Abstract:
A weir is designed against uplift pressure. Higher the uplift pressure means provision of more height of hydraulic structure. This leads to high cost of the structure. The uplift pressure can be reduced by providing drain at the base of structure.
Analytical solution for finding pressure acting on the base of a depressed weir with a drain is not available.
In the thesis, it is aimed to derive an analytical solution for the seepage problem using conformal mapping method of fragments. The hydraulic structure generally used in practice by providing several cut-offs, therefore we apply method of fragments which was proposed by Pavlovsky (vide Harr, 1962). This method divides flow region into fragment by means of vertical lines drawn through the ends of the cut-offs. The dividing lines are taken for lines of constant potential. Actually they differ from equipotential
lines, but they approach the latter as the depth of the pervious stratum become smaller. The solution to this problem is obtained with the help of conformal mapping and numerical integration. Gauss quadrature has been used for numerical integration.
