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Rispri LabsENGINEERING A CIRCULAR FUTURE

Free tool · Soil and groundwater

Hydraulic Gradient Calculator

Hydraulic gradient i = (h₁ − h₂) ÷ L, the drop in hydraulic head over the distance between two points. Darcy flux q = K × i, and the actual seepage velocity v = q ÷ effective porosity. A 1.5 m head drop over 250 m is a gradient of 0.006.

Your inputs

Results update as you type. Example values are filled in.

m

Water level elevation, not depth to water.

m
m
m/day

Gravel 100 to 1,000, sand 1 to 50, silt 0.01 to 1, clay under 0.001.

Sand 0.2 to 0.35, silt 0.1 to 0.2, fractured rock 0.01 to 0.05.

How to use this calculator

  1. Enter water level elevations (heads) at two wells on the same flow line.
  2. Enter the distance between them.
  3. Add K and effective porosity to get flow velocity and travel time.

How do you calculate hydraulic gradient?

i = (h₁ − h₂) ÷ L

q = K × i (Darcy's law)

v = q ÷ ne

Travel time = L ÷ v

Worked example

With hydraulic head at point 1 (up gradient) 106 m, hydraulic head at point 2 104 m, distance between the points 250 m, hydraulic conductivity k 10 m/day, effective porosity 0.25:

Hydraulic gradient: 0.006 m/m

The calculator also gives gradient 6 m per km; darcy flux (specific discharge) 0.06 m/day; seepage (average linear) velocity 0.24 m/day.

Assumptions and limits

  • Assumes the two points lie along the flow direction. With three or more wells, contour the heads first (three point method).
  • Seepage velocity is an average; contaminants also spread by dispersion and may be retarded by sorption.

Frequently asked questions

What is a typical hydraulic gradient for groundwater?

Regional gradients in alluvial aquifers are often 0.0001 to 0.005. Near pumping wells or hillslopes they can exceed 0.01.

What is the difference between Darcy flux and seepage velocity?

Darcy flux is flow per unit total area. Water only moves through pores, so the real speed (seepage velocity) is the flux divided by effective porosity, and is always higher.

Is hydraulic gradient dimensionless?

Yes. It is metres of head per metre of distance, often written m/m or as a decimal.

References

  • Freeze and Cherry (1979). Groundwater. Prentice Hall
  • Todd and Mays (2005). Groundwater Hydrology, 3rd ed.
  • CGWB, Aquifer Mapping and Management guidelines

Built and maintained by the Rispri Labs engineering team. Last updated .