DERIVATION OF LEWIS-KOSTIAKOV INTAKE EQUATION

The empirical M. R. Lewis-A. N. Kostiakov intake equation takes a power form in an algebraic equation that eplicitly relates the cumulative infiltration depth, d, to the intake time, t, as d equals kt**n, 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 Y. S. Fok power-law infiltration equations to enable the interpretation of the physical meanings of k and n according to the infiltration time zones.