Environmental Engineering Reference
In-Depth Information
2000
1000
0
0.50
0.60
0.70
0.80
0.90
1.00
Velocity (m/s)
Figure 5.19. Effect of velocity
in the prediction of the
equilibrium concentration.
Engelund-Hansen
Brownlie
Ackers-White
also small and the capacity will increase with the B / y ratio. For B / y ratios
larger than about 5 the transport capacity remains almost constant for the
Engelund-Hansen method and it decreases for the Ackers-White method.
The Brownlie predictor shows a larger transport capacity for the smallest
B / y ratio and it decreases with an increasing B / y ratio.
All three methods predict that more gentle side slopes give lower trans-
port capacities. For a given B / y ratio steeper side slopes result in an increase
in water depth and flow velocity and hence, in the transport capacity.
5.3.5 Velocity distribution in a trapezoidal canal
The velocity distribution in a trapezoidal canal is not only influenced by
the effect of the boundary shear stress, but also by the changing water
depth along the slope. This influence is significant for non-wide canals
and the concept of a uniform velocity distribution across the section cannot
be used. Moreover the roughness is not constant along the perimeter due
to the presence of bed forms and protection works or vegetation on the
sides. Einstein (1942) suggested that the total area of these canals can be
divided into an area that corresponds to the bed ( A b ) and the other to the
sidewalls ( A w ). The average shear stress in the bed and on the sidewalls
for a constant friction slope can be written as:
τ b =
ρgR b S
(5.84)
τ w =
ρgR w S
(5.85)
The shear stress depends on the distance R , which means that the surplus
energy in any volume of flowing water will be dissipated by the shortest-
distance boundary.
Based on this subjective concept, the surplus energy at any point in
the column CD above the line EF will be dissipated by the side slope and
 
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