Radial well aquifer benchmark (Water Module)

This testcase demonstrates a situation where a well is pumping up ground water. A characteristic ground water level curve will form over time.

Formulas

Stationary lowering of the ground water table in a closed water transmissive layer can be described by the following formula Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \phi(r) - \phi_0 = \frac {Q_0}{2\pi\cdot kD} \ln{\left ( \frac{r}{R} \right )}}

where:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle phi(0)} : stable water level at the considered stable water table edge

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle phi(r)} : water level between the considered stable water table edge and the well

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle phi(rw)} : water level in the well

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle kD} : transmissivity of the aquifer in m² / day

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r} : distance to the well

$R$: distance of the considered stable water table edge to the well

$Q_{0}$: amount of water pumped out in m³ / day