CIV E 634 - SURFACE WATER HYDROLOGY
SPRING 2015
HOMEWORK 4:   OVERLAND FLOW

  1. Derive Eq. 4-35 in the textbook.

  2. 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 ].

  3. 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].

  4. 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.

  5. 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).

  6. 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.