.3619
9
9
9
9
. 410
. 461
. 52
. 58
.649
9
9
9
9
. 70
. 83
. 98
. 13
.30H
H
9
9
9
. 48
.67
. 87
. 08
. 29mw
h-l
(if? Rive te dVe ry Ste e lSmooth 2233: 1
1311136.ducts . e w .
c= 130 c = 120 c = 1 10
Ste e lPipe 10Ye arsO ld ,BrickSe w e rs .c 100
0 052
. 066
. 032
. 100
1199
9
9
9
141
163
239
. 2979
9
9
9
9
.361
.430
51
59
68
Loss of Head in Fee t per 1000 fe e t of length.
Rough .
e =go
. 006
. 013
. 022
. 034
. 0479
9
9
9
9
. 063
. 080
. 100
. 122
. 1459
9
9
9
9
. 171
. 198
. 228
9
9
9
9
9
.361
. 439
. 52
.62
. 71
. 829
9
9
9
9
. 93
. 04
. 17
.30
. 44H
H
D—‘M
O
. 58
. 88
. 21
. 57
. 96M
NJ
NJ
H
H
. 37
. 78
. 22
. 70
. 290'
Ve ryRough .
e = 80
. 008
. 016
. 028
. 042
. 0599
9
9
9
9
. 078
. 100
. 124
. 152
. 1819
9
9
9
9
212
. 247
. 282
. 361
. 4509
9
9
9
9
55
65
76
89
. 04H
O
O
O
O
. 16
. 30
. 46
.62
. 79H
H
H
H
b—t
. 97
.35
. 77
. 20
.689
9
M
N
H
9
01
01
1t
01
9
9
RI
Discharge inCubicFe e tper
S e cond .
20
25
30
35
40
45
5 0
60
70
80
90
100
1 10
120
130
140
1 50
160
170
180
190
200
220
240
260
280
300
320
340
360
380
400
420
440
MillionGallonsper 24Hours .
32 .
38 .
45 .
78
24
5 1 .
58 .
64 .
71 .
77 . CJ'l
b—‘9
l0
\1
84 .
90
96.
103.
109 . (0
1h
¢>
b1
c>
1 16.
122
129
142
155 . hs
ka
to
in
on
168 .
181 .
193.
206.
219 .
232 .
245 .
258 .
271 .
284 . A
9
9
9
fl
V43
0
1
323? He ad ,Se cond.
Fe e“
() A93
90-INCH PIPE .
E xtrem elySmooth
anStraightc 140
. 004
. 007
. 01 1
.015
. 0209
9
9
9
9
. 026
. 032
. 038
. 054
. 0729
9
9
9
9
. 092
. 1 14
. 139
. 166
9
9
9
9
o
. 226
. 259
. 294
.332
.3719
9
9
9
9
. 413
. 457
. 50
.60
. 709
9
9
9
9
. 82
. 93
. 07
. 19
.33H
r—tr—to
o
. 49
.65
. 8 1
. 98
. 17M
H
H
H
H
. 194 .
Ve rySmoothc = 130
. 005
. 008
. 012
. 017
. 023
c>
c>
c3
<3
. 029
. 036
. 044
. 062
. 0839
9
9
9
9
. 105
. 131
. 160
. 190
. 2229
9
9
9
9
. 259
. 298
. 338
. 38 1
4259
9
9
9
9
. 472
. 52
. 58
. 69
. 819
9
9
9
9
. 94
. 07
. 21
.37‘
. 53H
H
H
H
O
. 71
. 89
. 08
28
. 4810
10
10
I—‘H
GoodMa
sonryAqueducts .c = 120
. 006
. 009
.014
. 020
. 0269
9
9
9
9
. 034
. 042
. 05 1
. 072
. 0969
9
9
9
9
. 122
152
186
. 221
. 2599
9
9
9
9
.301
.344
.39 1
. 442
. 4939
9
9
9
9
. 55
. 61
.67
. 80
. 949
9
9
9
9
.08
. 24
. 41 '
. 58
. 78l—lI—‘b—‘H
r—t
. 98
. 20
. 41
.63
. 8910
10
10
10
H
Stee lR lve ted Pipe 10NeW:
9
9
9
9
9
9
9
9
9
9
M
H
H
H
H
H
O
O
O
O
9
9
10
10
10
. 007
. 01 1
. 017
. 023
. 031
. 040
050
. 060
. 084
. 1 13
. 143
. 179
. 218
. 259
.303
.353
. 404
. 460
. 52
. 58
.64
. 72
78
. 94
. 10
. 27
. 46
. 65
. 86
. 09
. 32
58
. 82
. 10
. 39
Ye arsBrickSew e rs .c 100
03008
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
I—‘H
H
l—‘O
A
hh
hh
9
9
Loss of Head in Fee t per 1000 fe e t of length .
. 009
016
.024
.034
. 045
. 058
. 072
. 087
. 122
. 163
. 208
. 260
.316
.376
.440
. 51
. 59
.67
. 76
. 84
. 94
. 03
. 14
.36
. 59
. 84
. 1 1‘
40
. 70
. 02
. 39
. 73
10
. 50
. 90
c= 80
. 012
. 020
. 030
. 042
. 0569
9
9
9
9
.072
.090
. 108
. 152
. 2029
9
9
9
9
. 259
322
.392
.468
559
9
9
9
9
.64
. 73
. 83
94
.04H
O
O
O
O
. 17
. 29
.69
. 98I—‘l—‘l—‘l—lb—fl
.30
62
98
. 38
. 789
9
10
10
10
. 20
.65
CR
A
A
D ischarge inCubicFe e tpere cond .
15
20
30
40
50
60
70
80
90
100
1 10
120
130
140
150
160
170
180
190
200
220
240
260
280
300
320
340
360
380
400
420
440
460
480
M il lionGallons Se cond .
Fee t .er 24ours .
12 .
19 .
25
32 .
38 .
45 .
