CE522 Engineering Hydrology
Jorge A. Ramirez

Homework No. 3

1. You are in charge of releasing water from a reservoir into a river with channel properties as given below. There are four downstream water users whose daily withdrawals during a one-week period are forecast as indicated in the table below. Calculate the amount of water you would release from the reservoir on the first day of this period to supply these users and have a surplus of 200 cfs flowing past the last user. Assume that the release was constant at 2500 cfs for the previous week, the withdrawals were constant during that week at the values shown for day 1 in the table, and that there is no lateral inflow.

Channel characteristics are: channel width, B = 200 ft; slope S_o = 0.00035; and Manning n = 0.045.
 

1. Select a critical storm duration according to the physical properties of the watershed.
2. From frequency analysis of local storm data, select the storm intensity of the critical duration which has the return period for which flood protection is sought.
3. Use this temporally uniform intensity in some rainfall-runoff model to calculate the design discharge for the storm drain.

However, the short duration storms which are usually critical in urban drainage are known to have a time-varying intensity which may be represented by a triangular distribution. Thus, you are to use a new procedure which assumes a triangular distribution for rainfall such that intensity increases linearly from zero. For the same critical rainfall duration, and the same storm depth, do you expect the new procedure to lead to larger or smaller drainage structures? Support your answer with the appropriate analysis. Obtain a relationship between the times of concentration for the rectangular hyetograph and for the triangular hyetograph cases. Explain your results. In order to facilitate your analysis, you may assume the value of m to be equal to two.

3. Assume that you have an effective rainfall event of infinite duration and constant intensity.

1. Use the method of characteristics to derive an exact solution for the hydrograph at the outlet, under kinematic wave assumptions.
2. Obtain an approximate solution to the above problem by first obtaining an instantaneous unit hydrograph (using kinematic wave assumptions), and then using the unit hydrograph concept in order to derive the overland flow hydrograph for an effective rainfall of constant intensity and infinite duration.

Obtain maximum outflow for both cases. Please comment on the differences observed between the characteristics of the two responses obtained.

4. Assume we have surface runoff from a two-dimensional, plane impermeable surface such that we may assume the following values to be constant:

L = 10 m
m = 2
a = 5 s^-1

This basin is subjected to the following precipitation, all of which runs off:

Calculate and plot the outflow hydrograph at the downstream end of the plane. In order to do so, decompose the above rainfall event into two different rainfall pulses and assume that the solution to this problem can be obtained as a linear superposition of kinematic wave solutions to the two different rainfall pulses, each beginning with a dry bed.

Determine whether the solution obtained by this method depends on the choice of pulses in the decomposition of the storm. Be specific and support your answers.