Darcy's Law Groundwater Flow Calculator

How it works

Q = K × i × A, i = (h₁ − h₂) ÷ L; Darcy flux q = K × i; seepage velocity v = q ÷ nₑ; travel time = distance ÷ v

Darcy's 1856 sand-column experiments showed that groundwater discharge is proportional to the hydraulic gradient (head loss per unit distance) and the cross-sectional area, with a proportionality constant — hydraulic conductivity — that captures how easily the porous medium passes water. The Darcy flux q is a volume rate per unit area and understates how fast water actually moves, because flow happens only through the connected pore space; dividing by effective porosity gives the average linear velocity that governs how long a contaminant plume or tracer takes to reach a well or river. Conductivity ranges over thirteen orders of magnitude between clay and gravel, so the gradient and area are usually known far better than K, and any answer inherits K's uncertainty.

Worked example

A sand aquifer with K = 1×10⁻⁴ m/s, a 2 m head drop over 400 m (i = 0.005), 200 m wide and 12 m thick passes 1.2 L/s — 104 m³/day. The Darcy flux is 0.043 m/day, but with an effective porosity of 0.25 water actually travels 0.17 m/day, about 63 m a year, so a plume needs roughly 16 years to move 1 km.

Frequently asked questions