Seepage from Parallel Trapezoidal Channels

An exact solution is presented for the seepage flow from a system of parallel trapezoidal channels through a layer of homogeneous, isotropic soil. Under this layer there is a drain that might be represented physically by a bed of gravel or coarse sand. The flow is assumed to obey Darcy's law and hence there is velocity potential which satisfies the Laplace equation. By constructing the complex potential and the complex velocity planes, the solution is obtained through conformal mapping. General expressions are given for the discharge and shape of the free streamline. A numerical example is presented for which the free surface and the velocity distribution on the channel's profile were drawn. The quantity of seepage from the bottom and sides were also computed.