71
77
84 .
90 .
96. co
mo
hn
r-a
103
109 .
1 16.
122 .
129 . 09
00
09
33
49
142 .
155 .
168 .
181
193. co
'o
o
r-w
206
219
232
245
258 O1
9
\1
\1
00
271 . 5
93
39
85
32
78
24
H
H
H
H
r—t
si
sl
xi
ou
o:
9
9
9
9
9
10
10
10
10
10
9
9
9
9
9
. 30
40
60
. 80
. 99
. 19
.39
59
79
. 99
19
39
. 59
. 79
. 99
19
.39
. 59
. 78
98
38
77
17
57
97
37
76
16
56
96
36
75
15
55
95
. 16
18
. 20
22
. 259
9
9
9
9
.30
.36
48
55
is
.63
. 71
. 80
. 89
. 989
9
9
9
9
. 09
. 19
.30
. 42HHHHH
96—INCH PIPE .
Loss of Head in Fee t per 1000 fee t of length.
Ste e lE x Good Rive te d Pipe 1033331.$2321. $
133;$233
1
, 51s Rough .
g uc 8 ’ Sew e rs .c= 140 c= l30 c= 120 c= 1 10 c = 100 c=90
0 003
0 006
0 013
0 021
0 032
0 99
1 17
l 34
1 55
1 122 1 76
1 98
2 22
1 25 2 47
1 38 2 72
1 52 3 00
1 66 3 28
3 58
1 96 3 88
2 13
2 29
Discharge inCubicFe e tperSecond.
20
30
40
50
60
70
80
90
100
1 10
120
130
140
150
160
170
180
190
200
220
240
260
280
300
320
340
360
380
400
420
440
460
480
500
550
Ve lce
102-INCH PIPE .
ite2?
vii?
“
E x
Million Head , trem elgsv
Gilt-1
238 Second Fee t . Smoo t
ours . Straightc= 140
0 004
0 008
0 02
2 47
2 64
3 88 0 23
4 23
4 58
4 93
5 29
5 64 0 65
5 99
6 34
0 89
0 98
0 85 1 08
7 75 0 93 1 17
1 02 1 27
1 1 1 1 38
8 81 1 20 1 48
9 69 1 46 1 77
Loss of Head in Fee t per 1000 fee t of length.
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
H
H
I—‘O
O
10
1-1k
9
9
9
9
9
m oo th
. 004
.009
. 016
. 024
. 034
O
. 045
057
071
086
103
. 122
. 141
. 162.
. 182
. 207
. 231
. 258
. 283
. 311
.371
438
. 5 1
58
66
74
84
93
03
13
23
34
46
58
71
02
GoodMa
sonryAqueduc ts .c= 130 c= 120
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
H
H
H
H
O
N
H
H
H
H
9
9
9
9
9
. 005
. 01 1
. 018
. 028
039
052
066
. 083
101
1 19
. 141
163
187
. 212
. 239
268
299
330
361
431
. 5 1
59
68
77
86
97
07
18
31
43
56
69
83
98
36
c= 1 10
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
l—‘b—‘
I—iI—‘H
10
10
10
H
H
9
9
9
9
9
H
9
9
9
9
. 006
. 013
. 022
. 033
046
. 061
. 078
. 097
. 1 18
. 141
. 165
192
. 220
. 249
. 281
.315
. 350
.388
. 424
. 5 1
.60
.69
. 79
. 90
.02
. 13
. 27
.39
. 53
.68
. 83
. 98
. 16
.32
. 76
Ste e lPipe 10Ye arsOld ,BrickSew e rs .c 100
0 007
0 015
0 .026
0 .039
055
073
093
0 . 116
141
167
0 197
228
262
298
0 335
088
. 1 13
. 141
. 171
. 2049
9
9
9
9
239
278
319
. 361
.4089
9
9
9
9
. 456
. 5 1
. 56
62
. 749
9
9
9
9
86
.00
14
31
47I—ih—‘I—‘t—‘O
65
83
02
23
4410
10
10
1—H
67
89
12
389
9
10
10
\
Ve ryR ough
. 110
. 141
. 175
. 212
. 2539
9
9
9
9
. 298
345
398
. 450
519
9
9
9
9
. 57
.63
. 70
. 77
929
9
9
9
9
. 07
. 25
. 43
.63
. 8314
1—1w
. 05
28
52
77
.029
10
10
10
10
30
59
89
. 20$
9
9
9
108-INCH PIPE .
Discharge in Loss of Head in Fee t per 1000 fee t of length.
Veloc Velocity in it E G d Ste e ly X 00
Cubic Million Fe e t H ead , trem ely M aR lve te d Pme 10per Ve ry Ste e l Ye arsFest Se cond Fe e t . S r
glogth Sm oo th Ron‘s: Pipe , O ld , Rough .
S egond . Hours . Straight drilcts .
New . BrickSew e rs .c= 140 c= 130 c= 120 c = 1 10 c= 1 00 c= 90 c=80
0 0 003
30 0 006
40 0 010
50 0 016
60 0 022 0 029 0 041
70 0 029 0 034 0 055
80 0 038 0 043 0 070
90 0 047 0 054 0 087
100 0 066 0 106
1 10 0 078 0 126
120 0 148
130 0 172
140 0 198
150 0 122 0 225
160 0 136 0 252
180 0 169 0 225 0 314
200 0 272 0 382
220 0 326 0 457
240 0 289 0 54
260 0 335 0 445 0 62
280 0 382 0 5 1 0 72
300 0 58 0 81
320 0 66 0 92
340 0 73 1 03
360 0 81 1 14
380 0 90 1 26
400 0 99 1 38
420 1 08 1 51
440 1 18 1 65
460 1 11 1 28 1 78
480 1 19 1 38 1 94
500 1 28 1 49
550 1 34 1 54 1 78
600 1 57 1 81 2 09
650 1 82 2 09 2 42
D ischarge inCubicFe e tperSecond .
