How does Darcy's law describe water flow through porous materials?

Darcy’s law is the fundamental mathematical relationship in hydrologic sciences that describes the laminar, or nonturbulent, flow of fluids through porous, granular media.12

Developed by the French engineer Henri Darcy in 1856, the law establishes that the discharge of water through a material is proportional to the cross-sectional area, the hydraulic gradient, and the material's permeability. This relationship is expressed by the formula:12

$$Q_d=PIA$$

In this equation:
* $Q_d$: The discharge of water (e.g., in litres per day).
* $P$: The coefficient of permeability, which measures the ease with which a fluid can move through the medium.
* $I$: The hydraulic gradient, representing the change in head per unit of length.
* $A$: The cross-sectional area through which the flow occurs.1

By quantifying how groundwater moves through an aquifer, Darcy’s law serves as the essential theoretical foundation for modern quantitative hydrology.12