civil - Applied Hydraulic Engineering: Uniform Flow
Velocity distribution in open channels
The measured velocity
in an open channel will always vary across the channel section because of
friction along the boundary. Neither is this velocity distribution usually
axisymmetric (as it is in pipe flow) due to the existence of the free surface.
It might be expected to find the maximum velocity at the free surface where the
shear force is zero but this is not the case. The maximum velocity is usually
found just below the surface.
The explanation for
this is the presence of secondary currents which are circulating from the
boundaries towards the section centre and resistance at the air/water
interface. These have been found in both laboratory measurements and 3d
numerical simulation of turbulence.
The figure below shows some typical velocity distributions across some channel cross sections. The number indicates percentage of maximum velocity.
Determination of energy and momentum
coefficients
To determine the values
of a and ß the velocity distribution must have been measured (or be known in
some way). In irregular channels where the flow may be divided into distinct
regions a may exceed 2 and should be included in the Bernoulli equation.
The figure below is a typical example of
this situation. The channel may be of this shape when a river is in flood -
this is known as a compound channel .
If the channel is divided as shown into
three regions and making the assumption that ? = 1 for each then
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