30
40
50
60
70
80
90
100
1 10
120
140
160
180
200
220
240
260
280“300320
340
360
380
400
420
440
460
480
500
550
600
650
700
750
800
Velocit in
(1341111011
F
IE?Second.
Hours .
1 02
1 15
2 29
2 55
2 80
3 06
3 31
3 56
3 82
4 07
4 33
4 58
4 84
5 09
5 35
5 60
5 86
6 1 1
6 37
7 00
7 64
8 27
8 9 1
9 55
517 10 18
120-INCH PIPE .
Loss of Head in Fee t per 1000 fee t of length.
Ve lceHityd 63
315121
(i62
9
F369 ,
S igro
ot8 1113
1
3111 zonry $232
1
, O ld , R ough .
que
Straight ducts . ew .
egg“c= 140 c=130 c= 120 c= 1 10 c = 100 c=90
0 03
0 022 0 04
0 028
0 034 01039
0 041 0 076
0 048 0 089
0 064 0 118 0 144
0 082 0 152 0 184
0 102 0 188 0 229
0 123 0 163 0 229 0 279
0 147 0 195 0 273 0 332
0 229 0 321 0 390
0 372 0 452
0 428 0 52
0 . 47 0 484 0 59
0 55 0 66
0 328 0 61 0 74
0 68 0 82
0 402 0 75 0 92
0 442 0 82 1 00
0 484 0 64 0 90 1 10
0 53 0 70 0 98 1 19
0 57 0 76 1 07 l 30
0 62 0 83 1 16 1 42
0 67 0 90 1 25 1 52
0 80 1 07
0 94 1 25
1 08 1 45
1 25 1 67
1 42 1 88
1 59 2 12
Ve ryRough.
c=80
. 010
. 018
. 027
. 037
.0509
9
9
9
9
. 063
. 079
.096
114
. 134‘
9
9
9
9
9
. 179
. 229
. 284
.348
. 4139
9
9
9
9
.485
56
65
74
. 92
. 03
. 14
. 25
.37H
H
H
H
O
. 49
.62
. 76
. 88
.26NJ
H
H
H
v—l
132-INCH PIPE .
Loss of Head in Fee t per 1000 fe e t of length .
Velocity in V?IOC Stee l
Cubic Million Fee t Head , 9 55513:(ix/13
9R is‘
g
e t‘
fd 10Fe e t Gallon s
86133n Fee t . Smoo th somry
Pig; ($1eper per 24 39 d A qua”
N BrickSe cond . Hours . Straight ducts . Sew e rs .c= 140 c= 120 c= 1 10 c= 100
30 0 002
40 0 004
50 0 00 0 006
60 0 01 0 009
80 0 01 0 014
100 0 02 0 021
120 0 02 0 030
140 0 03 O 040160 0 04 0 052
180 0 06 0 064
0 O7 0 078
0 08 0 092
0 10 0 108
0 12 0 126
0 13 0 144
3 16 0_
15 0 164 0 188 0 219 0 305
3 37 0 18 0 184 O 21 1 0 246 0 344
3 58 0 20 0 207 0 238 0 276 0 386
360 3 79 0 22 O 230 0 262 O 306 0 429
4 00 0 25 0 254 0 29 1 0 339 0 472
4 20 0 27 0 279 0 320 0 372 0 52
4 42 0 30 0 306 0 35 1 0 407 0 57
4 62 0 33 0 332 0 382 0 442 0 62
4 84 0 36 0 361 0 415 0 481 0 68
5 05 0 40 0 39 1 0 449 0 52 0 73
5 26 0 43 0 483 0 56 0 79
5 79 0 52 0 58 0 67 0 94
6 30 0 62 0 68 0 78 1 11
6 84 0 73 O 78 0 92 1 28
7 36 0 84 0 90 1 05 1 47
750 7 89 0 97 1 03 1 18 1 67
8 42 1 10 1 16 1 34 1 88
8 94 1 24 1 29 1 50 2 10
9 47 1 39 1 44 1 67 2 33
9 99 1 55 1 59 1 84 2 59
Discharge inCubicFe e tSecond .
240
MillionGallon sper 24Hours .
01
77 .
90 .
103.
1 16.
129 .
142 . 10
9
9
19
01
155 .
168 .
18 1 .
193.
2060033
0
0
94
219
232 .
245 .
258
271 01
01
0
a
284
297 .
310 .
323.
355 . 01
10
10
9
14?
387
420
452
484 «1
19
1—400
00
01
Velocity inFee tperSecond.
.35
. 53
. 71
. 88
. 061
. 24
. 41
. 59
. 77
. 94i—‘F—‘
I—‘H
H
. 12
.30
. 48
.65
. 8310
10
10
10
10
. 18
.36
. 54
. 719
9
9
9
. 89
. 07
. 24
. 42
. 86bk
n-h
vh
n-P-9
.30
. 75
. 19
.63
. 07Q
9
9
01
01
. 5 1
. 96
. 40
. 84
. 729
m00
\l
\l
9
9
9
9
9
9
9
9
9
9
9
9
9
. 00
. 00
01
01
02
02
03
04
05
06
07
08
. 09
1 1
. 12
. 18
. 19
. 21
. 23
. 26
. 28
.30
.37
. 44
. 5 1
. 59
68
. 78
. 88
. 98
144-INCH PIPE .
