Chapter 12, Problem 3RQ

1. 3. When rain falls over an area for a sufficiently long time, it will run off and collect at the bottom of hills and eventually find its way into creeks and rivers. A simple way to estimate the maximum discharge flowrate Q (in units of cubic feet per second [cfs]) from a watershed of area A (in units of acres) with a rainfall intensity i (in units of inches per hour) is given by an expression commonly called the Rational Method, as

Q=CiA

Values of C vary between about 0 (for flat rural areas) to almost 1 (in urban areas with a large amount of paved area).

A survey of a number of rainfall events was made over a 10-year period for three different watersheds. The data that resulted is given in the following table. Watershed A is 120 acres, B is 316 acres, and C is 574 acres.

Storm event	Watershed	Rainfall Intensity {i) [in/h)	Maximum Runoff (Q) [cfs]
1	A	0.5	30
2	A	1.1	66
3	A	1.6	96
4	A	2.1	126
5	B	0.3	47
6	B	0.7	110
7	B	1.2	188
8	B	1.8	283
9	C	0.4	115
10	C	1	287
11	C	1.5	430
12	C	2.4	690

1. a. Create a graph containing all three watersheds, with flowrate on the ordinate, and fit linear trendlines to obtain a simple model for each watershed.

   From the information given and the trendline model obtained, answer the following:

2. b. What is the value and units of the coefficient C?
3. c. What would the maximum flowrate be from a watershed of 200 acres if the rainfall intensity was 1.8 inches per hour?
4. d. How long would it take at this flowrate to fill an Olympic-sized swimming pool that is 60 meters long, 30 meters wide, and 2 meters deep?