Watershed Explorer

Darcy's Law describes the flow of fluid through a porous medium. The specific discharge (Darcy velocity) is proportional to the hydraulic gradient.

Where $K$ is hydraulic conductivity (m/day), and $dh/dl$ is the hydraulic gradient. The actual pore velocity is $v_s = v/n$ where $n$ is porosity.

The water budget partitions precipitation into infiltration, surface runoff, and evapotranspiration.

Runoff is estimated using the SCS Curve Number method, where $S = \frac{25400}{CN} - 254$ is the maximum soil retention and $Q = \frac{(P - 0.2S)^2}{P + 0.8S}$ for $P > 0.2S$.

The Theis equation gives the drawdown at distance r from a pumping well in a confined aquifer.

For small $u$ (large time or small distance), the Cooper-Jacob approximation gives $W(u) \approx -0.5772 - \ln(u)$.

A contaminant plume spreads by advection (bulk flow) and dispersion (mixing). The 2D Gaussian solution describes concentration in space and time.

The dispersion coefficients are $D_L = \alpha_L v$ (longitudinal) and $D_T \approx 0.1 D_L$ (transverse), where $\alpha_L$ is dispersivity.