Dupuit Equation for Unconfined Radial Flow

Reference

The Dupuit equation estimates steady pumping from an unconfined aquifer, where the water table itself is drawn down toward the well.

The equation

Q = πK (H² – hw²) / ln(R / rw)
  • H is the saturated thickness far from the well in meters
  • hw is the water depth at the well in meters
  • R is the radius of influence, rw the well radius, both in meters
  • K is hydraulic conductivity in meters per day

Worked example

A well of radius 0.2 meters in an aquifer with K of 8 meters per day, saturated thickness 20 meters, drawn down to 15 meters at the well with influence extending 300 meters, yields about 601 cubic meters per day.

When to use it

Good for steady state yield estimates when drawdown is a modest fraction of saturated thickness. The squared heads carry the water table geometry, but the result is sensitive to the poorly known radius of influence, so quote a range.

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