Drainage of Agricultural Lands - Practices of Irrigation and On-farm Water Management - page 352

Fig. 9.13 Schematic of
definition sketch of
Hooghoudt's drain spacing
formula

H

h

2r

d e

D

S

Hooghoudt's Equation Under Different Situation of Drain Placement

If the drain lies on the impervious layer, i.e., D = 0 (in Fig. 9.13 ) , then consequently

d e = 0, and the Eq. ( 9.15 ) reduced to

4 k a h 2
q

S 2

= (9.16)

If the head of water above the drainage base is too small and the flow from below
the drain dominates, then the flow above the drain can be neglected and thus the
Hooghoudt's formula reduces to

8 k b d e h
q

S 2 = (9.17)

Assumptions in Hooghoudt's Formula

Hooghoudt's formula is based on Dupuit-Forcheimer assumptions. The assumptions
of Hooghoudt's formula can be summarized as follows:

• The soil is homogeneous

• Darcy's law is valid for flow of water through soil into the drain

• The drains are evenly spaced

• An impermeable layer underlies the drain

• There is a vertical recharge uniformly distributed in the horizontal plane

• Surface inflow rate, from irrigation or rainfall, is equal to the inflow to the drain

• The hydraulic gradient at any point in the flow regime is equal to the slope of

water-table above the point

• The diameter of the drain is small compared to saturated thickness below the

drain

•

The drains have no entrance resistance

• The flow through drain is half-full