Analytical solution to seepage problem from a soil channel with a curvilinear bottom

An exact analytical solution for the quantity of seepage from a semicircular channel is not available because of difficulties in the conformal mapping. In the present study an inverse method has been used to obtain an exact solution for seepage from a curved channel whose boundary maps along a circle onto the hodograph plane. The solution involves inverse hodograph and Schwarz-Christoffel transformation. The solution also includes a set of parametric equations for the shape of the channel perimeter and loci of phreatic lines. The channel shape is an approximate semiellipse with the top width as the major axis and twice the water depth as the minor axis and vice versa. The average of the corresponding ellipse and parabola gives nearly the exact shape of the channel. Also, this channel is non-self-intersecting and is feasible from a very deep channel to a very wide channel, unlike Kozeny's trochoid shape, which is self-intersecting for a top width to depth ratio less than 1.14. Its seepage function is a linear combination of seepage functions for a slit and a strip. However, this channel allows more seepage loss than a trochoid channel. A special case of the resulting channel is an approximate semicircular section.