Flow net for unsaturated infiltration from periodic strip sources

Using unsaturated flow theory, general equations have been obtained of the stream functions for a variable infiltration rate over periodic strip sources located on the soil surface. Solutions are obtained for the water table located at infinite and finite depths. The steady state unsaturated flow equation, linearized using the KirchhofF transformation based on the exponential relationship between the unsaturated hydraulic conductivity and soil water pressure, is solved with the Fourier analysis technique. Then the solutions for equally spaced strip sources are obtained with the constant infiltration rate as a special case. Also, as another special case, an approximate result for infinite water table depth is obtained for an array of equally spaced line sources which was first obtained by Raats [1970]. Using the matric flux potential distribution for the infinite water table depth [ Batu , 1978], flow nets are presented for equally spaced strip sources. The stream functions corresponding to the saturated flow cases are also obtained. Comparisons between the saturated and unsaturated streamlines are made, and it is concluded that the discrepancies between the two are larger with decreasing matric flux potential in the flow field. These solutions are of interest in connection with sprinkler and furrow irrigation. Other than these, the results may be used for different purposes in civil and agricultural engineering applications.