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Specific energy in an open channel is defined as the energy per unit weight
measured with respect to the channel bottom. Let E = specific energy, y =
channel depth, V = flow velocity, g = acceleration of gravity, then we write
The flow velocity, in turn, is given by V = Q/A, where Q = water discharge, A
= cross-sectional area. The area depends on the cross-section used, for
example, for a trapezoidal cross-section, as shown in the figure below, A =
(b+m
⋅y) ⋅y, where b = bottom width, and m = side slope of cross section.
We can type in the equation for E as shown above and use auxiliary variables
for A and V, so that the resulting input form will have fields for the fundamental
variables y, Q, g, m, and b, as follows:
Θ First, create a sub-directory called SPEN (SPecific ENergy) and work
within that sub-directory.
Θ Next, define the following variables:
Θ Launch the numerical solver for solving equations: ‚Ï@@OK@@.
Notice that the input form contains entries for the variables y, Q, b, m,
and g:
Θ Try the following input data: E = 10 ft, Q = 10 cfs (cubic feet per
second), b = 2.5 ft, m = 1.0, g = 32.2 ft/s
2
:
.
2
2
g
V
yE +=
z
c
2
n