Comparison of Empirical Relationships between Pressure Head and Hydraulic Conductivity and Some Observations on Radially Symmetric Flow

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Abstract
It is shown that the critical pressure head used by Bouwer is equal to the difference in matric flux potential at pressure heads zero and minus infinity divided by the hydraulic conductivity at pressure head zero. The critical pressure head and the saturated hydraulic conductivity are used to define a dimensionless pressure head, hydraulic conductivity, and matric flux potential. For six empirical relationships between pressure head and hydraulic conductivity, the associated matric flux potential and critical pressure head have been evaluated. The plots of the dimensionless hydraulic conductivity and mattic flux potential versus pressure head provide a clear basis for comparing the six models. A discussion of steady, p‐dimensional, radially symmetric flow (without gravity) illustrates the occurrence of the matrio flux potential and the critical pressure head in flow problems. Expressions are obtained for the steady flux, the maximum steady flux, and the change in steady flux as a function of changes in pressure head at two points. One‐dimensional, cylindrically symmetric, and radially symmetric flows are discussed as special cases. The results for the radially symmetric case suggest a new method for in situ determination of the hydraulic conductivity as a function of the pressure head.