HY D-RAULIC PROPE.RTlES OF- PIPE, BOXES, AND RECTANGULAR CHANNELS

BUREAU OF ENGINEERING City of Leg Ar?ge!es

: LYALL A. PAROLE City Engineer

OFFICE STANDARDS No. 116 and 117

STORM DRAIN DESIGN DIVISION

STORM DRAIN DZSIGN DIVISION OFFICE STAXD.;IRD NO. 116

rnaly of the hydraulic properties

of part-full pipe us:ially found

in individual tables. The

tabular values range from j.

depth/diameter rd.ti.0 of .COIi to

0.549 in increments of O.Wl.

The tables dre b;ised upon the following formula:

Aii2'3 The vdlues for tl-ie convedace factor - Z.rld t'r:e D a/3

*.w,

reciprocal v.IIi~c lJ are btlsed upon the crlssumption that I .486~R'~

uniform flow condition=; exist.

Tr, 813 %cili.t,titte tht: calculations, vdiues for D , 5h D ‘13 , D 9

D2, D", dre included in t~~;iijular form after tne T;;rble of I",ydrstiiic

PropertiG:s. The viilui.:;; v dr'y i'?orn t inches to 12 Incne3 iii

Increments oi' 2 inches; from 13 iriches to ij4 Inches in incremerlts

Oi’ :j inches; and from >jG inche;; to 144 inches I:i increments of

6 inches.

- l-

D d A R

s" TW dc hvc %

P

Column 1

Column 2

Column 3

Column 4

Discharge, cubic feet per second (cfs.) Pipe Diameter, feet Depth of flow, feet Area of water, square feet Hydraulic radius, feet Mannings roughness coefficient Slope of energy gradient, feet per foot Top width of water surface, feet Critical depth, feet Velocity head where d = d,

Critical slope where d = d, Static pressure, cubic feet

(1)

(2)

EXPLANATION OF TABLES

$; ratio of depth to diameter

-$ value x D2 = Area

;; value x D = Hydraulic Radius

K, = AR""; Q e/,' D = K, (l.;,,) $3 $2

Given: Q, D, S, n

Required: d, A, V

Solve for K,. From Table read $, -.k, D2

Solve for d, A, V

Given: d, D, S, n

Required: Q, A, V

Determine $. From Table read K,, A D2

Solve for Q, A, V

-2-

Column 5 K2 = Dti . 1.486AR"'

S

Given: d, D, n, Q

Required: S, A, V

Determine g. From Table read K,, A D2

Solve for S, A, V

Column 6 % value x D = Top width

Column '7 2. x value x D6k= Q (d = dc) D

(1) Given: Q, D

Required: d,, A V,

Determine 3; dc A D

From Table read D, D'

Solve for d,, A, V,

(2) Given: d,, D

Required: Q, A, Vc

Determine g; From Table read &, 4 D=/2 D-d

Solve for Q, A, V,

Column 8 hVC 7); value x D = Velocity head (d = dc)

-3-

Column 9

Column 10

IRC 12-l-66

S,D'jS yz--;

value x n2 D ‘13

= S,(d = dc)

Given: Q, D, n

Required: S,

Determine Q d, S,D"3 -%* D

From Table read D, n

Solve for S,

value x D3 = Pressure

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HYDRAULIC PROPERTIES OF PART-FULL PIPE

d A R AR% 0% TW D v 0 m=Kc ,_a6AR%=K2 7

Q DH

hi ScD” P D n2 7

.OlO .0013 .0066 .00004 14360.1690 .1989

.011 .0015 .0072 .00005 11687.7140 .2086

.012 .OOl? .0079 .00006 9685.1971 .2177

.013 .0019 .0086 .00008 8147.9219 .2265

.014 .0021 .0092 .00009 6943.3754 .2349

.015 .0024 .0099 .OOOll 5982.8586 .2431 ,016 .0026 .0105 .00012 5205.2172 .2509 .017 .0029 00112 .00014 4567.2235 .2585 .018 .0032 .0118 .00016 4037.6460 .2659 .019 .0034 .0125 .00018 3593.4682 .2730 .020 .0037 .0132 .00020 3217.4274 .2799