E
Loss of He ad in Fee t per 1000 fe e t of length .
trem e lSmootda9Straightc 140
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
H
H
9
9
9
9
9
9
9
9
9
9
9
9
9
. 003
. 005
. 009
. 014
.020
. 026
. 034
. 042
. 050
. 060
. 071
. 082
. 094
. 107
. 121
. 136
. 15 1
. 167
. 183
. 201
. 218
. 237
. 256
. 277
330
.388
. 450
52
. 58
.66
. 74
. 82
. 9 1
.00
. 19
Good353325 mfgducts .c= 130 c= 120
0 249
0 98
1 09
1 21
1 33
1 37 1 58
Rive tedSte e lPipe ,BW.
c= 1 10
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
I—‘D—‘l—il—ir—l
“9
9
9
9
. 004
. 009
. 014
. 022
.031
. 041
. 052
. 065
. 079
094
. 11 1
. 128
. 148
. 168
. 188
. 211
. 235
. 260
. 287
.313
.341
.371
. 400
. 432
. 52
.61
. 70
. 80
92
03
. 16
. 28
. 42
. 56
. 86
Stee lPipe 10Ye arsO ld ,BrickSe w e rs .c 1 00
0 .010
0 281
0 309
0 341
0 373
0 406
0 441
0 477
0 52
0 62
0 72
0 84
0 96
1 09
1 23
R ough .
c=90
n—AH
H
H
O
ooooo
o
o
o
o
c
ooooo
ooooo
ooooo
10
10
10
1
-4
006
012
021
032
045
059
076
094
1 15
137
161
186
213
242
273
307
341
377
414
455
494
54
58
63
75
88
02
17
33
49
67
86
06
. 27
. 70
Ve ryRough .
c = 80
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
1—41—4
1—1—1-4
10
10
9
9
9
9
9
. 007
.015
. 026
. 040
. 055
. 074
.094
117
. 143
. 171
. 200
232
267
302
341
381
424
. 469
52
. 57
.62 .
.67
72
. 78
. 93
. 08
. 27
.46
.66
. 86
. 08
.32
. 57
. 37
RELATIVE DISCHARG’ING CAPACITIES OFAQU E D U CTS .
Q
Re lative E lemen ts of Conduits w hen At Approximate Point of Maximumow ing Full. Dis charge .
Mean(1112111110 Ve locity. Area .
AQUEDUCTS , — 8 TO 14 FE E T .
c=125 . At po int of maximum d ischarge the quantity is taken as 12% greaterthan in a circular aqueduct of the same he ight and w idth runn ing full .Slope Slopein Fe e t in Fe e tper 1000. per Mile . Discharge in Million Gallons Daily.0 .030 0 158 34 46 60 78 98 120 146
0 035 0 185 36 50 66 84 106 130 159
0 . 040 39 53 71 9 1 1 14 140 171
42 57 75 97 121. 150 182
0 .050 0 . 264
(44 79 102 128 158 192
0 290'
46 84 108 135 167 203
49 88 1 12 142 175 212
5 1 9 1 1 18 148 182 221
0 . 070 53 72 95 122 154 190 231
0 . 080 0 422 57 78 102 132 166 205 248
0 .090 61 83 109 140 176 218 265
0 10 64 88 1 16 148 186 230 280
0 1 1 68 92 122 156 196 242 295
0 12 71 97 127 164 205 254 309 .
0 14 77 105 138 178 224 276 336
0 16 83 1 13 149 192 240 297 361
0 18 88 120 159 204 256 316 385
0 . 20 93 127 168 215 271 335 407
0 22 1 . 162 98 134 177 227 285 352 428
0 . 24 1 . 267 103 140 185 239 300 370 450
0 . 26 1 . 373 108 147 194 249 313 386 469
0 . 28 1 12 153 201 259 325 402 488
0 30 1 584 1 16 159 209 269 338 418 508
0 35 1 848 126 172 227 29 1 366 453 550
0 40 136 185“
244 314 395 487 59 1
0 . 45 145 197 260 335 420 5 19 631
153 209 275 354 445 549 668
.0 55 2 . 904 162 219 290 373 468 579 701
0 60 3 168'
169 230 304 390 490 606 736
177 240 317 407 5 11 631 770
0 70 3 696 184 250 330 424 533 659 800
197 269 355 456 573 709 860
210 287 378 485 610 754 9 18
1 . 00 223 304 400 5 14 647 800 970
1 10 235 319 421 541 680 840 1020
AQU E D U CTS ,— 15 TO 21 FE E T .
c 125 . At po int of maximum discharge the quantity is taken “as 12% greater
,
than in a circular aqueduct‘ of the same he ight and w idth runn ing full .Slope Slopein Fee t in Fe e tper 1000. per Mi le . Discharge in M ilhon Gallons Daily.0 .020 0 . 106 140
.167 196 228 263 300 341
0 1 16 148 176 239 276 316 358
0 .024 0 127 155 184 215 250 289 330 376
0 . 026 162 192 227 261 303 346 392
0 .028 169 200 237 274 315 360 410
0 .030 0 158 176 208 245
.
285 326 374 426
0 . 035 0 185 190 226 266 310 355 406 460o . 040 0 . 21 1 205 243 286 330 381 495
0 . 045 0 . 238 218 258 305 352 406 528
0 .050 0 . 264'
232 274 323 372 430 560
0 . 055 0 . 290 243 288 340 395 453 518 588
0 . 060 0 317 254 300 353 410 475 617
0 . 065 0 343 266 315 372 433 495 642
0 . 070 277 328 388 450 5 16 670
0 .080 0 .422 298 353 410 480 552 720
0 .09 317 376 440 5 10 59 1
0 10 0 528 336 398 470 542 625
0 1 1 0 581 354 420 490 570 660
370 439 5 10 600 690
0 14 0 . 739 404 477 562 650 750
0 16 432 5 12 600 700 8 10 1050
0 . 18 0 . 950 461 547 640 740 860 1 120
0 . 20 1 .056 488 579 680 790 9 10 1040 1 180
0 . 22 5 13 610 710 830 960 1 100 1240
540 640 750 870 1000 1300
0 . 26 1 .373 562 668 780 9 10 1050 1360
0 .28 1 . 478 585 694 8 10 940 1090 1250 1420
0 .30 1 584 608 720 840 980 1 130 1300 1470
660 780 9 15 1060 1230 1410 1600
0‘
40 710 841 990 1 140 1320 1520 1720
0 .45 758 8 96 1050 1220 1410 1620 1830
2 .640 800 950 11 10 1290 1490 1700 1940
842 1000 1 170 1360 1570 1800 2040
0 60 885 1040 1230 1420 1650 1880 2130
3. 432 921 1090 1280 1480 1720 1960 2230
SEWE RS .
