Ernst Drainage equation

Alternatively, the correction factor is based on estimated sums of the radial, r_r, horizontal, r_h, and vertical, r_v, resistances for each layer. The correction factor is then given as:

                                    (2.46)

where the r_href is the horizontal resistance that corresponds to eq.(2.43). The separate resistances for each compartment within the z_D layer are given :

                                                          (2.47)

                                (2.48)

                                               (2.49)

where r_p is the wet perimeter of the drain and can be used for ditches as well as for pipes. As opposed to the Hooghoudt formula, r_p does not stand for the radius of the pipe directly, even though the parameter is still given to the model as RadiusPipe. To get an estimation of the parameter r_p, which should be given to the model as input, the following two formulas can be used for ditches and for pipes respectively, i.e. these functions are not included in the model.

r_p  for ditches:

                                                     (2.50)

where b is the bottom width of the ditch, y is the water depth in the ditch and s is the side slope of the ditch.

r_p  for pipes:

                                                                (2.51)

where b is the width of the trench and r₀ is the radius of the drain.