We assume that the total storm water runoff (R, given in volume units) from a plot of land depends on the length of time that it rains (t), the area of the land (A), and the rainfall rate (r, given in inches per hour).
Rainfall Rate (r) [in/h] | Land Area (A) [acres] | Rainfall Duration (t) [h] | Measured Runoff (R) [ft3] |
0.50 | 2 | 3.0 | 49 |
0.30 | 14 | 2.5 | 172 |
0.78 | 87 | 4.1 | 4,563 |
0.15 | 100 | 2.2 | 541 |
0.90 | 265 | 0.4 | 1,408 |
0.83 | 32 | 7.6 | 3,310 |
1.40 | 18 | 1.8 | 744 |
0.22 | 6 | 4.7 | 102 |
0.67 | 26 | 3.1 | 886 |
0.48 | 62 | 4.9 | 2,392 |
(a) Using the data, construct a plot of the runoff versus the time that it rains. You should see that this plot is of little help in understanding the relationships between the various parameters.
(b) Using this plot, estimate the total runoff from 200 acres if rain falls for 3 hours at a rate of 1.2 inches per hour. Is this even possible using this plot?
(c) Using the variables in the table, complete a dimensional analysis to help you plot the data. You should obtain two dimensionless ratios. Plot these, with the ratio containing the total runoff on the ordinate. This plot should collapse the values to a single line. Draw a smooth curve through the values.
(d) Use this line to answer question (b) again.
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