Enter the permeability, dynamic viscosity, and pressure drop into the calculator to determine the instantaneous flow rate using Darcy’s Law.

Darcy’s Law Formula

The following formula is described by Darcy’s law:

q = - (k/u) * p 
  • Where q is the instantaneous flow rate
  • k is the permeability
  • u is the dynamic viscosity
  • p is the pressure drop

To calculate the flow rate from Darcy’s Law, divide the permeability by the dynamic viscosity, multiply by -1, then multiply by the pressure drop.

Darcy’s Law Definition

Darcy’s law states that the discharge flow rate of a fluid is proportional to the pressure drop and the hydraulic conductivity.

How is Darcy’s law used?

Darcy’s law is directly used to related the viscosity, permeability, flow rate, and pressure drop of the movement of a fluid through a porous medium. This has many applications but one of the most common is in the analysis of water flow through an aquifer.

When is Darcy’s law valid and invalid?

Darcy’s law is valid for applications in which the flow of the fluid is laminar such as the flow of fluid through fine sediments. Darcy’s law is invalid for fluid flow that is turbulent such as flow through a pipe with a Reynold’s number of more than 4,000.

What are the assumptions for Darcy’s law?

The main assumption of Darcy’s law is that the flow of the fluid through the membrane is laminar. Darcy’s law also assumes a single-phase fluid flow analysis. Another assumption is that the viscous resisting force is linear with the speed of the flow.

How to calculate Darcy’s law?

  1. First, determine the permeability of the membrane the fluid is moving through.
  2. Next, determine the dynamic viscosity of the fluid.
  3. Next, determine the pressure drop across the membrane.
  4. Finally, calculate the instantaneous flow rate using the formula derived from Darcy’s law.
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darcy's law