CIVIL ENGINEERING FORMULAS

HYDRAULICS AND WATERWORKS FORMULAS 297

section, however, varies with velocity. Usually, Zp/wat the midpoint and
the average velocity at a section are assumed when the Bernoulli equation is
applied to flow across the section or when total head is to be determined. Aver-
age velocity, ft/s (m/s)Q/A, where Qis the quantity of flow, ft^3 /s (m^3 /s),
across the area of the section A, ft^2 (m^2 ).
Momentumis a fundamental concept that must be considered in the design
of essentially all waterworks facilities involving flow. A change in momentum,
which may result from a change in velocity, direction, or magnitude of flow, is
equal to the impulse, the force Facting on the fluid times the period of time dt
over which it acts (Fig. 12.4). Dividing the total change in momentum by the
time interval over which the change occurs gives the momentum equation, or
impulse-momentum equation:

(12.8)

where Fxsummation of all forces in Xdirection per unit time causing change
in momentum in Xdirection, lb (N)
density of flowing fluid, lbs^2 /ft^4 (kgs^2 /m^4 ) (specific weight
divided by g)
Qflow rate, ft^3 /s (m^3 /s)
Vxchange in velocity in Xdirection, ft/s (m/s)

FxpQ Vx

Total energy per lb of liquid

Vg^2

2 g

P

w

Pa

w

Va

Elemental volume

of liquid

Velocity

distribution

Arbitrary datum plane

ZZa

FIGURE 12.3 Energy in a liquid depends on elevation, velocity, and pressure.