Darcy's law is the law that states that in a laminar flow in a saturated soil, the velocity is directly proportional to the hydraulic gradient. This law is named after Henry Darcy, a French engineer who conducted extensive research on fluid flow in porous media in the mid-19th century.

Darcy's law is a fundamental principle in hydrogeology and is widely used in the field of groundwater flow. It provides a mathematical relationship between the flow rate of water through a porous medium, the hydraulic conductivity of the medium, the cross-sectional area through which the flow occurs, and the hydraulic gradient.

Now let's break down the key points about Darcy's law:

1. Definition of Darcy's law:
- Darcy's law is a fundamental principle in hydrogeology that describes the flow of water through a porous medium.
- It establishes a linear relationship between the velocity of water flow and the hydraulic gradient.

2. Laminar flow in a saturated soil:
- Laminar flow refers to the smooth and orderly movement of fluid particles in distinct layers or streamlines.
- Saturated soil means that all available void spaces within the soil are filled with water.

3. Velocity and hydraulic gradient:
- Velocity refers to the speed at which water flows through a porous medium.
- Hydraulic gradient is the change in hydraulic head per unit distance in the direction of flow.

4. Direct proportionality:
- Darcy's law states that the velocity of water flow is directly proportional to the hydraulic gradient.
- This means that as the hydraulic gradient increases, the velocity of water flow also increases, and vice versa.

5. Mathematical representation:
- Darcy's law can be mathematically represented as:
Q = -kA(dh/dl)
where Q is the flow rate, k is the hydraulic conductivity of the porous medium, A is the cross-sectional area, dh is the change in hydraulic head, and dl is the distance over which the change occurs.

In conclusion, Darcy's law states that in laminar flow in a saturated soil, the velocity of water flow is directly proportional to the hydraulic gradient. This law is widely used in hydrogeology to understand and analyze groundwater flow in porous media.