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.