Rainwater runoff from a 200 x 500 ft parking lot is to drain through a circular

Question

Rainwater runoff from a 200 x 500 ft parking lot is to drain through a circular concrete pipe that is laid on a slope of 5 ft/mi. Determine the pipe diameter if it is to be full with a steady rainfall of 1.5 in/hr

Explanation / Answer

discharge of runoff = Area of lot*intensity of rainfall => Q = 200*500*[1.5/(12*60*60)] ft^3/s => Q = 3.472 ft^3/s hydraulic radius, R = A/P = D/4 slope, S = 5 ft/miles = 5 ft/5280 ft = 0.000947 Manning's constant, n = 0.012 (for concrete) Kn = 1.486 (in English units) from Manning's formula; v = (Kn/n)*R^(2/3) *S^(1/2) => v = (1.486/0.012) *(D/4)^0.67 * (0.000947)^0.5 => v = 1.51 *D^(0.67) Q = A*v => Q = (pi*D^2/4) * [1.51 *D^(0.67)] => 3.472 = (3.14*D^2/4) *[1.51 *D^(0.67)] => 3.472 = 1.185 * D^(2.67) => D = 1.496 ft

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