Environmental Engineering FOURTH EDITION

Water Supply 123

When combined with the continuity equation, Q = Av, the discharge Q, in gallons per

minute for a circular pipe of diameter D, in inches, is given by

Q = 0.285CD2.63~o.54. (6.9b)

In metric units, these two equations are

v = 0.849Cr0.63s0.54

Q = 0.278CD2.63so.54,

(6.10a)

(6.10b)

where D and rare in meters and v and Q are in meters per second (ds) and cubic meters

per second (m3/s), respectively. The nomographs shown in Fig. 6-11 are solutions to

the above equations in both English and metric units. Table 6-3 summarizes Hazen-

Williams coefficients for various pipe materials.

EXAMPLE! 6.6. The pressure drop through a 6-in. asbestos-cement pipe, 3000 ft in

length is 20 psi. What is the flow rate?

hL = (20 pei)(2.31 ft watedpsi) = 46.2 ft

46.2 ft 15.4 ft

s=-- -

3000 ft 1000 ft’

From Table 6-3, C is 140 and from Fig. 6-1 1, the discharge is 460 gpm.

Energy or head is lost at the entrance to apipe or conduit; at valves, meters, fittings,

and other irregular features; at enlargements; and at flow contractions. These losses,

called minor losses, are in excess of friction losses over the same length of straight

pipe or conduit and may be expressed as

(6.11)

where K = the energy loss coefficient of minor losses in closed conduits, and for which

values of K may be estimated by using Table 6-4.

EXAMPLE 6.7. The loss for a flow of 1.0 cfs through a given 6-in. main with a gate
valve wide open is 20 ft. Find the head loss with the gate valve 75% closed.
From Table 6-4, the increase in K value when the valve is partially closed is
K = 24.0:

Q 1.0

A 0.2

v = - = - = 5 ft/s