CIV E 634 - SURFACE WATER HYDROLOGY
SPRING 2005
HOMEWORK 1: OVERLAND FLOW
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Derive Horton's solution for overland flow (Eq. 4-36 in the book).
[Hint: Integrate Eq. 4-35 by making the following change of
variable: (q/qe)1/m = z].
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Convert Horton's solution such that q/qe is the independent variable
and t/te is the dependent variable. [Hint: Express in logarithmic form].
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Using the equation derived in 2, calculate and plot Horton's solution
at intervals of 0.01 q/qe from 0.00 to 0.99, then 0.999 q/qe
and 0.9999 q/qe.
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Given the following overland flow conditions:
i = 72 mm/hr, n = 0.1, So = 0.01, and L = 100 m;
calculate the equilibrium outflow qe and the time-to-equilibrium te.
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Using the data of item 4 and the equation derived in item 2, calculate how
long will it take for
the outflow discharge from the overland flow plane to attain
50, 70, 90, 99, 99.9 and 99.99 percent of its equilibrium value. Express time in seconds.
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