Darcy's Law Calculator (Groundwater Flow, Seepage Velocity, Travel Time)
Flow of water through soil or rock from its hydraulic conductivity, the head difference and the path length, with the real seepage velocity and the time a tracer needs.
Results
The dashed line marks the value you entered.
What this tool does
Henry Darcy found in 1856 that flow through sand is proportional to the head loss and inversely proportional to the length, and the constant is the hydraulic conductivity K. The Darcy flux is the flow divided by the whole section, but water actually moves only through the pores, so the true seepage velocity is faster by the effective porosity: a flux of 0.2 m/day in a soil with 25 % effective porosity means water that moves 0.8 m/day. The law holds for slow, smooth flow, which suits sands and silts but not open fractures or coarse gravel under steep gradients.
Formula
Q = K A Δh ÷ L · i = Δh ÷ L · q = K i · v = q ÷ nₑ · t = L ÷ v
Variables
| Symbol | Meaning | Unit |
|---|---|---|
k | Hydraulic conductivity K | m/day |
a | Cross-section area of the flow | m² |
dh | Head difference between the two ends | m |
l | Length of the flow path | m |
ne | Effective porosity | % |
Q | Flow through the section | m³/day |
I | Hydraulic gradient | — |
QQ | Darcy flux (specific discharge) | m/day |
V | Seepage velocity (what a tracer moves at) | m/day |
T | Travel time along the whole path | day |
Worked example
- Hydraulic conductivity K10 m/day
- Cross-section area of the flow50 m²
- Head difference between the two ends2 m
- Length of the flow path100 m
- Effective porosity25 %
- Flow through the section10.00 m³/day
- Hydraulic gradient0.0200
- Darcy flux (specific discharge)0.200 m/day
- Seepage velocity (what a tracer moves at)0.800 m/day
- Travel time along the whole path125.0 day
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.