Calculator 1 - Darcy Flux and Average Linear Groundwater Velocity

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Darcy's law is the basic equation that describes fluid flow through porous media.  There are many ways to write Darcy's Law, and a few of them will be presented here.  The first equation contains a velocity term, v (L/T), a conductivity term, K (L/T), a head term, h (L), and a distance term, l (L):

v = -K(∆h/∆l)

This is the Darcy velocity (or Darcy flux) which is defined as the flow per unit cross sectional area of the porous medium. Since you have a porous media the water must move through the pores, around the solid particles, at a speed greater than the flux.  This speed is called the average linear groundwater velocity and is calculated by dividing the Darcy flux by the porosity of the media. 


Hydraulic Gradient:
Hydraulic Conductivity:
Effective Porosity (%):

Darcy Flux:
Average Linear Groundwater Velocity

Note: Units of Darcy flux and average linear velocity are the same as those used for conductivity



Not to scale

L =100m                     K = 1 x 10-5 m/s       Porosity = 30% or 0.3

A = 5 x 10 = 50m2     dh = (h2 - h1) = (10 - 12) = -2 m


i = (-2)/100 = -0.02

v = - (10-5) x (-0.02) = 2 x 10-7 m/s

Q = - (10-5) x (-0.02) x 50 = 1 x 10-5 m3/s

Note: To Calculate Average Linear Velocity which is what we use for groundwater calculations you must divide v by porosity.

Average Linear Velocity

v/porosity = 2 x 10-7 m/s / 0.3  =  6.6 x  10-7   m/s