Seepage Velocity Calculator
Enter hydraulic conductivity, hydraulic gradient and effective porosity to compute seepage velocity v=K·i/n. K=1e-5, i=0.01, n=0.3 → v=3.33e-7 m/s. Groundwater actually moves far slower than Darcy flux.
Input Data
Results
At a glance:Seepage velocity (interstitial velocity) v is the true average speed of groundwater moving through the pores of a porous medium. Darcy's law gives the specific discharge (Darcy flux) q=K·i — the average flow over the entire cross-section including the solid skeleton. But water only travels through the voids, so the actual speed is v=q/n=K·i/n, where K is hydraulic conductivity (m/s, a property combining the medium's permeability and the fluid viscosity), i the hydraulic gradient (dimensionless, Δh/ΔL), and n the effective porosity (0–1, the fraction of voids actually connected for flow). Meaning: the actual water speed is much higher than the Darcy flux because the same flow is squeezed into the pore space. Example: K=0.001 m/s, i=0.01, n=0.3 → q=K·i=1e-5 m/s (Darcy flux), v=q/n=3.33e-5 m/s — the water moves 30× faster than the Darcy flux. History: Darcy discovered the linear law in 1856 (Dijon fountain); later work separated Darcy flux from real velocity via porosity. Uses: (1) predict groundwater flow path and transit time (a contaminant plume moves at v, not q); (2) contaminant transport (advection term); (3) well-field and recharge design; (4) seepage control of dams/foundations; (5) landfill liner and barrier design. Notes: (1) n is the effective porosity, not total porosity (isolated pores do not count); (2) K must be at the actual temperature and medium (clay very low, gravel high); (3) i is dimensionless (Δh/ΔL); (4) this is the average pore speed; in heterogeneous media local speed varies; (5) keep consistent units (K, v in m/s). In short, seepage velocity v=K·i/n is the real groundwater speed — always larger than the Darcy flux — the basis of contaminant travel-time estimates.
Formula
Darcy flux: q = K·i
Seepage velocity: v = q / n = K·i / n
K hydraulic conductivity (m/s), i gradient (dimless), n effective porosity (0–1)
$$q = K\,i, \quad v = \frac{q}{n} = \frac{K\,i}{n}$$How to Use
- Enter hydraulic conductivity K (m/s; sand 1e-4–1e-3).
- Enter hydraulic gradient i (Δh/ΔL, dimensionless).
- Enter effective porosity n (sand 0.3, clay 0.05).
- The tool computes Darcy flux q and real seepage velocity v.
Case Studies
Contaminant travel time
Sand layer K=1e-4 m/s, i=0.005, n=0.3 → q=5e-7, v=1.67e-6 m/s.
A 100 m plume reaches a well in 100/1.67e-6≈6.0e7 s ≈1.9 years (use v, not q).
If you wrongly used q, you would over-estimate the time 3× (n=0.3).
Clay barrier vs sand
Clay K=1e-9, i=0.01, n=0.05 → v=1e-9×0.01/0.05=2e-10 m/s.
A 1 m barrier delays seepage ~1.6e9 s ≈50 years — clay is an excellent liner.
Sand K=1e-4 same i,n → v=3.3e-6 m/s, 1 m passes in ~3.4 days — sand is leaky.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.