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The AAPG/Datapages Combined Publications Database

New Orleans Geological Society


Introduction to Ground-Water Hydrology, 1993 - Darcy's Law
Pages 12-18

Darcy's Law


The foundation of the quantitative study of ground water is Darcy's Law, first published in 1856 by Henry Darcy of France. The Law is an empirical relationship based on an experiment using the apparatus shown in Fig. 2.1. Darcy observed that the volume of water coming out of the apparatus per unit time, Q, was proportional to the change in head, delta.gif (54 bytes)h, and the cross-sectional area of the tube, A, but inversely proportional to the length of the tube, delta.gif (54 bytes)l. Thus, Q alpha.gif (53 bytes) [delta.gif (844 bytes)h]/[delta.gif (844 bytes)l] A. The constant of proportionality, K, depended on the material he packed into the tube, such as clay, silt, or sand. This property of the material is called the hydraulic conductivity, K. Darcy's Law is then

Q = -K[delta.gif (844 bytes)h]/[delta.gif (844 bytes)l]A.    (2.1)

(The negative sign indicates that the flow is "downhill.") This is often expressed in differential form,

Q = -K[dh]/[dI]A.    (2.2)

In the remainder of this section, we will look at each part of this equation in more detail, and extend it to estimating ground-water velocity.

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