Derivation of Lewis‐Kostiakov Intake Equation

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Abstract
The empirical Lewis‐Kostiakov intake equation takes a power form in an algebraic equation that explicitly relates the cumulative infiltration depth, d, to the intake time, t, as d=ktn, in which k and n are the empirical constants. Although users of this well‐known intake (infiltration) equation are convinced that k and n have physical meanings, this equation is still regarded as empirical. This paper presents the physical derivation of the Fok power‐law infiltration equations to enable the interpretation of the physical meanings of k and n according to the infiltration time zones.

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