Hydraulic Gradient Calculator

Determine the change in the head with respect to the distance using this hydraulic gradient calculator.

Hydraulic gradient0.042 m of head over 50 m of path — a dimensionless slope

Flow rate0.0004 m³/s34.56 m³ a day, 0.4 litres a second

Darcy velocity4 µm/s126.144 m a year — this is a FLUX per unit total area, not the speed of any actual water

Hydraulic conductivity100 µm/sFine sand

Seepage (pore) velocity13.3333 µm/s420.48 m a year — the Darcy velocity divided by porosity, and the speed a tracer or contaminant actually travels

Travel time along the path0.1189 yearsusing the seepage velocity — using the Darcy velocity instead would overstate it by a factor of 3.33

Effective porosity30%water only moves through the connected pore space, so the real velocity is higher than the flux suggests

Range across the soil table1e+9×gravel to granite spans about nine orders of magnitude, so identifying the material correctly matters far more than measuring the gradient precisely

Through clean gravel0.04 m³/sk = 1e-2 m/s

Through clay4.0e-9 m³/sk = 1e-9 m/s

Darcy's law assumes laminar flowvalid at low Reynolds numberit breaks down in coarse gravel at steep gradients, where flow becomes turbulent and discharge no longer rises linearly with gradient

The formula

Q = kA(dh ÷ dL); seepage velocity = Darcy velocity ÷ porosity

Darcy velocity is not a velocity

Darcy's law gives a flux — volume per unit total cross-sectional area — and dividing it by area gives something with the units of velocity that is not the speed of any water. The actual water moves only through the pore space, so its speed is the Darcy velocity divided by the effective porosity, typically three to five times higher.

That distinction decides contamination timescales. A plume travels at the seepage velocity, so estimating arrival times from the Darcy velocity overstates them by the reciprocal of porosity — a factor of three or more, which is the difference between a decade and thirty years.

Hydraulic conductivity spans roughly nine orders of magnitude from clean gravel to unfractured granite. Nothing else in the calculation comes close to that range, so identifying the material correctly dominates every other source of error. A gradient measured to 1% is wasted effort if the soil class is wrong.

The law assumes laminar flow, and it holds over an extraordinary range because groundwater moves so slowly. It does break down in coarse gravel under steep gradients, where flow turns turbulent and discharge stops rising linearly with gradient.