Drainage of Agricultural Lands - Practices of Irrigation and On-farm Water Management - page 347

Two types of approximate solutions of steady-state drainage condition have been
proposed and are widely used:
(1) Based on horizontal flow assumption
(2) Based on radial flow assumption
Most techniques applied in analyzing the flow of water to subsurface drains are
based on one-dimensional horizontal flow assumptions. Most solutions also assume
that water percolates vertically from the soil surface through the unsaturated soil-
water zone, so that the flux through the soil surface is also that through the water
table. It is also commonly assumed that at steady state, the water table height at
the top of the drain is negligible and that the drains do not flow completely full, a
realistic assumption in all but extreme events and in systems with submerged outlets.
Horizontal Flow Assumption
Dupuit-Forcheimer's Assumption for Unconfined Flow
These assumptions regarding configuration of the flow and potential lines allow
to derive solution of the flow of water toward drain without the use of Laplace's
equation. These assumptions can be stated as follows:
(i) The flow lines (streamlines) are horizontal
(ii) The equipotential lines are vertical
(iii) The flow velocity in the plane at all depths is proportional to the slope of water
table only and independent of the depth in the flow system.
The schematic of Dupuit-Forcheimer assumptions is shown in Fig. 9.11 .
9.3.6.2 Non-steady State Drainage Situation
The non-steady state drainage situation is one in which the water table varies (falls
or rises) with time. Although the non-steady state situation arises or exists in some
cases and also in some parts of the operational period, steady-state assumptions are
made for simplicity.
9.3.7 Sample Workout Problems
Example 9.2
A 1.2 m deep soil column consists of three layers, having 0.50, 0.4, and 0.3 m
depth of the layers. The horizontal hydraulic conductivity of the layers are 0.20,
0.15, and 0.25 m 3 /m 2 /h, respectively. Determine the resultant horizontal hydraulic
conductivity of the soil column.