Calculate the missing coefficient of permeability, hydraulic gradient, or Darcy flux from any two values in metric or imperial units.
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Coefficient Of Permeability Formula
The calculator uses Darcy’s law in flux form. Darcy flux is the amount of water flowing per unit area per unit time, so its units reduce to a velocity such as m/s or ft/s.
q = k*i
k = q/i
i = q/k
- 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.
Typical Coefficient Of Permeability Values
Permeability varies widely by soil type, density, grain size, and saturation conditions. The values below are broad reference ranges.
| Material | Typical k range, m/s | Drainage behavior |
|---|---|---|
| Gravel | 10-2 to 1 | Very high permeability |
| Clean sand | 10-5 to 10-2 | Drains readily |
| Silty sand | 10-7 to 10-5 | Moderate to low drainage |
| Silt | 10-9 to 10-7 | Low permeability |
| Clay | 10-11 to 10-9 | 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.
q = k*i
q = 0.0002*0.75 = 0.00015 m/s
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.
k = q/i
k = 0.00006/0.30 = 0.0002 m/s
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 porosity.
