Streamlit Apps for the topic

04 Basic Hydrogeology

Groundwater Movement

Analytical solution for 1D unconfined flow with two defined head boundaries

Conceptual model

The conceptual model considers the aquifer as a homogeneous and isotropic structure with a horizontal bottom. The aquifer is bounded by two defined-head boundary conditions on the in- and outflow part. From the top, the aquifer receives uniform groundwater recharge.

Mathematical model

The equation for 1D groundwater flow in a homogeneous aquifer is

\(\frac{d}{dx} \left(-hK \frac{dh}{dx} \right) = R\) with

  • x is spatial coordinate along the flow,

  • h is hydraulic head,

  • K is hydraulic conductivity,

  • R is recharge.

A solution for the equation can be obtained with two boundary conditions at x = 0 and x = L:

\[h(0) = h_0\] \[h(L)=h_L\]

The solution for hydraulic head h along x is

\[h(x) = \sqrt{h_0^2 - \frac{h_0^2 - h_L^2}{L} x + \frac{R}{K} x (L - x)}\]

Computation and visualization

Subsequently, the solution is computed and results are visualized. You can modify the parameters to investigate the functional behavior. You can modify the groundwater recharge R (in mm/a) and the hydraulic conductivity K (in m/s).

screenshot of the app

You can access the app here: https://gwf-1d-unconf-analytic.streamlit.app/