82 Computational Modelling in Hydraulic and Coastal Engineering
It should be noted that in Equations 5.2 and 5.3 the bed slope (S o ) is
being used for the estimation of the normal depth, that is, uniform flow.
For non-uniform flow, the energy gradient (S e ) should be used instead.
For an arbitrary-shaped cross-section area, the critical depth (y c ) is estimated from the equation
Q T
gA
2
3
1
=
(5.5)
where Q is the discharge and T is the surface flow width. Equation 5.5 is
a generalized expression of the Froude number raised to the second power.
For rectangular channels, Equation 5.5 can be simplified and solved for the
critical depth (y c ) as
Ch an ne l be d
(a)
(b)
y
h
ζ
Water free surface
En er gy gr ad e lin e
z
S e
S o
y
u 2 /2g
Reference datum
A
T
y
P w
u
H
Figure 5.2 Schematic illustration of open channel characteristics. (a) Longitudinal view
and (b) cross-sectional area.