Free-Boundary Seepage from Asymmetric Soil Channels
We present an inverse method for the study of the seepage from soil channels without lining. We give integral representations of the complex potential, velocity field, stream lines, free phreatic lines, and contour of the channel by means of Levi-Civita's function 𝜔. For different values of the Taylor coefficients of 𝜔, we calculate numerically the contour of the channel, the phreatic lines, the seepage loss, the velocity field, the stream lines, and the equipotential lines. Examples are given for various symmetric or asymmetric channels, with smooth contours or with angular points.
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.
Design of minimum water-loss canal sections
The canal water losses constitute of seepage and evaporation losses. Whereas seepage loss depends on the channel geometry, evaporation loss is proportional to the area of free surface. On account of complexities of analysis, the design of minimum water loss section has not been attempted as yet. In this investigation explicit equations for the design variables of minimum water loss sections for triangular, rectangular, and trapezoidal canals have been obtained using non-linear optimization technique. The proposed equations along with tabulated section shape parameters facilitate easy design of the minimum water loss section and computation of water loss from the section without going through the conventional and cumbersome trial and error method. A design example has been included to demonstrate the simplicity of the method.