# EPA On-line Tools for Site Assessment Calculation

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#### Theory

The recharge calculator is based upon two solutions of the one-dimensional Dupuit equation for flow in unconfined aquifers. These solutions are combined to determine the position of the phreatic surface (water table) and a streamline originating at the water table, the gradient, ground water fluxes and travel times for sorbing contaminants. The following sections outline the methods used for calculating these quantities.

#### Phreatic Surface

The first solution is used to determine the location of the phreatic surface
Bear (1972, page 379)
and is given by

where h is the elevation of the phreatic surface above the datum (bottom of the aquifer) [L], N is the recharge rate [L^{3}/L^{2}/T], K is the hydraulic conductivity of the aquifer [L/T], x is the distance [L]. The constants C and B are determined from

and

where x_{1} and x_{2} [L] are up and down gradient locations in the aquifer, and h_{1} and h_{2} [L] are the corresponding phreatic surface elevations or heads.

Bear's solution does not require that the water table elevation decrease monotonically downgradient. Depending on the values input for recharge, hydraulic conductivity and heads, there could be a ground water divide between the two specified end points.

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