Question

What is the correct expression of Horton’s equation?

(a) ft = fC + (fC – fO) e^-K.t

(b) ft = fC + (fC – fO) e^K.t

(c) ft = fC + (fO – fC) e^K.t

(d) ft = fC + (fO – fC) e^-K.t

This question was posed to me in a national level competition.

This interesting question is from Ground Water through Wells and Tubewells in portion Ground Water for Irrigation through Wells and Tubewells of Irrigation Engineering

Answer 1

The correct answer is (d) ft = fC + (fO – fC) e^-K.t

Explanation: Horton’s equation assumes an infinite water supply at the surface i.e. it assumes the saturation conditions at the soil surface. The infiltration rate at any time‘t’ is given by –

ft = fC + (fO – fC) e^-K.t

Where fC = final constant rate of infiltration at saturation, fO = initial rate of infiltration capacity, k is the decay constant depending upon soil and vegetation and t = time from the beginning of the storm.