Darcy’s Experiment
In the year 1856, Henry Darcy, a French hydraulic engineer investigated the flow of water through a vertical homogeneous sand filter. Based on his experiments, he concluded that the rate flow through the porous media is proportional to the head loss and is inversely proportional to the length of the flow path. Figure 3.1 shows the setup of Darcy's experiment. As shown in the figure, the length of the vertical sand filter is L, the cross sectional area of the filter is A, the piezometric heads at top and bottom of the filter are h1 and h2. Thus the head loss is (h1 - h2). The piezometric heads are measured with respect to an arbitrary datum. As per the conclusions made by Darcy, the flow rate Q is
 |
Fig. 3.1 Darcy’s Experiment in vertical sand filter |
- proportional to the cross sectional area (A) of the filter
- proportional to the difference in piezometric heads
- inversely proportional to the length (L) of the filter
After combining these conclusions, we have
|
(3.1) |
Where,
Q is the flow rate, i.e. the volume of water flows through the sand filter per unit time.
K is the coefficient of proportionality and is termed as hydraulic conductivity of the medium. It is a measure of the permeability of the porous medium. It is also known as coefficient of permeability.
h1 and h2 are the piezometric heads.
Now, defining 
and 
Where J is the hydraulic gradient and q is the specific discharge, i.e. the discharge per unit area.
The equation 3.1 can also be written as,
q = KJ |
(3.2) |
Now consider an inclined homogeneous sand filter as shown in Fig. 3.2 In this case, the Darcy’s formula can be written as,
 |
Fig. 3.2: Darcy’s Experiments in inclined sand filter |
|
(3.3) |
or,
|
(3.4) |
or,
q = KJ |
(3.5) |
Where, 
and 
and 
z1 and z2 are the datum head or elevation head
and 
are the pressure head