Ground flow formula (Water Overlay): Difference between revisions
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<math>\Delta w_t = w_{1,t} - w_{2,t}</math> | <math>\Delta w_t = w_{1,t} - w_{2,t}</math> | ||
<math> | <math>KD = min(KD_{1} , KD_{2} )</math> | ||
<math>V_t = \frac{\Delta w \cdot KD \cdot \Delta_x }{ \Delta x} \cdot \Delta t</math> | <math>V_t = \frac{\Delta w \cdot KD \cdot \Delta_x }{ \Delta x} \cdot \Delta t</math> | ||
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: <math>KD_n</math> = The hydraulic conductivity of the cell, multiplied with the thickness of the layer, defined in [[Terrain hydraulic conductivity with thickness md (Water Overlay)|HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS_MD]] of the underground terrain. | : <math>KD_n</math> = The hydraulic conductivity of the cell, multiplied with the thickness of the layer, defined in [[Terrain hydraulic conductivity with thickness md (Water Overlay)|HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS_MD]] of the underground terrain. | ||
: <math>d_{ground}</math> = The configured ground bottom distance, defined in [[Ground_bottom_distance_m_(Water_Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay. | : <math>d_{ground}</math> = The configured ground bottom distance, defined in [[Ground_bottom_distance_m_(Water_Overlay)|GROUND_BOTTOM_DISTANCE_M]] of the Water Overlay. | ||
: <math>\Delta w</math> = Underground water level difference at time <math>t</math>. | : <math>\Delta w</math> = Underground water level difference at time <math>t</math>. | ||
: <math>\Delta t</math> = Computational timestep. | : <math>\Delta t</math> = Computational timestep. | ||
Revision as of 09:53, 2 February 2023
Underground flow is different from surface flow, since it has to account for the slowdown and porousness of the medium. In general, horizontal underground flow is calculated using formulas described in Harbaugh 2005[1][2]. However, when an aquifer is present, the aquifer variant is applied.
Hydraulic Conductivity without Thickness
The flow between the two cells is calculated as:
where:
- = The underground water level of cell at time .
- = The surface height of cell n.
- = The hydraulic conductivity of the cell, defined in HYDRAULIC_CONDUCTIVITY_MD of the underground terrain.
- = The configured ground bottom distance, defined in GROUND_BOTTOM_DISTANCE_M of the Water Overlay.
- = Area of conductance at time ..
- = Underground water level difference at time .
- = Computational timestep.
- = Size of grid cell.
- = Averaged underground water level at time , based on water levels in underground, WATER_STORAGE_PERCENTAGE and potentially the surface water level, when the underground is filled to the top.
- = The amount of water to be transported at time between one cell and the other
Hydraulic Conductivity with Thickness
The flow between the two cells is calculated as:
where:
- = The underground water level of cell at time .
- = The surface height of cell n.
- = The hydraulic conductivity of the cell, multiplied with the thickness of the layer, defined in HYDRAULIC_CONDUCTIVITY_WITH_THICKNESS_MD of the underground terrain.
- = The configured ground bottom distance, defined in GROUND_BOTTOM_DISTANCE_M of the Water Overlay.
- = Underground water level difference at time .
- = Computational timestep.
- = Size of grid cell.
- = Averaged underground water level at time , based on water levels in underground, WATER_STORAGE_PERCENTAGE and potentially the surface water level, when the underground is filled to the top.
- = The amount of water to be transported at time between one cell and the other
Aquifer formula
When an aquifer is present, its hydraulic diffusivity is used to calculate the water flow.
First the following condition is checked in order to allow water movement through the aquifer:
Based on this condition being true, the transported volume V is calculated:
Where:
- = Ground water level in the cell at time ;
- = the datum height of the aquifer at the cell.
- = Volume in that flows between the two adjacent cells due to the aquifer.
- = Ground water level difference between the two adjacent cells at time ;
- = Computational timestep.
- = The AQUIFER_KD attribute of aquifer.
Related
The following topics are related to this formula.
- Features
- Aquifer
- Formulas
- Groundwater level formula
- Underground infiltration formula
- Models
- Underground model
- Infiltration model
- Tracer flow model
See also
References
- ↑ Harbaugh, A.W., 2005, MODFLOW-2005, the U.S. Geological Survey modular ground-water model-the Ground-Water Flow Process: U.S. Geological Survey Techniques and Methods 6-A16, variously paginated.
- ↑ Langevin, C.D., Hughes, J.D., Banta, E.R., Niswonger, R.G., Panday, Sorab, and Provost, A.M. (2017) ∙ Documentation for the MODFLOW 6 Groundwater Flow Model: U.S. Geological Survey Techniques and Methods, book 6, chap. A55 ∙ p 31 ∙ found at: https://doi.org/10.3133/tm6A55 (last visited 2019-02-04)
- 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