Unconfined Aquifer Well Design Calculator

Flow rate equals pi K times h1 squared minus h2 squared over ln r1 over r2

Solution

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How It Works

When you pump water from an unconfined (water-table) aquifer, the water surface forms a cone of depression around the well. The Dupuit equation calculates steady-state flow rate from the hydraulic conductivity, the water levels at two observation points, and their distances from the well. It assumes horizontal flow and a homogeneous aquifer.

You can rearrange the equation to solve for any of its six variables: flow rate Q, permeability K, head at either observation point (h₁ or h₂), and distance from the well at either point (r₁ or r₂).

Example Problem

An unconfined aquifer has K = 12 m/day. Observation wells at r₁ = 100 m and r₂ = 50 m show water levels h₁ = 20 m and h₂ = 18 m. What is the pumping rate?

  1. Q = π × 12 × (20² − 18²) / ln(100/50)
  2. Q = π × 12 × (400 − 324) / 0.693
  3. Q = π × 12 × 76 / 0.693 ≈ 4,134 m³/day

Frequently Asked Questions

What is the Dupuit equation for unconfined aquifers?

The Dupuit equation calculates steady-state well flow as Q = πK(h₁² − h₂²) / ln(r₁/r₂). It assumes the aquifer is homogeneous, flow is horizontal, and the well fully penetrates the saturated zone.

What is a cone of depression?

A cone of depression is the funnel-shaped drop in the water table around a pumping well. Its shape depends on pumping rate, aquifer permeability, and distance from the well. Observation wells at different radii measure the cone's profile.

How do I determine aquifer permeability from a pump test?

Measure water levels at two or more observation wells during steady-state pumping and record their distances from the well. Plug Q, h₁, h₂, r₁, and r₂ into the Dupuit equation and solve for K. Field values typically range from 1 to 100 m/day for productive aquifers.

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