What it does
Groundwater moves slowly through the pores of sand, gravel and rock. Darcy’s law describes how fast: the flow is proportional to how permeable the ground is (the hydraulic conductivity K) and to how steeply the water table slopes (the hydraulic gradient i). This page puts the everyday groundwater sums in one place:
- Darcy flow: the flux q = K·i, the discharge through an area Q = K·i·A, the seepage velocity v = q ÷ ne at which the water really moves, and the travel time over a distance.
- Three-point problem: the gradient and the direction of flow from the water levels in three or more wells.
- Grain size: d10, d30 and d60 from a sieve curve, the uniformity and curvature coefficients, and a rough K from Hazen’s rule.
- Intrinsic permeability k, which belongs to the rock alone, from K and the water temperature.
How to use it
- In the Darcy flow card, type K and choose its unit, or pick the Hazen estimate from the grain-size card.
- Give the gradient as a head drop over a distance, or pick the result from the wells card.
- Add the flow area (aquifer thickness × width), the effective porosity and a travel distance.
- For the three-point problem, paste each well’s name, x (east), y (north) and head in metres. With more than three wells the tool fits the best plane and reports how well it fits.
- For grain size, paste or open sieve sizes in mm with the percent passing.
Worked example
All numbers are made up. A sand aquifer has K = 10 m/day and the water table drops 0.5 m over 250 m, a gradient of 0.002. With an effective porosity of 0.25, the Darcy flux is 0.02 m/day and the seepage velocity is 0.08 m/day. Water takes 17.1 years to travel 500 m. Through a 100 m² cross-section the discharge is 2 m³/day. At 10 °C that K means an intrinsic permeability of about 1.5 × 10⁻¹¹ m², or 15.5 darcy.
Three monitoring wells with heads of 25.40, 24.95 and 25.10 m give a gradient of 0.0015, with water flowing towards 71°, roughly east-north-east.
The example sieve curve gives d10 = 0.129 mm and Cu = 3.76. Hazen’s rule with C = 100 then gives K ≈ 14 m/day.
Good to know
- The seepage velocity is an average. Real water moves faster along the best paths, and dissolved substances can lag behind through sorption.
- Effective porosity is smaller than total porosity, especially in clay, where much of the water is held in place.
- Hazen’s rule is a quick check for clean sand, not a substitute for a pumping or slug test.
FAQ
Why is the gradient direction given as a bearing? It is the compass direction the water flows, measured clockwise from north, straight down the slope of the water table.
Can I use feet? Choose ft/day for K. Lengths on this page are in metres.
Where the numbers come from
- Darcy's law, seepage velocity, the three-point gradient problem and grain-size statistics (d10, Cu, Cc): standard hydrogeology and soil mechanics, written by fibub from the definitions.
- Hazen's rule K = C·d10² with C roughly 40 to 150 (cm/s, cm): general textbook usage; the tool labels it approximate and lets you set C.
- Water viscosity from the Vogel-type fit μ = 2.414 × 10⁻⁵ · 10^(247.8/(T − 140)) Pa·s and density from a common approximate formula: general engineering approximations.
- Example data are made up by fibub for illustration.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-08.