Capillarity and evaporation exacerbated seepage losses from unlined channels

Steady, essentially two-dimensional, tension-saturated seepage from a flat-bottomed soil channel in an arid environment is studied analytically. Physically, the action of capillary spreading, evaporative drive to the atmosphere both from the near-channel banks and capillary fringe boundary, Darcian resistance of the matrix and gravity are juxtaposed and result in trifurcation of infiltrated water into deep percolation and semi-infinite evaporation "wings" with two hinge points on the soil surface and two dividing streamlines. Mathematically, free boundary problem is solved by conformal mappings and the Polubarinova-Kochina boundary-value problem method. The dependence of deep percolation losses and evaporative return flow on the channel width, conductivity, static capillary rise height, and intensity of evaporation is found.