Select hydraulic conductivity, hydraulic gradient or Darcy flux to solve, then enter the two known values in metric or imperial units. Use head loss along the chosen flow direction, so q = k × i; a signed flux and gradient share their sign.
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Coefficient Of Permeability Formula
The calculator uses Darcy’s law for saturated laminar flow through a representative porous medium. Here i is head loss divided by length along the chosen direction (−dh/dl), so q = k × i. Darcy flux is Q/A, with velocity units; it is not pore-water velocity. Hydraulic conductivity depends on both the medium and fluid and differs from intrinsic permeability, which has area units.
- q = Darcy flux, or amount of water per unit area per unit time, equal to Q/A
- k = coefficient of permeability, also called hydraulic conductivity
- i = hydraulic gradient, equal to Δh/L
- Δh = difference in hydraulic head
- L = flow length over which the head loss occurs
If you enter hydraulic gradient and coefficient of permeability, the calculator finds Darcy flux using q = k × i.
If you enter Darcy flux and hydraulic gradient, it finds coefficient of permeability using k = q / i.
If you enter Darcy flux and coefficient of permeability, it finds hydraulic gradient using i = q / k.
The hydraulic gradient is dimensionless, so m/m and ft/ft are numerically equivalent. The calculator converts permeability and Darcy flux between m/s and ft/s as needed.
Published Hydraulic Conductivity Reference Ranges
Hydraulic conductivity depends on material structure, fluid and test conditions. The historical reference ranges below come from USGS Louisiana Technical Report 49, Table 3, converted from ft/day to m/s. They are illustrative, not universal soil values or substitutes for site-specific tests.
| Material | Reported k range, m/s | Drainage behavior |
|---|---|---|
| Gravel | 1.0583 × 10-3 to 1.0583 × 10-2 | Very high permeability |
| Fine to coarse sand | 1.0583 × 10-5 to 1.0583 × 10-3 | Drains readily |
| Sand and gravel mixtures | 7.0556 × 10-5 to 1.0583 × 10-3 | Depends on grading and conditions |
| Silt | 2.1167 × 10-9 to 3.175 × 10-6 | Low permeability |
| Deep clay beds | 1.0583 × 10-13 to 1.0583 × 10-7 | Very low permeability |
Unit Relationships Used For Darcy Flux
| Quantity | Calculator unit | Equivalent base meaning |
|---|---|---|
| Hydraulic gradient | m/m or ft/ft | Dimensionless ratio |
| Coefficient of permeability | m/s or ft/s | Hydraulic conductivity as a velocity |
| Darcy flux, Q/A | m³/(s·m²) or ft³/(s·ft²) | Reduces to m/s or ft/s |
| Length conversion | 1 ft/s | 0.3048 m/s |
Example Calculations
Example 1: Calculate Darcy flux
Suppose the coefficient of permeability is 0.0002 m/s and the hydraulic gradient is 0.75.
The Darcy flux is 0.00015 m³/(s·m²).
Example 2: Calculate coefficient of permeability
Suppose Darcy flux is 0.00006 m/s and the hydraulic gradient is 0.30.
The coefficient of permeability is 0.0002 m/s.
FAQ
Is coefficient of permeability the same as hydraulic conductivity?
In most soil mechanics and groundwater calculations, coefficient of permeability and hydraulic conductivity refer to the same quantity, usually represented by k. It describes how easily water can move through a porous material under a hydraulic gradient.
Why is hydraulic gradient unitless?
Hydraulic gradient is the head loss divided by flow length: i = Δh/L. Since both Δh and L are lengths, the units cancel. A gradient of 0.5 m/m is numerically the same as 0.5 ft/ft.
What is the difference between Darcy flux and actual seepage velocity?
Darcy flux is flow rate divided by total cross-sectional area, q = Q/A. Actual seepage velocity is usually higher because water only flows through pore spaces, not through the solid soil particles. To estimate seepage velocity, Darcy flux is commonly divided by effective porosity, the interconnected flowing pore fraction. The widget does not calculate this velocity.
