The Darcy’s Law formula, `Q = (-k*A(P_b-P_a))/(mu*L)`, computes the flow rate of a fluid through a porous medium. The law was derived by Henry Darcy from empirical data he obtained performing experiments on water flowing through layers of sand. Darcy’s Law is often used to define permeability of substances and serves as an important formula in hydrogeology and civil engineering disciplines. In civil engineering applications, this formula helps to determine how saturated a medium will remain.
The inputs to this equation are as follows:
- k = the intrinsic permeability of the medium
- A = the cross-sectional area through which the fluid will flow
- `P_b - P_a` = the total pressure drop
- `mu` = viscosity of the fluid
- L = the length over which the pressure drop occurs
Darcy's Law returns the fluid flow in volume / time
Notes
Darcy's law depicts familiar properties of groundwater flow as experienced in aquifers. Some common examples are:
- Increased pressure results in increased flow rate
- Hydrostatic condition prevail when there is no pressure gradient over the length (depth) of the medium
- In hydro-dynamic conditions, fluid will flow from high to low pressure (thus the negative sign on Darcy's equation)
As a prime example of the application of Darcy's Law, the steady-state flow equation, derived from Darcy's Law as it applies to groundwater, along with the conservation of mass, is used to quantify the amount of groundwater flowing under a dam.