Radial well aquifer benchmark (Water Module): Difference between revisions
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This testcase demonstrates a situation where a | This testcase demonstrates a situation where a well is pumping up ground water. A characteristic ground water level curve will form over time. | ||
[[File:drainage_freatic_benchmark.png]] | [[File:drainage_freatic_benchmark.png]] | ||
===Formulas=== | ===Formulas=== | ||
Stationary lowering of the ground water table in a closed water transmissive layer can be described by the following formula <ref name="verruijt70"/> | |||
<math>\phi(r) - \phi_0 = \frac {Q_0}{2\pi\cdot kD} \ln{\left ( \frac{r}{R} \right )}</math> | <math>\phi(r) - \phi_0 = \frac {Q_0}{2\pi\cdot kD} \ln{\left ( \frac{r}{R} \right )}</math> | ||
where: | where: | ||
: <math>phi(0)</math>: stable water level at the considered edge | : <math>phi(0)</math>: stable water level at the considered stable water table edge | ||
: <math>phi(r)</math>: water level between the considered edge and the well | : <math>phi(r)</math>: water level between the considered stable water table edge and the well | ||
: <math>phi(rw)</math>: water level in the well | : <math>phi(rw)</math>: water level in the well | ||
: <math>kD</math>: transmissivity of the aquifer in m² / day | |||
: <math>r</math>: distance to the well | |||
: <math>R</math>: distance of the considered stable water table edge to the well | |||
: <math>Q_0</math>: amount of water pumped out in m³ / day | |||
Revision as of 17:08, 15 December 2020
This testcase demonstrates a situation where a well is pumping up ground water. A characteristic ground water level curve will form over time. File:Drainage freatic benchmark.png
Formulas
Stationary lowering of the ground water table in a closed water transmissive layer can be described by the following formula [1] 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
- 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
- ↑ Cite error: Invalid
<ref>tag; no text was provided for refs namedverruijt70