Darcy's Law Calculator

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Choose which unknown Darcy's Law should solve for. The other three fields become inputs.
Unit for hydraulic conductivity k.
Unit for cross-sectional area A.
Unit for volumetric flow rate Q.
Unit for head difference and flow path length (used to compute gradient).
The ease with which water moves through the porous medium. Gravel ~0.01 m/s, fine sand ~0.0001 m/s, clay ~1e-10 m/s.
Hydraulic gradient is the head drop per unit length (dimensionless). You can enter it directly or let the calculator compute it from head difference and flow path length.
Head drop per unit length, dimensionless. Example: 1 m drop over 100 m = 0.01.
Difference in hydraulic head between the inlet and outlet.
Length of the flow path through the porous medium.
The face area of the porous medium through which flow occurs, perpendicular to flow.
Flow rate (Q)Moderate (fine sand)
0.000001

Volumetric discharge through the porous medium (Darcy's Law result)

Hydraulic conductivity (k)0.0001
Hydraulic gradient (i)0.01
Cross-sectional area (A)1
Darcy velocity (q)0.000001
Flow rate (Q)0.000001
Darcy velocity (q)0.000001

Darcy's Law gives a flow rate of 1.000e-6 m3/s.

  • The Darcy velocity (specific discharge) is 1.000e-6 m/s, which is the apparent average seepage velocity through the total cross-section.
  • A conductivity of 1.000e-4 m/s is typical of fine sand.
  • Darcy's Law applies in laminar (low Reynolds number) flow, which covers most groundwater and slow seepage scenarios. It does not hold for turbulent flow in very coarse gravel or fractured rock.

Next stepTo find pore velocity (the actual speed of water molecules), divide Darcy velocity by the porosity of the medium (typically 0.3-0.5 for sands).

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