Darcy's Law Calculator
Flow rate of fluid through a porous medium.
Formula first
Overview
Darcy's Law describes the flow of fluid through a porous medium, typically used to model groundwater movement through aquifers. It states that the discharge rate is directly proportional to the hydraulic conductivity, the cross-sectional area, and the hydraulic gradient.
Symbols
Variables
Q = Discharge, K = Hydraulic Conductivity, A = Cross-Sectional Area, i = Hydraulic Gradient (i)
Apply it well
When To Use
When to use: Apply this equation when analyzing laminar flow in saturated porous media such as sand, gravel, or silt. It is valid for low Reynolds numbers, typically less than one, where viscous forces dominate over inertial forces.
Why it matters: This principle is fundamental for managing groundwater resources, predicting the migration of underground contaminants, and designing construction projects like dams or landfills. It allows scientists to quantify how much water is moving through the subsurface and at what velocity.
Avoid these traps
Common Mistakes
- Using porosity instead of hydraulic conductivity.
- Failing to convert units (e.g. area to m² and conductivity to m/day).
One free problem
Practice Problem
A sandy aquifer has a hydraulic conductivity of 15 m/day and a cross-sectional area of 200 m². If the observed hydraulic gradient is 0.005, calculate the total discharge rate (Q).
Solve for:
Hint: Multiply the hydraulic conductivity by the area and the gradient.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Fetter, C.W., Applied Hydrogeology
- Freeze, R.A. and Cherry, J.A., Groundwater
- Britannica: Darcy's law
- Wikipedia: Darcy's law
- Freeze, R. Allan, and Cherry, John A. (1979). Groundwater. Prentice-Hall.
- Gupta, Ram S. (2008). Hydrology and Hydraulic Systems (2nd ed.). Waveland Press.
- Wikipedia: Darcy's law (article title)
- Freeze, R. Allan, and John A. Cherry. Groundwater. Prentice-Hall, 1979.