Page 390 - Civil Engineering Formulas

318 CHAPTER TWELVE

To solve the preceding head equation, it is necessary to try different values
of d and corresponding values of R until a value is found that satisfies the
n
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.
A uniform channel is one of constant cross section. It has uniform flow if 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.
The discharge Q at any section is defined as the volume of water passing
3
that section per unit of time. It is expressed in cubic feet per second, ft /s (cubic
3
meter per second, m /s), and is given by
Q VA (12.74)
where V average velocity, ft/s (m/s)
2
2
A cross-sectional area of flow, ft (m )
When the discharge is constant, the flow is said to be continuous and therefore
Q V 1 A 1 V 2 A 2 (12.75)
where the subscripts designate different channel sections. This preceding equa-
tion is known as the continuity equation for continuous steady flow.
Depth of flow d is taken as the vertical distance, ft (m), from the bottom of a
channel to the water surface. The wetted perimeter is the length, ft (m), of a line
bounding the cross-sectional area of flow minus the free surface width. The
hydraulic radius R equals the area of flow divided by its wetted perimeter. The
average velocity of flow V is defined as the discharge divided by the area of flow:
Q
V (12.76)
A
The velocity head H , ft (m), is generally given by
V
V 2
H V (12.77)
2g
where V average velocity, ft/s (m/s); and g acceleration due to gravity, 32.2
2
2
ft/s (9.81 m/s ).
The true velocity head may be expressed as
V 2
H Va (12.78)
2g