Environmental Engineering FOURTH EDITION

122 ENVIRONMENTAL ENGINEERING

Figure 6-10. Hydraulics for ideal closed-conduit flow.

The principle of constant energy is known as the Bernoulli theorem when applied
to fluid flow. Taking into account losses within the system, the Bernoulli theorem for
any two points in the system may be written

in which h~ represents the energy losses within the system. The energy loss may occur

in many places in a system, such as valves, bends, and sudden changes in pipe diameter.

One of the major losses of energy is in the friction between the moving fluid and the

pipe wall.

Because of the practical problems involved in the application of more elegant and

theoretically sound friction loss equations, engineers often use fitted or empirical expo-

nential equations for flow calculations. Among these, the Hazen-Williams formula is

most widely used in the United States for flow in pressure pipes and the Manning for-

mula for flow in open channels or pipes not having full flow. These formulas are limited

to turbulent flow of water and to common ambient temperatures. The Hazen-Williams

formula is

v = 1.318Cr0.63s0.54, (6.9a)

where

v = the mean velocity of flow (in ft/s),

r = the hydraulic radius (area divided by wetted perimeter, in ft),

s = slope of the hydraulic grade line, and

C = the Hazen-Williams fiiction.coefficient.