TABLE OF SLOPES REQUIRE D TO PRODUCE GIVEN VE LOCITIE S .
Tile , 0 1 10. Brick,c 100.
[Ill
ll
30”
30 Brick36”
421 1
IINIIIIII
( l
( l
( l
( l
l l
( K
( IN
l l
l ‘
!I( I( I( l
( lI !I t
( i
l l
9
9
9
9
9
33.
38 .
44 .
50 .
63
78 .
95
1 13
133
154
177
201
227
254
314
9
10
1—11-19
CD
Kl
flk
l-P9
. 087
136
196
349
545
785
. 23
77
41
. 14
9
9
9
9
9
9
9HHH
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
14k
01
9
9
9
9
9
9
. 80
. 39
. 94
. 80
. 70
.62
. 74
.60
. 50
. 428
372
330
. 295
. 267
242
222
205
. 190
. 166
. 147
. 131
. 1 19
. 108
. 099
. 091
085
. 079
.074
.065
pk
2 .
2 .
170‘
. 42
1—1—I
9
9
9
9
9
9
9
9
9
9
9
\I
9
9
9
l—‘O
H
9
9
9
9
9
9
9
9
9
9
1—103
00
. 39
73
10
22
. 06
. 94
12
. 90
.76
64
56
50
. 445
. 402
367
. 336
. 310
. 288
. 25 1
221
. 199
. 179
. 163
. 150
138
. 128
. 1 19
. 1 1 1
. 099
13.
10 .
bi
b
9
9
9
9
0
0
OH
H
H
H
h—t
9
9
9
9
9
9
9
9
9
9
S lope in Fe e t per 1000.
00
. 74
. 82
. 95
. 38
. 99
. 71
. 49
.31
. 56
. 26
. 06
. 9 1
. 79
.62
. 56
. 52
. 471
. 434
403
372
. 311
. 278
. 25 1
. 229
. 210
. 194
. 180
. 167
. 156
. 138
23.
18 .
14
10 .
8 .
OHH
H
H
9
9
9
9
9
9
9
9
9
9
10
9
Hk
01
9
H
CII
9
l
H
10
10
10
10
9
9
9
9
9
. 06
. 40
. 90
52
.24
.68
16
. 80
. 54
.34
. 19
. 06
. 96
80
74
69
60
53
. 472
. 428
390
358
. 330
. 306
. 285
. 266
. 236
35 .
27 .
22 .
15 .
12 .
H
H
H
N
M
10
9
A
9
9
O
H
H
H
l—l
114
01
05
t
9
9
9
9
9
9
9
9
9
9
10
00
9
9
01
va
r
. 82
. 39
. 04
. 27
. 72
. 33
.03
. 80
.61
.45
.32
. 21
. 12
. 04
. 90
. 80
72
.65
. 59
. 54
50
. 462
. 430
403
.356
66
5 1
41
29 .
22
18
14
11
H
H
b—‘b—ll—l
10
9
9
9
145
9
9
\1
9
\I
10
9
01
10
1h
00
01
H
9
9
H
H
10
10
10
9
9
9
9
9
1—41—401
03
1—4
. 79
.35
. 00
. 71
. 47
26
. 09
. 94
.69
. 49
. 33
. 21
. 10
. 01
. 93
. 86
. 80
.66
128‘
99
80
57
44
35 .
27 .
22 .
18 .
15 .
13.
12 .
14 .
1—510
10
10
10
H
H
b—‘
I—‘l—l
01
01
9
\I
OO
00
00
9
10
00
9
9
A
1¥k
flk
9
01
10
01
9
9
00
01
15
14;
. 90
. 59
.34
. 13
. 95
. 80
.67
. 55
.45
. 29
TILE SEWE R s,
— 15 To 36 INCHE S .
c= 1 10.
Discharge in Cubic Fe e t per Second , Runn ing Full .
. 4 2 .
1 8
54
59
63
67
71
78
53 85
57 92
60 98
35 6 64 103
51
53
56
58
60
Quantities corresponding to velocities betw een 2 and 3‘
and ove r 10 feet persecond are in ital ics .
B RICK SEWE R S,
— 30 To 66 INCHE S .
"
c = 100.
Discharge in Cubic Fee t per Se cond , Running Full . 4
29 39 52
30 41 5432 43 5 7
33 45
35 48
5 1
55
59
63
67
47 70
49 7451 77
7 53 1 14 1 55 263
8 57 122 166 282
9 61 130 1 78 301
10 65 138 1 88 248 319
1 1 68 145 198 261 335
Quantities correspbnding to ve locities betw een 2 and 3 and over 7 feet per second are in ital ics .
B RICK SEWE R S , — 72 TO 108 INCHE S .
c= 100.
D ischarge in Cubic Fee t '
p er Second , Running Full.
Quantities corresponding to velocities betw een 2 and 3 and ove r 7 feet per second are in ital ics .
B RICK SEWE R S,— 1O To 15 FE E T .
c= 100.
Discharge in Cubic Fe e t p e r Second , Running Full .
Quantities corresponding to velocities betw een 2 and 3 and over 7 feet per second are in ital ics .
COMPUTATION OF DECREASE IN THE VALUE OF 6 INCAST-IRON PIPE,WITH AVERAGE SOFT UNFI L
TE R E D RIVER WATER,THROUGH A PERIOD OF
Y E AR S .
lst. Assume that the original value of c is 130.
2d. As sume that the increase in loss of head due to tube rculation , etc. ,amounts
to 3% per year.3d. Assume that the diamete r of the pipe is reduced by tube rculation at the rate
of inch per year , and that the value of 6must be modifi ed to correct for this .
