Darcy's Law (Specific Discharge) Calculator
Flow of fluid through a porous medium.
Formula first
Overview
Darcy's Law defines the relationship between the flow rate of a fluid through a porous medium and the hydraulic gradient. In hydrogeology, it is primarily used to calculate the specific discharge, also known as the Darcy flux, which represents the volume of water flowing through a unit cross-sectional area per unit time.
Symbols
Variables
v = Velocity (v), K = Hydraulic Cond., i = Gradient (i)
Apply it well
When To Use
When to use: Apply this equation when analyzing laminar flow through saturated materials like sand, gravel, or fractured rock. It assumes steady-state conditions and is most accurate for low-velocity groundwater systems where the Reynolds number is less than 1 to 10.
Why it matters: This principle is fundamental for predicting groundwater movement, managing water supply wells, and tracking the spread of underground pollutants. It allows engineers to design effective drainage systems and assess the stability of earth-fill dams or embankments.
Avoid these traps
Common Mistakes
- Ignoring the negative sign when calculating direction.
One free problem
Practice Problem
A sandy aquifer has a hydraulic conductivity of 12 meters per day. If the measured hydraulic gradient between two observation wells is 0.005, calculate the specific discharge in meters per day.
Solve for:
Hint: Multiply the hydraulic conductivity by the hydraulic gradient to find the specific discharge.
The full worked solution stays in the interactive walkthrough.
References
Sources
- Applied Hydrogeology, C.W. Fetter
- Groundwater, R.A. Freeze and J.A. Cherry
- Wikipedia: Darcy's law
- Freeze, R. Allan, and Cherry, John A. Groundwater. Prentice-Hall, 1979.
- Fetter, C.W. Applied Hydrogeology. 4th ed. Prentice Hall, 2001.
- University Hydrogeology — Porous Flow