Dupuit Equation for Steady-State Flow to a Well in an Unconfined Aquifer1

1Dupuit, J., Etudes theoriques et pratiques sur le mouvement des eaux dans les canaux decouverts et a travers les terrains permeables, 2eme edition; Dunot, Paris, 1863.

One piezometer:


where:

Q = well discharge rate (m3/d)
K = hydraulic conductivity of aquifer (m/d)
rw = radius of the pumping well (m)
r1 = distance from piezometer to the pumping well (m)
hw = steady-state head in the pumping well (m)
h1 = steady-state head in the piezometer (m)


Assumptions2:
  1. The aquifer is unconfined.
  2. The aquifer has an infinite areal extent.
  3. The aquifer is homogeneous, isotropic and of uniform thickness over the area influenced by the test.
  4. Prior to pumping, the piezometric surface is horizontal over the area that will be influenced by the test.
  5. The aquifer is pumped at a constant discharge rate.
  6. The well penetrates the entire saturated thickness of the aquifer.
  7. The gradient between the pumping well and monitoring wells is at steady-state.
  8. The velocity of flow is proportional to the tangent of the hydraulic gradient instead of the sine as it is in reality.1
  9. The flow is horizontal and uniform everywhere in a vertical section through the axis of the well.1


References:

1Dupuit, J., Etudes theoriques et pratiques sur le mouvement des eaux dans les canaux decouverts et a travers les terrains permeables, 2eme edition; Dunot, Paris, 1863.
2Kruseman, G.P. and N.A. de Ridder, Analysis and Evaluation of Pumping Test Data (Second Edition), Publication 47; International Institute for Land Reclamation and Improvement, Wageningen, 1994.