318 CHAPTER TWELVE
To solve the preceding head equation, it is necessary to try different values
ofdnand corresponding values of Runtil a value is found that satisfies the
equation.
OPEN-CHANNEL FLOW
Free surface flow, or open-channel flow, includes all cases of flow in which the
liquid surface is open to the atmosphere. Thus, flow in a pipe is open channel if
the pipe is only partly full.
Auniform channelis one of constant cross section. It has uniform flowif the
grade, or slope, of the water surface is the same as that of the channel. Hence,
depth of flow is constant throughout. Steady flow in a channel occurs if the depth
at any location remains constant with time.
Thedischarge Qat any section is defined as the volume of water passing
that section per unit of time. It is expressed in cubic feet per second, ft^3 /s (cubic
meter per second, m^3 /s), and is given by
(12.74)whereVaverage velocity, ft/s (m/s)
Across-sectional area of flow, ft^2 (m^2 )
When the discharge is constant, the flow is said to be continuousand therefore
(12.75)where the subscripts designate different channel sections. This preceding equa-
tion is known as the continuity equation for continuous steady flow.
Depthof flow dis taken as the vertical distance, ft (m), from the bottom of a
channel to the water surface. The wetted perimeteris the length, ft (m), of a line
bounding the cross-sectional area of flow minus the free surface width. The
hydraulic radius Requals the area of flow divided by its wetted perimeter. The
average velocityof flow Vis defined as the discharge divided by the area of flow:
(12.76)
The velocity head HV, ft (m), is generally given by(12.77)
whereVaverage velocity, ft/s (m /s); and gacceleration due to gravity, 32.2
ft/s^2 (9.81 m/s^2 ).
Thetrue velocity headmay be expressed as
HVa (12.78)V^2
2 gHV
V^2
2 g