Figure 2.4. Pressure distribution in steady uniform and in steady nonuniform flow.
In general, when fluid acceleration is small (as in gradually varied flow) the pressure distribution
is considered hydrostatic. However, for rapidly varying flow where the streamlines are
converging, expanding or have substantial curvature (curvilinear flow), fluid accelerations are not
small and the pressure distribution is not hydrostatic.
In Equation 2.52, the constant is equal to zero for gage pressure at the free surface of a liquid.
For flow with hydrostatic pressure throughout (steady, uniform flow or gradually varied flow), it
follows that the pressure head p/γ is equal to the vertical distance below the free surface. In
sloping channels with steady uniform flow, the pressure head p/γ at a depth y below the surface
is equal to
p
= y cos θ
(2.53)
γ
Note that y is the depth (perpendicular to the water surface) to the point, as shown in Figure 2.5.
For most channels, θ is small and cosθ ~ 1.
Figure 2.5. Pressure distribution in steady uniform flow on steep slopes (after Chow 1959).
2.13
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