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

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The water level change due to seepage is calculated using the following formula:
The water level change due to seepage is calculated using the following formula:
: <math>\Delta s = \frac{h_{d}(t) - h_{x,y}}{c_{x,y}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>
: <math>\Delta s_{x,y} = \frac{h_{d}(t) - h_{x,y}}{c_{x,y}} \cdot \frac{\Delta t}{24 \cdot 60 \cdot 60}</math>


The external seepage head is variable over time by the introduction of h<sub>v,t</sub>
The external seepage head is variable over time by the introduction of h<sub>v,t</sub>
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Finally, calculate the actual amount of water seeping into (or out of) the ground from the bottom.
Finally, calculate the actual amount of water seeping into (or out of) the ground from the bottom.
: <math>\Delta w_{x,y} = {\Delta s}\cdot{ws}</math>
: <math>\Delta w_{x,y} = {\Delta s_{x,y}}\cdot{ws}</math>


Where:
Where:
* <math>\Delta s</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> = Ground water head in the grid cell.

Revision as of 08:56, 28 August 2020

Underground seepage (from (or to) outside the project area) is calculated per cell.

The water level change due to seepage is calculated using the following formula:

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, calculate the actual amount of water seeping into (or out of) the ground from the bottom.

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} = 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} = 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.

See also

Water Module
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Water Module
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Tutorials
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Overview
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Theory
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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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