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The unsteady-state (or Theis) equation, which was derived from the analogy between the flow of groundwater and the conduction of heat, is perhaps the most widely used partial differential equation in groundwater investigations: (11.39) U D t H ( s , t ) = T D s s H ( s , t ) + 1 s D s H ( s , t ) .
The steady-state, or predevelopment, version of the model represents an approximation of the aquifer before the construction of water wells and pumping of groundwater. Predevelopment conditions are not as well known as later conditions in the aquifer because there are few records of early water-level measurements.
Water flow rate can be calculated with the help of a simple formula which is: Q = V/t, where: Q = Flow rate (typically measured in liters per minute or gallons per minute). V = Volume of fluid (in liters or gallons).
average pore water velocity v = -K/n(∆h/∆L) The average velocity of the water is the Darcy equation divided by the porosity of the sediment.
How is it measured? There are various methods engineers, hydrogeologists, and environmental specialists, deploy to measure groundwater flow. This involves pumping water from a well at a constant rate or decreasing rates (step down) and measuring the water level response in nearby monitoring wells.
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Darcys law says that the discharge rate q is proportional to the gradient in hydrauolic head and the hydraulic conductivity (q = Q/A = -K*dh/dl). Definitions of aquifers, aquitards, and aquicludes and how hydraulic conductivity relates to geology.

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