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Rapid changes in stage and velocity occur whenever there is a sudden change in cross-section, a very steep bed-slope or some obstruction in the channel. This type of flow is termed rapidly varied flow .

**The Application of the Energy equation
for Rapidly Varied Flow**

Rapid changes in stage
and velocity occur whenever there is a sudden change in cross-section, a very
steep bed-slope or some obstruction in the channel. This type of flow is termed
rapidly varied flow .

Typical example are
flow over sharp-crested weirs and flow through regions of greatly changing
cross-section (Venturi flumes and broad-crested weirs). Rapid change can also
occur when there is a change from super-critical to sub-critical flow (see
later) in a channel reach at a hydraulic jump.

In
these regions the surface is highly curved and the assumptions of hydro static
pressure distribution and parallel streamlines do not apply. However it is
possibly to get good approximate solutions to these situations yet still use
the energy and momentum concepts outlined earlier. The solutions will usually
be sufficiently accurate for engineering purposes.

**1 The energy (Bernoulli) quation**

The
figure below shows a length of channel inclined at a slope of and flowing with
uniform flow.

Recalling the Bernoulli equation

And assuming a
hydrostatic pressure distribution we can write the pressure at a point on a
streamline, A say, in terms of the depth d (the depth measured from the water
surface in a direction normal to the bed) and the channel slope.

Tags : civil - Applied Hydraulic Engineering: Rapidly Varied Flow

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