Page 374 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 303

where V velocity, ft/s (m/s)
C coefficient, dependent on surface roughness of conduit
S slope of energy grade line or head loss due to friction, ft/ft (m/m) of
conduit
R hydraulic radius, ft (m)
Hydraulic radius of a conduit is the cross-sectional area of the fluid in it
divided by the perimeter of the wetted section.

Manning’s Formula

Through experimentation, Manning concluded that the C in the Chezy equation
1/6
should vary as R :
1.486R 1/6
C (12.22)
n
where n coefficient, dependent on surface roughness. (Although based on
surface roughness, n in practice is sometimes treated as a lumped parameter for
all head losses.) Substitution gives
1.486
V R S (12.23)
2/3 1/2
n
On substitution of D/4, where D is the pipe diameter, for the hydraulic
radius of the pipe, the following equations are obtained for pipes flowing full:
0.590
V D S (12.24)
2/3 1/2
n
0.463
8/3 1/2
Q D S (12.25)
n
LQ 2
h f 4.66n 2 (12.26)
D 16/3
1/2
2.159Qn 3/8
D S (12.27)
3
3
where Q flow, ft /s (m /s).

Hazen–Williams Formula
This is one of the most widely used formulas for pipe-flow computations of
water utilities, although it was developed for both open channels and pipe flow:
S
V 1.318C 1 R 0.63 0.54 (12.28)