Value of 0 ,A ge of w i th no A1Pipe in low ance forYears . Reduction inDiam e te r . Value of c afte r Making Allow ance for Decrease in Diame te r .
130 130 30 l30 130 130 130 130 130 130 130 130 130
113 106 08 109 110 110 111 1 11 112 112 112 1 12 112
i
88 92 94 96 97 98 99 99 99 99 100 100
75 80 83 85 86 87 88 89 90 90 90 9 1
64 71 74 76 78 79 80 81 82 83 83
79 3 56 63 67 69 71 73 74 75 76 76 77 78
48 56 61 63 65 67 69 70 71 71 72 73
42 5 1 55 58 60 62 64 65 66 67 67 68
67 . 1 37 46 5 1 54 56 58 60 61 62 63 64 65
64 2 33 42 47 50 52 55 57 58 59 60 61 62
29 38 43 47 49 52 54 55 56 57 58 59
COMPARISON OF THE LOSS OF HEAD OF WATER INPIPES OF VARIOUS AGES,AS COMPUTED B Y
THE METHODS USED(1) by CO E FIN :
“Graph i c a l So lut ion of Hydraul ic Problems .
(2) by WE S T ON :“Fr ict ion Of Wat er in Pipes .
”
(3) by HA zE N WI L L I A M s : F igures used in th is volume .
Ve locity ofVe locity of5 Fee t per Second.Ve locity of
3 Fee t per Second .1 Foot per Second .
Haz en Hazen HazenCo ffi n . We ston Wil Co ffi n . We ston Wil Coff in . We ston William s . liams . liams .
New 4 1 18
16 . 25 2 09 2 00
48 . 080 0 5 1 0 55
10 4 . 54 16 0 15 0
16 . 33 2 9 2 7
48 . 10 0 7 0 7
20 4 . 90 21 0 21 0
16 . 41 3 8 3 4
48 . 13 0 9 0 9
40 4 .60 23 0
16 . 56 5 6 5 0
48 . 18 1 4 1 3
SHORT METR IC EQUIVALENT PIPE TAB L E .
D ischarge inGallonsDaily.c= 100O ld.
1
1
Cubic M e tersDaily.D = 0. 1
c= 100 c= 130O ld. New .
1 11 8
100 130
150 195
200 260
250 325
300 390
350 455
400 520 7 . 4
500 650
600 780
800
57
76
97
120
146
220
310
5 15
800
130 000
Loss of Head in Me te rs per 1000 m e te rs of length .
D =O.2
I ns .
9
9
9
9
9
9
9
9
9
9
A
w
w
u
b—t
10
18
27
38
65
99
138
183
235
292
356
02
04
07
1 1
15
20
25
38
54
9 1
38
93
58
30
10
9
9
01
9
D =O.3
I ns .
9
9
9
9
9
9
9
9
9
9
9
9
9
10
H
l
13
19
25
32
41
50
75
105
180
272
01
01
02
03
03
05
07
13
19
27
36
46
57
69
05
47
50
6:
10
q
00
D iame te rs in Me te rs .D =O.4
I ns .
9
9
9
9
9
9
9
9
9
9
9
9
9
9
Ca
ta
co
mb-A
12
18
25
43
67
93
160
240
01
01
02
03
05
07
09
1 l
14
17
26
36
62
93
31
23
38
70
D =O.5 D = O.6
I ns .
10
1-i
l
9
9
9
9
9
9
9
9
9
9
00
9
9
9
10
01
01
02
02
03
04
05
06
09
12
21
31
44
75
13
60
10
7040
10
Ch
i-P
OO
I ns .
9
10
1—‘Ll-dl-ml
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
9
9
01
01
01
02
02
02
04
05
09
13
18
31
47
65
87
12
38
68
55
9
9
9
9
9
9
9
9
9
9
00
01
9
10
1
01
O2
03
04
08
12
16
22
28
34
42
63
88
50
26
20
9
9
9
9
9
9
9
9
9
9
10
b—‘HOO
01
01
02
03
04
05
07
09
12
14
21
29
50
76
07
80
73
9
9
9
9
9
H
9
9
9
9
9
9
9
9
9 . 01
.01
02
. 02
.03
. 04
. 05
. 06
. 09
. 12
. 21
. 31
. 44
. 75
. 13
‘ UNDERDRAINS FOR SAND FILTERS .
Rate of fi ltration,million gallons per acredaily
Assumed resistance of
clean sand,feetTotal allow able friction
and ve locity head in
(No compensating orifi ces used . )
10
unde rdrainage systemApproximate ratio of
fi lte r area to area of
main drainApproximate ve locity inmain drain (varyingsomew hat w ith s ize) 0 67 0 80 1 .00 1 18 1 .34
Approximate ve locityin late rals .(varyingsomew hat w ith size ) .
MAXIMUM AREAS DRAINED IN SQUARE FEET .
79 70 64 59 53 48 41
180 160 147 137 122 1 11 93
325 264 245 218 200 168u 7
5 17 420 390 345 316 266
750 610 570 500 460 390
I I I c 1 ,340 1,200 1
,090 900 820 690
360 320 290 270 240 220 180
640 570 520 490 430 400 320
1 ,020 900 830 770 680 630 5307 7
1,320 1
,200 1
,120 1
,000 910 770
11,200
11 ,400
31 ,500
31 ,000
Note — For main drains , c is taken as 1 10, and it is assumed that the spacedrained is tw ice as long as w ide . For lateral drains , c is taken as 100, and it isassumed that the space drained is four times as long as w ide . Cons iderable changein shape of area drained does not greatly affect the results , and the fi gures maybe used as approximations for all ordinary conditions .
62
THE FL OW or WATE R OVE R w Erns .
SHARP-EDGED WEIRS .
THE basis of our experimental knowledge of the discharge of waterover
’
w eirs of size applicable to the ,cases usually encountered in praetice rests primarily upon three investigations , viz . :
(a) That of Mr . Jas . B . Francis,M . Am . SoclC . E .
