Conclusions and Summary
It was assumed when this problem was undertaken that there existed a function f of the moisture content that could be multiplied by the permeability constant k of the Darcy equation to make it applicable to movement of moisture in unsaturated soil. It would appear, however, from the experimental data obtained for a typical soil, that in addition to a pressure gradient due to variation of soil moisture content from point to point in the soil, there may be a gradient due to the dynamic process itself.
It is perhaps unfortunate that f is not a function of ρ alone, but this should not constitute an insurmountable obstacle in applications. Modifications may be made to simplify the analysis at the expense of some precision.
The experimental data do indicate that the permeability decreases rapidly with the moisture content, and this is in agreement with the observed phenomena that irrigation water moves very rapidly when first applied but slows down very appreciably as it moves out from the source.
Even though the problem is difficult, requiring a rather complicated mathematical approach, it is an important one and deserves further consideration. An attempt should be made to eliminate the geometrical variable R from equation (41) by use of a relationship such as that of equation (25) from which R can be obtained as a function of r, ρ, and ∂ρ/∂r. This will permit the expression of f in terms of ρ with the gradient of ρ as a parameter, both of which may be measured in the soil.
Other soils should be studied and attempts should be made to find approximations that will render the principles involved useful to irrigation engineers.