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The steady-state unsaturated flow equation linearized by using the Kirchhoff transformation with an exponential relationship between unsaturated hydraulic conductivity and soil-water pressure is solved for the two-dimensional case. A general equation in integral form is obtained for the stream function under a variable infiltration rate from a strip located on the soil surface. The total potential functions are derived using the matrix-flux potential distributions. Several graphical flow nets are presented for different soil parameters. Comparisons between the saturated and unsaturated streamlines are made and it is concluded that the discrepancies increase with decreasing water content in the flow field.
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Vedat Batu (1979) studied this question.
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