2.4 STEADY UNIFORM FLOW
2.4.1 Introduction
In steady, uniform open channel flow there are no accelerations, streamlines are straight and
parallel, and the pressure distribution is hydrostatic. The slope of the water surface Sw and the
bed surface So and the energy gradient Sf are equal. Consider the unit width of channel shown in
Figure 2.6 as a control volume. According to Equation 2.50, the conservation of energy for this
control volume is:
Figure 2.6. Steady uniform flow in a unit width channel.
α1 V12 p1
α 2 V22 p 2
+
+ z1 =
+
+ z 2 + HL
(2.54)
γ
γ
2g
2g
The pressure at any point y below the surface is y cosθ. Then according to Equation 2.46
1
y
p1 =
o1 γy cos θ v 1 dy
(2.55)
V1y1
Assuming only small variations in the point velocity v with y we have:
γy1 cos θ
p1 ~
-
(2.56)
2
Similarly,
γy 2 cos θ
p1 ~
-
(2.57)
2
2.14
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