STEADY INFILTRATION FLOWS WITH SLOPING BOUNDARIES

General theorems are established that enable immediate solution of the quasilinear steady infiltration equation for any distribution of line and point sources at or beneath a sloping upper soil surface, or on o r above a sloping impermeable base. The required solutions are readily deduced from the known simple solutions for buried line and point sou rces. Corollary to the theorems, similar relations hold for downslope and cross-slope flux density components. Illustrative solutions are pr esented for line and point sources in the various configurations. Dist ributions of both potential and stream function are mapped for line so urces and also for point sources at or beneath a horizontal surface. F or other point sources, potential is mapped in the normal plane throug h the source. For sources beneath a surface, distortion due to the sur face is relatively small, even for dimensionless normal source depth a s small as 1. On the other hand, for sources above a sloping base, the base strongly skews the distributions of both potential and streamlin es. Far downslope the flow is purely (line sources) or primarily (poin t sources) parallel to the base. Upper bounds exist on total source st rength, beyond which a saturated region emerges, perched on a horizont al base. Consistent with earlier results and theorems, physically acce ptable steady flows do not exist above the base.