Analytical Computation of Seepage from Ponded Fields into Drainage Ditches Using Conformal Mapping

Drainage of agricultural lands is very important and without drainage a sustainable agriculture isn’t possible. In the absence of natural drainage in agricultural lands, artificial drainage is necessary. Construction of drainage ditches is one of the usual methods of artificial drainage. Study of the governing equations of flow to drainage systems is an interesting subject to researchers. In this study, an analytical solution for steady-state seepage of ponded water into drainage ditches is developed. The ditches are partly penetrating, parallel to each other and excavated by rectangular cross section in a homogeneous and isotropic soil layer. In order to derive the relevant equations of seepage quantities and velocities, first hodograph and complex potential planes were drawn with attention to the boundary conditions of physical plane; then the conformal mappings of physical and hodograph planes on auxiliary planes were found using Schwarz-Christoffel transformation. The chain rule was used to find the relation between complex potential plane and auxiliary plane. This method can be used to calculate the seepage quantities and velocities as well as ditches drainage designing. The results showed that near the ditches, seepage velocity along the ponded surface was very high as compared with that between the ditches, so leaching was non-uniform.