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.
Optimal Design of a Special Class of Curvilinear Bottomed Channel Section
Section elements of a new class of curvilinear bottomed channel whose boundary maps along a circle onto the hodograph plane have been investigated in the study. The perimeter of this type of channel always lies between an ellipse and a parabola of the same top width and flow depth. Presented herein are optimal section properties from least area and minimum seepage loss point of view for the curved channel section. The study also addresses the constraints on the channel dimensions and the velocity of flow. A nondimensional parameter approach has been used to simplify the analysis. Design procedures for different cases have been presented to demonstrate the simplicity of the method.
Seepage from Shallow Open Channel
An approximate Darcy solution is obtained for the two-dimensional seepage from an open channel which is placed upon a homogeneous, isotropic aquifer of relatively large depth. The linearized solution is obtained for an arbitrary channel cross section by assuming that the maximum channel depth is small compared to the channel width. A comparison with a known exact solution for a particular channel shape suggests that this solution is probably accurate enough for design purposes when the channel depth is less than 40% of the channel width.