Darcy's Law describes, based on laboratory experiments, the characteristics of the movement of water through a porous medium.
The mathematical expression of Darcy's law is:
The mathematical expression of Darcy's law is:
Where:
Q= Flow, discharge or flow rate in m3 / s.
L= Length in meters of the sample
K= A constant, now known as Darcy permeability coefficient, which varies depending on the sample material, m / s.
A= Area of cross section of the sample in m2.
h3= Height above the reference plane and the water reaches a tube placed at the entrance of the filter bed.
h4= Height above the reference plane and the water reaches a tube placed at the exit of the filter bed.
The hydraulic gradient
Darcy's Law is one of the cornerstones of soil mechanics. From the initial work of Darcy, a monumental work for the time, many other researchers have analyzed and tested this law. Through these later works has been determined and is applicable for most types of fluid flow in soils. In order to seepage of liquids at very high speeds and gas at very low speeds, Darcy's law becomes invalid.
In the case of water flowing in soils, there is overwhelming evidence for the purposes of verifying the validity of Darcy's law for soils ranging from silts to medium sands. It is also perfectly applicable in the clays, for steady flows. For soils of higher permeability than the sand media, determined experimentally in the actual relationship between the gradient and velocity and porosity for each soil studied.
In the second half of the 19th century, a French engineer, Henry Darcy, developed the first systematic study of water movement through porous media. This study analyzed the movement of water through beds of sand used for water filtration for drinking. Darcy found that the rate or speed at which water flows through the medium pore is directly proportional to the difference in height between the two ends of the bed filter, and inversely proportional to the length of the bed.
The figure shows a horizontal pipe filled with sand, in which water is applied by pressure through the end A, which flows and is discharged through the end B.
The observed pressure at each end of the pipe (or somewhere in between) can be is measured using a small diameter standpipe (piezometer). Darcy found experimentally that the discharge, Q, is directly proportional to the difference in height Water from the piezometers A and B and inversely proportional to the length of the pipe, L:
The figure shows a horizontal pipe filled with sand, in which water is applied by pressure through the end A, which flows and is discharged through the end B.
The observed pressure at each end of the pipe (or somewhere in between) can be is measured using a small diameter standpipe (piezometer). Darcy found experimentally that the discharge, Q, is directly proportional to the difference in height Water from the piezometers A and B and inversely proportional to the length of the pipe, L:
Fuente:
- T.W. Lambe y R.V. Whitman - Mecánica de suelos. Mexico, 1997 .
- Bouwer H., 1999, Predicting infiltration and ground-water mounds for artificial recharge,
- Journal of Hidrologic Engineeering, October 1999, pp. 350-357. Canter, L.W. & Knox, R.C. (1985). “Septic Tank System Effects on Ground Water Quality”,Lewis Publishers, Inc.
Single phase flow