,made at L owell
,Mass ,in 1852 .
(b) That of Messrs . Alphonse Fteley and Frederic P . Stearns,Members Am . Soc . C . E .
,made at Boston , Mass ,
in 1877,1878
,
a nd 1879 .
(c) That of M . Henry Bazin,Inspecteur General des Ponts et Chaus
sees,made at D ijon , France , in 1886, 1887, and 1888 .
E ach of these investigations has given rise to a formula for determining the fl ow of water over a sharp-edged vertical weir without endcontractions,named from the observers
,and these three formulas comprise those most commonly applied in practice .The symbols used in these formulas and in the following tables are
H= the total head or height from the crest of the weir to still water,measured in feet;h=the observed head or height of the surface of the running waterabove the crest of the weir
,at some convenient point
,meas
ured in feet;hv=the head to which the mean’ velocity of the approaching water is
2
due , measured in feet— Le ,hv=g—g
—where v=velocity in feetper second;
L =the total length of the crest of the weir,or the mean width of theover-falling sheet at the plane of the weir
,measured in feet;
p=the height of the crest of the weir above the bottom of the channe lof approach
,measured in feet;
Q= the quantity of water discharged per second over a weir, measured in cubic feet;
g= the acceleration due to gravity=32 . 16feet per second .
63
64 THE FLOW OF WATER OVE R WEIRS .
The Francis formula,then
,is
Q=3-33LH % or Q=3 - hv% l Ri fl e
The Fteley and Stearns formula isQ G.OO7L or Q 3.31L (h+ Q.OO7L .
The Bazin formula 18 ’
where m= 0405 +
The several observers used different methods Of reading the head 11,and for an accurate application Of the formulas the head should be readin the same manner as in the original experiments .Mr . Francis
,in the experiments upon which his formula is based
,
Observed the head as communicated through a small orifice (about31 inch diameter) . in the side Of the channel O f approach
,about 1 footbelow the level Of the crest and 6 feet up
-stream therefrom,
'whichw as connected through a pipe about 18 inches long .to a cistern
,
i
w here
the surface w as read by a hook gage . The weir w as of L = 10 ‘
feet .
In a part Of their experiments,which were made on a weir With L = 5feet
,Messrs .
‘
Fteley and Stearns made use of a small orifice in thecenter of a plank 10 inches long , set with its face vertical and parallelto the axis Of the channel of approach,and about 16 inches from theside wall
,so that the orifice w as about 10 inches above the bottom and
6feet up—stream from the weir,the orifice being connected by piping toa movable cistern
,in which the head w as read by a hook gage . For therest Of their experiments these Observers made use Of eight small ori
fi ces s imultaneously,which were connected in pairs
,Opening in Opposite
directions . These orifices were in the center Of steel plates about6 inches long
,located parallel to the current at about the level Of the
crest Of the weir,and were 6 feet up-stream therefrom , and 18 inchesand 7 feet respectively from the side walls Of the channel , the weir
being Of L = 19 feet .
In the experiments Of M . Bazin , who worked on weirs Of L =6.56feet,
feet,and feet
,the head was communicated through anorifi ce 4 inches in diameter, at the bottom Of the channel of approachand feet up-stream from the weir , connecting with a pit , wherein thesurface of water w as located by a hOOkgage and a dial-fl oat.
E xperimental comparisons Of these formulas , where the heads wereObserved in the manner described for each , has shown them to agree
THE FLOW OF WATER OVER WEIRS.c 65
within 21} per cent forheads from up to 3 feet,and that the Fteleyand Stearns and“ the Bazin formulas agree within 2 per cent for headsup to 4 feet . The Francis formula w as only intended to apply betweenheads Of and feet
,and should not be us ed for higherx heads .
Wh ere'
other methods Of reading
'
the head are used,errors Of as "
much
as 10 per cent may be introduced . One Of the most erroneous of theseis by the aid of a pipe placed in the current parallel to the weir andperforated upon its bottom or top .A very convenient as well as accurate means Of reading the headupon a weir
,and one which introduces but a small error
,is by the use
Of a sharp-pointed plumb-bob suspended U pon a steel tape,the latter
pass ing over a block on which a line is drawn at right angles to thetape,the reading taken being that 0Of the tape where the line intersects
it. The reading Of the tape corresponding to the pos ition Of the bobwhen in contact with the water surface , when the latter is at the levelOf the crest Of the weir,must be determined and used as the datum .The point Of Observation should be far enough away from the crest ofthe weir to be beyond the curve Of the approaching sheet
,and the elevation Of the water surface may be read by allowing the point Of thebob to come in contact with it
,the bob being still
,or by swinging the
bob and allowing it to cut the water surface . Whichever method isadopted should be used in determining the datum reading,as the indications are somewhat different . Such readings will b e found to fit theBazin formula more accurately than they will either Of the others .
TO facilitate the use Of this formula , the following table giving thedis charge over weirs of various heights from 2 to 30 feet and for headsfrom to «feet is presented . The discharges in this table can onlybe used in cases where the level of the water surface On the down-streams ide of the weir is below the crest
,and the space between the face Ofthe weir and the over-falling sheet is in free connection with the outside air . I f a partial vacuum be formed behind the sheet
,from lackOf free circulation
,the discharge will be increased
,under some conditions as much as 5 per cent . If the water on the down-stream side riseabove the crest
,the weir then becomes submerged or drowned and thedischarge is consequently decreased .
DISCHAR GE FER FOOT OF LENGTH OVE R SHARP-E DGEDVERTICAL WEIRS,WITHOUT END CONTRACTIONS .
COMPUTED B Y BA!IN’S FORMULA .
Obse rved head=h . He ight O f w e ir= in. D ischarge =Q. g=32 . 17 feet.Length of w eir=L .
p =2 Ft . p =3 Ft . p =4 Ft . p= 5 Ft . p
=6Ft . p=7 Ft . p =8 Ft .
a h hin Fee t . Q Q Q Q Q Q Q in Fee t .
