Environmental Engineering FOURTH EDITION

158 ENVIRONMENTAL ENGINEERING

The velocity in sewers is usually calculated by using the Manning equation, based on
the Chezy open channel flow equation

v = CAS,

where

v = velocity of the flow (ds),

r = pipe hydraulic radius, or the area divided by the wetted perimeter (m),

s = slope of the pipe, and

c = Chezy coefficient.

For circular pipes, the Manning equation is developed by setting

c=-R 116 ,

n

where n = roughness factor and k = constant, so that

V=-R k 2/3 s 1/2.

n

If v is in feet per second and r is in feet, k = 1.486. In metric units with v in meters

per second and I in meters, k = 1 .O. The slope s is dimensionless, calculated as the fall

over distance. The term n is the roughness coeflcienf, and its value depends on the

pipe material, increasing for rougher pipe. Table 8-1 gives values of n for some types

of sewer pipe.

EXAMPLE 8.1. An 8-in.-diameter cast iron sewer is to be set at a grade of 1-m fall per

500-m length. What will be the flow in this sewer when it is flowing full?

Using English units and noting that n = 0.013 from Table 8-1, by Q. (8.3)

v = 1.54ft/s,

and since the area is

Q = AV = (0.35)(1.54) = 0.54cfs.