CIV E 632 - COMPUTATIONAL HYDRAULICS AND HYDROLOGY
SPRING 2009
HOMEWORK No. 3

A flood wave passes through a point located at the upstream end of a river reach 500 miles long and generates the following sinusoidal hydrograph (unit-width analysis):

q(t)= 125 - 75 cos ( π t / 48)                            (0 ≤ t ≤ 96 hr)

q(t) = 50                                                                 (t ≥ 96 hr)

Discharge is given in cfs/ft. The channel bed slope is 1 ft/mi. The Manning n = 0.02972.

  1. Calculate the constant-parameter Muskingum-Cunge method of flood routing.

  2. Plot the flood hydrograph at the downstream end of the river reach.

    • Use a reference discharge qo = 125 cfs/ft (the average of peak and base flows).

    • Time interval (Delta t) Δt = 6 hr.

    • Space interval (Delta x) Δx = 25 mi.

    • Total simulation time = 30 days.

    • Report the Courant and cell Reynolds numbers, the peak flow, the time-to-peak, and the percentage of mass conservation (excluding baseflow).

  3. Recalculate the hydrograph obtained in step 1 four times, each time increasing the space interval to 50, 100, 250 and 500 miles. Plot the results and compare with the results that you obtained in step 2.

  4. Analyze the results using Muskingum-Cunge accuracy criteria.

  5. Verify the applicability of the diffusion wave model to this particular routing problem.