Darcys Law: Flow Through Porous Media

Reference

Darcys law is the foundation of groundwater hydraulics: flow through a porous medium is proportional to the hydraulic gradient driving it.

The equation

Q = K i A
  • Q is discharge in cubic meters per day
  • K is hydraulic conductivity in meters per day
  • i is the hydraulic gradient, dimensionless
  • A is the cross sectional area of flow in square meters

Worked example

A sand aquifer with K of 5 meters per day, a gradient of 0.002, and a flow face of 1000 square meters passes Q = 5 × 0.002 × 1000 = 10 cubic meters per day. The Darcy velocity is Ki = 0.01 meters per day, and dividing by a porosity of 0.25 gives a true seepage velocity of 0.04 meters per day.

When to use it

Valid for slow laminar flow through saturated granular media, which covers almost all natural groundwater movement. It breaks down in karst conduits, open fractures, and immediately around pumping wells where flow can become turbulent.

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