Dupuit Equation for Steady-State Flow to a Well in an Unconfined Aquifer^{1}

^{1}Dupuit, 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 (m^{3}/d)

K= hydraulic conductivity of aquifer (m/d)

r= radius of the pumping well (m)_{w}

r= distance from piezometer to the pumping well (m)_{1}

h_{w}= steady-state head in the pumping well (m)

h_{1}= steady-state head in the piezometer (m)

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

^{1}Dupuit, 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.

^{2}Kruseman, 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.