.021 .0040 .0138 .00023 2896.4142 .2867 .0027 .0070 60.6030 .00003

.022 .0043 .0145 .00025 2620.2916 .2933 .0029 .0073 59.7297 .00003

.023 .0046 .0151 .00028 2381.1385 .2998 .0032 .0077 58.9092 .00004

.024 .0049 .0158 .00030 2172.7068 .3060 .0035 .0080 58.1363 .00004

.025 .0052 .0164 .00033 1989.9971 .3122 .0038 .0083 57.4066 .00005

.026 .0055 .0171 .00036 1828.9900 .3182 .0041 .0087 56.7159 .00005 cO27 .0058 .Ol77 .00039 1686.4119 .3241 .0044 .0090 56.0611 .00006 .028 .0061 .0184 .00043 1559.5804 .3299 .0048 .0093 55.4389 .OOOOh .029 .0065 .0190 .00046 1446.2835 .3356 .0051 .0097 54.8468 .00007 .030 .0068 .0197 .00050 1344.6802 .3411 .0055 .OlOO 54.2823 .00008

.031 .0072 .0203 .00053 1253.2308 .3466 ,032 .0075 .0210 .00057 1170.6396 .3519 .033 .0079 .@216 .00061 1095.8092 .3572 .034 .0082 .0223 .00065 1027.8064 .3624 .035 .0086 .0229 .00@69 965.8336 .3675 .036 .0090 .0235 .00074 909.2057 .3725 .037 .0093 .0242 .00078 857.3313 .3775 .038 .0097 .02fi8 .00083 809.6985 .3823 .039 .0101 .0255 .00087 765.8606 .3871 .040 .0105 .0261 .00092 725.4307 .3919

.041 .0109 .0268 .00097 688.0646 .3965

.042 .0113 .0274 .00102 653.4675 .4011

.043 .0117 .0280 .GO108 621.3739 .4057

.044 .0121 .0287 .00113 591.5488 .4101

.045 .0125 .0293 .00119 563.7867 .4146

.046 .01.?9 .0300 .00125 537.9026 .4189

.047 .0133 .0306 .00130 513.7333 .4232

.048 .0138 .0312 .0,0137 491.1320 .4275

.049 .0142 .03?9 .00143 469.9670 .4317

.050 .0146 .0325 .00149 450.1210 .4358

.0006 .0033 76.7099 .ooooo

.0007 .0036 74.3963 .00000

.0008 .0040 72.3505 .ooooo

.OOlO .0043 70.5229 .00001

.0012 .0046 68.8763 .00001

.0013 .0050 67.3819 .00001 r0015 .0053 66.0169 .00001 .0017 .0056 64e7632 .00002 .0019 .0060 63.6061 .00002 .0022 .0063 62.5334 .00002 .0024 .0066 61.5352 .00003

.0058 .0103

.0062 .0107

.0066 .OllO

.0070 .0114

.0075 .0117

.0079 .0120

.0083 .0124

.CO88 .0127

.0093 .0131

.0098 .0134

.0102 .0137

.0108 .0141

.0113 .0144

.0118 .0148

.0123 a0151

.0129 .0154

.0135 .0158

.ol.40 .0161

.0146 .0165

.0152 .0168

53.7434 .00008 53.2282 .00009 52.7350 .OOOlO 52.2622 .OOOll 51.8@85 .00012 51.3726 .00013 50.9534 .00013 50.5498 .00014 50.1610 .00015 49.7860 .00016

49.4240 .00017 49.0743 .odo19 48.7363 .00020 48.4092 .0@021 48.0927 .00022 47.7859 r00023 47.4886 .00025 47.2003 .00026 46.9204 .00028 46.6487 .00029

-5-

This table combines many of the hydraulic properties of

rectangular channels and box structures usually found In individual

tables. The tabular values range from a depth/width ratio of 0.020

STORM DRAIN DESIGN DIVISION OFFICE STANDARD NO. 117

HYDRAULIC PROPERTIES OF

RECTANGULAR CHANNELS AND

BOX STRUCTURES

to 1.500 1n Increments of 0.001.

The structures have a 'V" shape Invert with a slope

toward the center of 0.04. The usual fillets In the upper cor-

ners of the box section have been ignored.

b . w

t-

b .

d

S -

Channel Box

s = 0.04

The tables are based upon the following formula:

For the open channel, the values for the conveyance Y3

factor AR and the reciprocal value bQ3 bW3 1 486A~~~

are based upon the .

assumption that uniform flow conditions exist. The box structure

is assumed to be flowing with a full wetted perimeter.

