Question

1. The text gives a metric-unit version of the equation (p. 151, eq. 6.6). The older U.S. rational method equation (but still used!) is: “q=C i A”, where q is the peak flow from a given storm (cfs), C is a runoff constant (dimensionless), i is the intensity of the rainfall (in/hr), and A is the watershed area (acres). Using a dimensional analysis, show why there need not be a conversion factor with this equation (i.e., Km = 1 for English units).

Answer 1

q = C*i*A

unit of q is cfs i.e cubic foot per second.

now unit of i is in/hr.

converting it in foot per second .since one inch = 1/12 foot and one hr means 3600 sec

so 1 in/hr = 1/12*3600 ft/s

now unit of A is in acres.

since one acre = 43560 square foot.

now putting these in equation

C*i*A = 1/12*3600 ft/s * 43560 ft² = 1.008 cfs

hence it is evident that conversion factor is 1 for english unit.