Unformatted text preview: sumed that the bottom slope S0(x) and
the cross-sectional shape parameters (b0, P, A) are known everywhere along the channel.
Then one may solve Eq. (10.51) for local water depth y(x) by any standard numerical method.
The author uses an Excel spreadsheet for a personal computer. Step sizes x may be selected so that each change y is limited to no greater than, say, 1 percent. The solution
curves are generally well behaved unless there are discontinuous changes in channel parameters. Note that if one approaches the critical depth yc, the denominator of Eq. (10.51) approaches zero, so small step sizes are required. It helps physically to know what type solution curve (M-1, S-2, etc.) you are proceeding along, but this is not mathematically necessary. EXAMPLE 10.8
Let us extend the data of Example 10.4 to compute a portion of the profile shape. Given is a
wide channel with n 0.022, S0 0.0048, and q 50 ft3/(s ft). If y0 3 ft at x 0, how far
along the channel x L does it take the depth to rise to yL 4 ft?...
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This note was uploaded on 10/27/2009 for the course MAE 101a taught by Professor Sakar during the Spring '08 term at UCSD.
- Spring '08