Hooghoudt drainage equation

A more physically correct picture of the flow situation may be considered based on either the classical equations presented by Hooghoudt (1940) or those by Ernst (1956). Using any of these equations drainage flows below the pipes are also considered.

Following Hooghoudt the total flow to the pipes is given by:

                           (2.41)

where k_s1 and k_s2 are the saturated conductivities in the horizon above and below drainage pipes respectively, z_D is the thickness of the layer below the drains and d_p is the spacing between parallel drain pipes. See viewing function Physically based drainage equation.

The model uses the first term in the Hooghoudt equation to calculate the flows for specific layers above the drain depth, z_p. These calculations are also based on the horizontal seepage flow for heterogeneous aquifers (Youngs 1980):

                      (2.42)

where h_u and h_l are the heights of the top and bottom of the compartment above the drain level z_p and k_s is the saturated conductivity. Below the drain depth (corresponding to the second term in the Hooghoudt equation) the flow is calculated for each layer as:

                                    (2.43)

where the correction factor r_corr  may be calculated based on the equivalent layer thickness, z_d as:

                                                           (2.44)

where z_d and d_p are related as:

                                     (2.45)

where r_p is the diameter of the drain pipe. The diameter of the pipes affects the resistance to the flow in the pipes.