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.
Seepage from a special class of a curved channel with drainage layer at shallow depth
In the present study an inverse method has been used to obtain an exact solution for seepage from a curved channel passing through a homogeneous isotropic porous medium underlain by a drainage layer at shallow depth 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 contour and loci of phreatic line. Variation in the seepage velocity along the channel contour is presented as well. All these expressions involve improper integrals along with accessory parameters. A particular solution corresponding to the water table below the top of the drainage layer has also been deduced from the general solution.
Optimal Design of Parabolic Canals
This paper presents optimality conditions for a parabolic-canal design accounting for freeboard and limitations on velocity and canal dimensions. Freeboard may be based on a design discharge or specified as a function of flow depth, which is more general. The analysis reveals that the side-slope parameter for the best hydraulic section is 0.514, not 0.7 as reported in the literature for parabolic canals. The aforementioned hydraulic considerations tend to shape the optimal canal narrow and deep. A formulation for the minimization of the sum of excavation and lining costs favors slightly wider canals when the ratio of cost of lining to cost of excavation is high. The necessary conditions for minima are stated analytically. It is shown that the optimal side-slope parameter of 0.514 sets an upper bound with the implication that no optimal parabola can be wider than the classical best section for a given discharge. Design aids in the form of tables are presented.