To facilitate the calculations, values for b4"", b6', b'3,

b2, b3, are Included in tabular form after the Tables of Hydraulic

Properties. The values vary from 4.00 to 25.00 In increments of

0.,25. - 26 -

Formulas for the hydraulic properties included in the

tables follow the section titled "Explanation of Tables".

Symbol

Q b d A R n S de Sc P

Column 1

Column 2

Column 3

Column 4

Discharge, cubic feet per second (cfs.) Width of channel or box, feet Depth of flow, or depth of box, feet Area of water, square feet Hydraulic radius, feet Manning's roughness coefficient Slope of energy gradient, feet per foot Critical depth, feet Critical slope, when d=d, Static pressure, cubic feet

EXPLANATION OF TABLES

Channel and Box d. -> b

ratio of depth to width

A. F' 'value x b2 = Area

Channel R -_; b

value x b = Hydraulic Radius

Kl =AR2/3. Q 93 ’ b

(1) Given: Q, b, S, n

Required: d, A, V

Solve for K,. From Table read d* A b' F

Solve for d, A, V

(2) Given: d, b, S, n

Required: Q, A, V

Determine g. A From Table read K,, i;z-

Solve for Q, A, V

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Column 5 value x be - Q

Column 6

Column 7

Column tj

(1) Given: Q, b

Required: d,, A, Vc

Determine Q i?=

From Table read d + , $

Solve for dc, A, Vc

(2) Given: d,, b

Required: Q, A, V,

% Determine b. From Table read Q A p?F

Solve for Q, A, V,

&b"=_ 7

value x n* -_ S, (d ‘h

= dc) b

Given: Q, b, n

Required: S,, A, V,

De.terml.ne Q dc 35' From Table read b

S,d/" * Solve for S,, A, V, -7 n

P. i7

value x b3 = Pressure

K2 = b e/, .

1.486AR' S

Given: d, b, n, Q

Required: S, A, V

Determine $. From Table read K2, A 7

Solve for S, A, V

- 28 -

Box

Column 9 value x b = Hydraulic radius

Column 10 K3 = AR'/".. Q_K -p’

(1) Given: Q, b, S, n

Required: d, A, V

Solve for K3. From Table read d A 6' p

Solve for d, A, V

(2) Given: b, d, S, n

Required: Q, A, V

Determine g. From Table read K,, -!&

Solve for Q, A, V

- 29 -

FORMULAS

s= 0.04

t =x

S 3

Channel Box

Channel

1. Area

A zbd-$

qb2 - $b2 = b2 (x-0.01)

$= x-o.01

2. Netted Perimeter

'JJ.P. = 2 (d-3) + 2 [($ + ($br]"

= 2 (xb-gb) + 2 @)(1+sll"

r= b [(2x-S) + (l+S2)""]

Assume 1+S2 -1

W.P. = b (2x-S+l)

= b (2x+0.96)

3. Hydraulic Radius

R= b2 ( 1 $k = b (2:i::;fi)

=: b(“-0.01) (2x+0.96)

x-o.01 -2!xr$E

- 30 -

4. Conveyance Fat tor

*k’/3 = b2(x-0.01)

5. Reciprocal

1 1.4& Conveyance Factor =

6. Plow At Critical Depth

f\ A3 “2

&=

=

=

\ bl

[gb6 (x-b0.CUf]v2

5.t5'75b5'* (x-O.Olp

$,*= 5.675 (x-O.Olp

‘7 l Critical Slope

S = (1.4~~AR~2where &= 5.675 ($r

6. Pressure

2x+0. g6)2’3 (bvs) (X-.Ol)a

P = “j;s; _ (bd) (;) - $ [d; (q)]

- 31 -

9.

10.

11.

12.

Sb2d + $ t

b3 x2 = - - 0.01b3x + .oooo667b3 2

P X2 =-- F 2 0.01x + 0.0000667

Box

Area

A = b2(x-0.01) A i7

= x-o.01

Netted Perimeter

W.P.

= 2d-Sb+2b

= 2xb-Sb+2b = b(2x+l.$h)

Hydraulic Radius

R=

=

R -= b x-o.01 'Yf5zXqT

Conveyance Factor

ARe'3 = b*(x-0.01)

IRC 12-l-66

- 32 -