DARCY'S LAW: WHAT IT CONSISTS OF, EXPERIMENT AND APPLICATIONS - PHYSICAL - 2025

The Darcy 's Law for describing the flow of fluids through porous materials. The law was deduced as a universalization applicable to the calculation of the flow of water through sand filters. It was obtained from a few experiments done by the French engineer Henry Darcy on coarse sand containing fine gravel from the Saone River.

Although over time it was subjected to modifications, the law formulated by Darcy from his experiments is the scientific basis of current hydrology. For her research Darcy used a device very similar to the permeameters currently used in most laboratories in fluid research.

Henry darcy

Today the law is widely used in fields as diverse as engineering, hydrogeology and the oil industry.

What does it consist of?

In its simplest form, the mathematical expression for Darcy's Law is as follows:

Q = K ∙ A ∙ ∆h / ∆L

In this expression, Q is the flow rate and K is a constant known as Darcy's permeability coefficient (constant that depends on both the material and the properties of the fluid that passes through it).

Furthermore, A is the cross-sectional area, ∆L is the distance between two points in the sample, and ∆h is the potential difference between those two same points.

A more correct expression of the law would be:

q = - K ∙ (dh / dl)

In this equation q = Q / A or flow per section, K is the hydraulic conductivity, and dh / dl is the hydraulic gradient.

Darcy's Law Considerations

When establishing Darcy's law, a series of considerations are taken into account, both about the porous medium and about the fluid:

- The fluid is not compressible.

- The porous medium that the fluid passes through is homogeneous.

- The flow is linear.

- The flow of the fluid is isothermal.

- The fluid does not react at any time with the porous medium it passes through.

Limitations

Two fundamental limitations to Darcy's law can basically be considered.

- In the first place, the fact that the constant K does not depend solely on the porous medium, since its value also depends on the fluid that passes through it.

- Secondly, the non-linear relationship between the flow and the hydraulic gradient, which happens if the constant takes a very low value or if the speeds are very high.

Validity

In general, it is considered that the law deduced by Darcy is applicable to water flows through porous media, such as soils, in which a laminar flow occurs.

The truth is that later work by other researchers has corroborated that Darcy's Law remains valid for most types of fluid flow that move through soils.

However, it is important to note that for filtration of liquids at very high speeds and of gases at very low speeds, Darcy's law is no longer applicable.

Darcy's experiment

The French engineer Henry Darcy was one of the most important pioneers in the development of urban drinking water supplies.

He was responsible for the study of the water supply network of the French city of Dijon. Apparently, his responsibilities also included the design of water purification filters; this was probably what led him to investigate water flows through sand beds.

The results of his studies on the subject were published as an annex to the report he presented on the water distribution network of the city of Dijon; It was in these annexes that the expression of what later ended up being called Darcy's Law was published.

The truth is that their research turned out to be so relevant that, since then, they have been considered both the basis of all subsequent studies on groundwater flows and the scientific basis for studying the permeability of liquids.

However, the value of Henry Darcy's work is not limited to his research. Henry Darcy is also recognized for his efforts making Dijon the second European city, after Rome, to have a complete water supply network. This network reached every floor of every house in the French city.

The permeameter

The device devised by Darcy for his experiments is the basis for current permeameters. Permeameters are used to determine the permeability of different materials to the passage of a fluid.

In general, they consist of a container filled with a sandy material with a constant determined section through which a flow of water is circulated.

The flow of water originates from a water reservoir in which the water level is constant. The outlet that is located at the other end of the container consists of a tap through which a constant flow comes out.

At least two measurements of the height of the water column are taken along the path of the fluid in order to know the permeability of the material.

Applications

Darcy's Law is widely used today in civil engineering, agricultural engineering, and the petroleum industry; and, of course, in hydrogeology.

Thus, one of the most relevant applications of Darcy's Law is to obtain the flow of water through aquifers.

As far as the oil industry is concerned, Darcy's Law is also used to describe the flows of oil, water, and gas through oil reservoirs.

References

1. Darcy's law (nd). In Wikipedia. Retrieved on April 23, 2018, from en.wikipedia.org.
2. Henry Darcy (nd). In Wikipedia. Retrieved on April 23, 2018, from es.wikipedia.org.
3. Darcy's Law (nd). In Wikipedia. Retrieved on April 23, 2018, from es.wikipedia.org.
4. Darcy, H. (1856). Les fontaines publiques de la ville de Dijon. Paris: Dalmont.
5. Arora, KR (1989). Soil Mechanics and Foundation Engineering. Standard Publishers.