Point and Line Infiltration—Calculation of the Wetted Soil Surface

Abstract

AbstractFor water introduced at a point on the soil surface a finite‐sized area becomes wetted which is not exceeded for large times. Similarly, a wetted strip develops parallel to a surface line source. In this paper, relationships are derived to provide the limiting (steady‐state) extent of these wetted areas. The quasi‐linear assumption necessary for solution is that the unsaturated conductivity K is Ko exp(αh) with h the pressure head (matric potential as a length) and Ko and α constants. Results for the area around a point is in near agreement with Wooding's (1968) approximation Ko/α2q = (πα2ro2 + 4αro)−1 for a slightly different surface boundary condition (ro is the wetted radius and q is the volume of discharge per unit time). For the strip the dimensionless quantity Ko/αqL = (3.96 αxo/2 + 0.721)−1 is a valid approximation for αxo/2 <5 where qL is the rate of discharge per unit length and 2xo the wetted width. For larger αxo/2 the simpler one‐dimensional relationship Ko/αqL = 1/(2αxo) suffices. The results are relevant with respect to trickle (drip) irrigation.