SEEPAGE FROM CANAL WITH ASYMMERIC DRAINAGES

Abstract

Canals are widely used in irrigation schemes as a major conveyance system. Most of the canals are unlined and the amount of actual water finally available for irrigation is significantly less than the quantity of water released at the head. One of the major causes of these losses is seepage from canals. Hence, an understanding of the mechanism of the seepage losses from canals leads to improved management of the water resources. Seepage losses from unlined canals depend on the shape and size of the canal cross section, depth of water in the canal, location of drainages on either side of the canal and the type of subsoil. Several analytical solutions for prediction of seepage loss had been presented for different canal cross sections and, boundary conditions. In the solutions thus far obtained, it is assumed that symmetric seepage flow takes from the canal to the drainages which are shallow or deep. However, in practice canals -seldom have symmetric drainages on either side. Exact solution of the problem of seepage from a canal in homogeneous medium to asymmetric drainage(s) located at finite distance(s) from the canal is presented in this work. Solutions are presented for the following problems : (i) seepage from a canal with negligible water depth to asymmetrically located drainages at either side of the canal; (ii) seepage from trapezoidal canal to asymmetrically disposed drainages at either side of the canal and iv. (iii) seepage from trapezoidal canal to a drainage on one side. The analytical solution for the determination of the shape of the free surface and the calculation of the seepage quantity through the system was obtained by finding the relationship between the physical plane (z-plane) and the complex potential plane (w-plane). This was done by employing successive transformations through the use of the Zhukovsky function as well as Shwarz-Christoffel and bilinear conformal mapping equations. The results of seepage discharge for various values of dimensionless physical parameters are prepared as nomographs for practical uses. The case of the symmetric drainages on either side of canal is a particular case of the present study and the results obtained in this study for symmetrical drainages agree with that presented by earlier workers. The computed seepage loss to asymmetric drainages by decomposing the asymmetric flow domain at the centre of the. canal and treating each part as a part of the corresponding symmetric cases is found to differ from the seepage loss computed by this method. The difference depends on the degree of variation in the drainage distance and elevation on either side. The present direct and exact solution to asymmetric drainages shows that the drainage which is at the higher level and farther from the canal is receiving less seepage from the canal. As the level of the drainage of the higher level is raised, the seepage to drainage reduces and at certain level the drainage does not receive any seepage water (hz = he). This critical ratio of the levels of the drainages (hc/hi) and the critical location of the drainages have been identified. This critical position of the drainage is found to depend on the canal cross section, depth of water in the canal and distance of the drainage on the other side. Free surfaces on either side of the canal rise with increase in the bed width and increase in drainage distances. Free surface also rises if drainage on the other side is located at a higher level. The effect of change of the side slope of canal on the free surface is negligible. However, increase in depth of water in the canal significantly raises the free surface. The results pertaining to the case of drainage on one side of the canal had been compared with that given by Polubarinov-Kochina, 1962. The seepage quantity computed for the case in which the depth of the canal is small compares well with the results given by the above author. In the present work, shape of the canal is considered and the shape of the phreatic lines on both sides of the canal have been plotted to show the effect of the physical dimensions.