# Darcy's Law: Ground Water – Understanding Direction and Flow Amount

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## Darcy’S Law

Laminar fluid flow

Flow regimes are classified in terms of the dimensionless Reynolds number (Fancher and Lewis, 1933). Reynolds number is the ratio of inertial (fluid momentum) forces to viscous forces.

A low Reynolds number corresponds to laminar flow, and a high Reynolds number corresponds to turbulent flow.

Henry Darcy, a French hydraulic engineer interested in purifying water supplies using sand filters, conducted experiments to determine the flow rate of water through the filters.

Published in 1856, his conclusions have served as the basis for all modern analysis of ground water flow

## Understanding Direction

Experiment with changes in pressure head and hydraulic head

Water flows from high elevation to low elevation and from high pressure to low pressure, gradients in potential energy drive groundwater flow

groundwater flows from high to low head

## Amount of Flow

Q A

Q

Q

Q

Head is a measure of the total mechanical energy per unit weight.

Hydraulic head gradient is

K is hydraulic conductivity

What happens if the head gradient is too steep? The fluid will have enough energy to accelerate in spite of the resistance of the grains, and inertial forces become important. In this case potential energy (head) is not dissipated linearly with distance and Darcy’s Law does not apply.

Notice that Darcy’s Law starts to fail when inertial effects are important, even though the flow is still laminar. It is not turbulence, but inertia and that leads to non-linearity. Turbulence comes at much higher velocities.

Darcy’s 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).

-Manishika