CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 303

where Vvelocity, ft/s (m/s)
Ccoefficient, dependent on surface roughness of conduit
Sslope of energy grade line or head loss due to friction, ft/ft (m/m) of
conduit
Rhydraulic radius, ft (m)

Hydraulic radiusof 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 Cin the Chezy equation
should vary as R1/6:

(12.22)

wherencoefficient, dependent on surface roughness. (Although based on
surface roughness, nin practice is sometimes treated as a lumped parameter for
all head losses.) Substitution gives

(12.23)

On substitution of D/4, where Dis the pipe diameter, for the hydraulic
radius of the pipe, the following equations are obtained for pipes flowing full:

(12.24)

(12.25)

(12.26)

(12.27)

whereQflow, ft^3 /s (m^3 /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:

V1.318C 1 R0.63S0.54 (12.28)

D

2.159Qn

S1/2 

3/8

hf4.66n^2

LQ^2

D16/3

Q

0.463

n

D8/3S1/2

V

0.590

n

D2/3S1/2

V

1.486

n

R2/3S1/2

C

1.486R1/6

n