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

$\phi (r)-\phi _{0}={\frac {Q_{0}}{2\pi \cdot kD}}\ln {\left({\frac {r}{R}}\right)}$

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

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 of the considered stable water table edge to 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 Q_0} : amount of water pumped out in m³ / day

References

Water Module

Tutorials

Overview

Theory

Benchmarks