TR(BR)-12/98-99 : Rigorous derivation of Hooghoudt's equation for drainage spacing

Abstract

Hooghoudt's drain spacing formula is based on an implied assumption that in the radial flow zone there is no spatial variation in the flux and hence no vertical recharge in this zone. The head loss in the radial flow zone has been accounted presuming that half of the total vertical recharge within the drains enters at the outer boundary of the radial flow zone. In the present report, a drain spacing formula has been derived rigorously considering the variation in radial flux and the area above the drain level in the radial flow zone. The Hooghoudt's formula computes maximum water table height very close to that computed by the present rigorous method. For a ratio of high recharge rate to hydraulic conductivity of drainage layer, R/K =0.5, and a ratio of close drain spacing to thickness of soil layer below the drains, L/D=4, the divergence between the two sets of results is 8%. For normal recharge rate, shallow soil layer below the drains and usual drain spacing, the error involved in computation of the maximum water table height by Hooghoudt's formula is less than 1 %. The water table height near the drains computed using the equivalent depth proposed by Hooghoudt differs considerably from that computed by the rigorous method.