Ground bottom flow formula (Water Overlay): Difference between revisions

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* <math>\Delta s_{x,y}</math> = The water level change due to seepage, in meters.
* <math>\Delta s_{x,y}</math> = The water level change due to seepage, in meters.
* <math>\Delta t</math> = Computational timestep in seconds.
* <math>\Delta t</math> = Computational timestep in seconds.
* <math>h_{x,y}</math> = Ground water head in the grid cell.
* <math>h_{x,y}</math> = [[Groundwater level formula (Water Overlay)|Ground water head]] in the grid cell.
* <math>h_{d}(t)</math> = additional ground water level (or head) of the external zone causing the seepage at time t, in meters
* <math>h_{d}(t)</math> = Additional ground water level (or head) of the external zone causing the seepage at time t, in meters
* <math>h_{c_{x,y}}</math> = constant ground water level (or head) of the external zone causing the seepage, in meters
* <math>h_{c_{x,y}}</math> = Constant ground water level (or head) of the external zone causing the seepage, in meters
* <math>h_{v}(t)</math> = additional variation of seepage head over time
* <math>h_{v}(t)</math> = Additional variation of seepage head over time
* <math>c_{x,y}</math> = resistance of the separating layer in days
* <math>c_{x,y}</math> = Resistance of the separating layer in days
* <math>ws</math> = water storage fraction of the soil
* <math>ws</math> = Water storage fraction of the soil
* <math>\Delta w_{x,y}</math> = seeped in water in m
* <math>\Delta w_{x,y}</math> = Seeped in water in m


==Notes==
==Notes==

Revision as of 10:57, 2 September 2020

Underground seepage from outside the project area is calculated per grid cell.

The water level change due to seepage is calculated using 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 \Delta s_{x,y} = \frac{h_{d}(t) - h_{x,y}}{c_{x,y}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}}

The external seepage head is variable over time by the introduction of hv,t:

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 h_d(t) = h_{c_{x,y}} + h_{v,t}(t)}

Finally, the actual amount of water seeping into the ground from the bottom is calculated as followed:

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 \Delta w_{x,y} = {\Delta s_{x,y}}\cdot{ws}}

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 \Delta s_{x,y}} = The water level change due to seepage, in meters.
  • 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 \Delta t} = Computational timestep in seconds.
  • 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 h_{x,y}} = Ground water head in the grid cell.
  • 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 h_{d}(t)} = Additional ground water level (or head) of the external zone causing the seepage at time t, in meters
  • 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 h_{c_{x,y}}} = Constant ground water level (or head) of the external zone causing the seepage, in meters
  • 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 h_{v}(t)} = Additional variation of seepage head over time
  • 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 c_{x,y}} = Resistance of the separating layer in days
  • 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 ws} = Water storage fraction of the soil
  • 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 \Delta w_{x,y}} = Seeped in water in m

Notes

  • 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 h_{c_{x,y}}} and 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 c_{x,y}} can both be provided as spatially variable values.
  • 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 h_{d}(t)} can be provided as a set of values, variable over time.
  • A seepage head lower than the water level in the project is also allowed, resulting in water seeping out to a region outside the project area.

See also

Water Module
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Introduction button.png
Water Module
Benchmarks button.png
Getting started button.png
Tutorials
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Overview button.png
Overview
Benchmarks button.png
Theory button.png
Theory
Benchmarks button.png
Benchmarks button.png
Benchmarks
Models
Surface • Ground • Rain • Evaporation • Infiltration • Elevation • Breach • Sewer • Storage • Tracer flow • Border • Order
Model formulas
Timestep • Season • Surface water level • Groundwater level
Flow formulas
Surface flow • Surface infiltration • Ground flow • Ground infiltration • Surface evaporation • Ground evaporation • Ground bottom flow
Hydraulic structure formulas
Culvert • Weir • Breach growth • Breach flow • Pump • Sewer Overflow • Inlet • Drainage
Related
Building attributes • Hydrological features • Hydraulic structures •  Terrain attributes • Model attributes • Results • Simulation data
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