Darcy's experiment established a quantitative relationship between water flow rate (Q) and other parameters through a column packed with sand. The results showed that: (1) Q is directly proportional to the pressure difference (Δh) between the inlet and outlet, (2) Q is directly proportional to the cross-sectional area (A), and (3) Q is inversely proportional to the column length (ΔL). Combining these relationships yields Darcy's law: Q = KA(Δh/ΔL), where K is the hydraulic conductivity, a material property representing its ability to transmit water. Darcy's law allows predicting parameters important for understanding groundwater flow, such as permeability and transmissivity.

2. Prerequisites
Darcy’s Experiment or Darcy’s Law is aimed at establishing a relation between the discharge rate of a fluid with
respect to the pressure loss along the flow paths. It could further allow us to understand the water discharge
rate through different layers of soil(in Hydrogeology).
For a thorough understanding of the given concept in an applied level, it is important to know the concept of:-
 Saturated and Unsaturated zones
 Aquifers, Aquicludes, Aquitards
 Potential energy & Hydraulic head

3. Unsaturated Zone
• Present between land surface & water table.
• Filled partly with air & partly with water.
Saturated Zone
• Present below the water table.
• Below the water table which all pore spaces are filled with water, and above which the
pore spaces are filled with air.

4. Aquifers Aquicludes Aquitards
Aquifers: A formation that contains sufficient saturated
permeable material to yield significant amount of water to
wells and springs.
Aquicludes : Saturated but impermeable material that does
not yield appreciable quantities of water to the wells.
Aquitards : Saturated but poorly permeable stratum that
impedes groundwater movement does not yield water
freely to wells that may transmit appreciable water to or
from adjacent aquifers.

5. Hydraulic head
It is a measure of liquid pressure expressed in terms of length or elevation with respect to a reference surface
(say. Mean sea level).
It is a crucial parameter for being a measure of determining the potential energy and pressure energy factor
Or vice versa.
Hydraulic head= Pressure head + Elevation head

6. Darcy’s experiment
Darcy’s experiments consisted of a vertical steel column,
with a water inlet at one end and an outlet at the other.
The water pressure was controlled at the inlet and outlet
ends of the column using reservoirs with constant water
levels.
The experiments included a series of tests with different
packing of river sand, and a suite of tests using the same
sand pack and column, but for which the inlet and outlet
pressures were varied.

7. Results
(1) Q was directly proportional to the difference in water
levels from inlet to outlet, h1 - h2 = Δh:
Q ∝ Δh
(2) Q was directly proportional to the cross sectional area
of the tube:
Q ∝ A
(3) Q was inversely proportional to the length of the
column:
Q ∝ 1/ΔL
The experiment was able to establish a quantitative relation between the flow rate Q with various parameters so as to
create a successful ground water flow model. i.e. From the experiment it was found that :-

8. Combining every element of proportionality and multiplying the proportionality constant K we get,
Q = KA(Δh/ΔL)
Where K is known as hydraulic conductivity which is the material property corresponding to the ability
to transmit water.
K is of high significance as being analogous with the Poiseulle’s law we are able to predict parameters such as intrinsic
permeability and factors like transmissivity which is primal in the determination of yield of an aquifer.

9. Poiseulle’s Law

10. Limitation
Darcy's law has been found to be invalid for high values of Reynolds number and at very low values of
hydraulic gradient in some very low-permeability materials, such as clays.
For Calculations Rather than calculating Q the factor Q/A is used sometimes represented as ‘q’ known as
specific discharge or Darcy's velocity. The porosity factor is often divided from q to obtain the exact velocity.

11. References
 LDEO Columbia lectures.
 Water : Science & Society Penn State University.