CIV E 634 - SURFACE WATER HYDROLOGY
SPRING 2009
HOMEWORK 3: OVERLAND FLOW
- Derive Eq. 4-35 in the textbook.
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Derive Horton's solution for overland flow (Eq. 4-36).
[Hint: Use Eq. 4-26 in Eq. 4-35, and integrate Eq. 4-35 by making the following change of
variable: (q/qe)1/m = z ].
-
Express Horton's solution (Eq. 4-36) in such a way that q/qe is the independent variable
and t/te is the dependent variable.
[Hint: Use
the logarithmic equivalent to the hyperbolic tangent].
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Using the equation derived in 3, 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.
-
Given the following overland flow conditions:
i = 36 mm/hr, n = 0.1, So = 0.01, and L = 90 m;
calculate the equilibrium outflow qe (L/s/m) and the time-to-equilibrium te (sec).
-
Using the data of item 5 and the equation derived in item 3, calculate how
long will it take for
the outflow discharge from the overland flow plane to attain 99%
of its equilibrium value. Express time in seconds.
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