Cu . Ft . Cu. Ft . Cu. Ft . Cu . Ft . Cu. Ft . Cu . Ft . Cu . Ft .
p e r S e c . p e r S ec . p e r S e c . p e r S e c . p e r S e c . p e r S ec . p e r S ec .
DISCHARGE PE R. FOOT OF LENGTH OVER SHARP-E DGEDVERTICAL WEIRS,WITHOUT END CONTRACTIONS .COMPUTED B Y BA!IN ’S FORMULA .
.00984
It
Observed head=h. He ight O f w e ir=p . D ischarge =Q. feet.Length O f w eir=L .
Q 405 +
p= 9 Ft, p
= 10 Ft . p = 16Ft . p =20 Ft . p =25 Ft . p =30 Ft .h h
in Fee t . Q 1 Q Q Q Q Q Q in,Fe e t .
Cu. Ft . Cu. Ft . Cu. Ft . Cu . Ft . Cu . Ft . Cu . Ft . Cu . Ft .p e r S e c . p e r S e c . p er S ec . p e r S ec . p e r S ec . p e r S e c . p e r S ec .
68 THE FLOW OF WATER OVER WEIRS .
LOW HE AD S .
For heads below foot the Bazin Formula gives d ischarges somewhat in excess Of t he experimental results Of Fteley and Stearns,andin practice accurate weir measurement at low heads becomes extremelydifficult '
Ou account Of the increased relative “ importance ~
Of errors OfObservation,and Of changes in the character Of the flow if the edge Ofthe weir has a measurable thi ckness . It may also be expected thatthe temperature Of the water will exercise considerable infl uence . Forthese low heads the formula deduced by Fteley and Stearns for theirsmall weir
,gives results varying from theexperiments by from 4 to 6per cent for heads from to foot
,thelowest Observed . The actual results were usually greater than thosegiven by the formula . For a head Of foot this formula gives a discharge Of cu . ft . per second , as compared with cu . ft . by Baz in .
A value Of cu . ft . seems quite nearly correct for this head .
END CONTRACTIONS .
For weirs having end contractions the formula‘
of Mr . Francis,modi
hed as he proposed by subtracting the quantity 0 17311 from the valueof L,making the formula Q=3.33(L — 0. 1nH)I
—I %,is the one generally
recognized . In this modification 71. is the number Of end contractions,or the proportion Of a complete contraction . Recent experiments
indicate that the effect Of end contractions is not to be provided for byso simple a formula , and until more data are available such weirs shouldbe avoided so far as circumstances will permit .
VE RY HIGH WE IRS .
Wh en the weir is Of such dimensions in proportion to the channelOf approach that the velocity Of the approaching water may becomezero
,the formula Of Bazin reduces to Q
which corresponds to p=infi nity, and the following table gives the valueOf the several factors
,and the discharge under this condition forfoot . In this and the preceding table 9 has been taken as feet
,that being its value for latitude 40° and an elevation above sea-level Of500 feet .
70 THE'
FLOW OF WATER OVER WEIRS .
FLAT-CREST AND OTHER WE IRS .
The formulas,for the discharge Of vertical sharp-edged weirs cease to
be applicable when the crest is widened Or the up-stream face inclined ,and in order to determine what modifications should be made in thecomputed results , experiments have been made U pon some twenty-fi vemodels Of different forms , with L = 16 feet and p as great as feet,using heads up to and in some cases a little above 4 feet .Fromthese experiments the factors by which to multiply the com
puted discharge for a sharp-edged weir Of the same L and p , to givethe actual discharge over each form Of crest , have been deduced for theheads given in the follow ing ' tables , ,wherein the first column gives thehead and the columns headed I I ‘
the multipliers . TO use the tables,the discharge for the weir Of given form should
.
be first computed asfor a vertical sharp-edged weir Of the same height and length , us ingany of the above formulas , or the tables On pages 66, 67, and 69 , and theresulting OS should then be multiplied by the factor in the propercolumn under II
,
" when the accuracy Of the result may be expected tocorrespond to that Of the first computation .
.
80 long as the top Of theweir is fl at and the up-stream face vertical , it appearsthat the factorsgiven should be applicable to any height of weir, but if the up-streamface or any part Of the profile up-stream , from the highest point Of theweir,is inclined , the factor will change with the height Of the weir, as
is shown by the table for triangular weirs .
On all the models having vertical dow n—s tream faces,includingmodel P
,air was admitted .to the space underneath the sheet . Onmodels D and E experiments were made with the Space underneaththe . sheet unaerated
,so that a partial vacuum existed there
,whichis shown to increase the d ischarge about 5 per cent at the high heads .
For the weirs with inclined down-stream faces , models F to O inclusive,no air w as admitted under the sheet . A comparison Of the resultsupon models G and H shows the effect Of rounding the up
—streamcorner of this Weir to be an increase in discharge Of about 4 per centat the high heads .
WEIR DISCHARGE .
RECTANGULAR FLAT-TOPPED WEIRS.
Multiplie rs Of Discharge ove r Sharp-e dged Ve rticalWe ir of Same L and p .
b= b b=Ft . 165/Ft . Ft .
P
0 . 957,l
1 000
WEIRS.
COMPOUND WEIRS .
S ee Opposite page .
Multip lie rs .M e F. Type G. Type H . Type I . Type J. Type ‘
K.
4 11 1
WEIR DISCHARGE.
COMPO
WEIR DISCHARGE .
T R A P D A L W E I R
30
x 3'
xX’
Angle
Multiplie rs of Discharge ove r S harp fiedged Ve rtical We ir of Same L and np .
D w ith 1 E w i thType A . TYPO B Type D ’ Vacuum .
Type E ' Vacuum .
WEIR DISCHARGE.
COMPLEX WEIRS .
in Fe e t Type M . Type N. Type 0 . Type P.
