Free boundary seepage from open earthen channels

We present in this paper a new inverse method for the study of the seepage from symmetrical earthen open channels. We map the half-strip from the complex potential domain onto the unit half-disk from an auxiliary ζ plane. We introduce Levi-Civitá’s function whose imaginary part vanishes on the diameter [−1, 1] of the half-disk by virtue of the boundary conditions imposed on the free lines. Then we give integral representations of the complex potential, velocity field, free phreatic lines and contour of the channel by means of σ, the real part of Levi-Civitá’s function on the unit half-circle. For various values of the Fourier coefficients of σ we calculate numerically the contour of the channel, the phreatic lines, the seepage loss, the velocity field, the streamlines and the equipotential lines.