Dupuit Equation for Steady-State Flow to a Trench 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.

Variable Recharge:


where:

Q = discharge per unit thickness (m2/d)
K = hydraulic conductivity of aquifer (m/d)
h2, h1 = steady-state heads measured along flow path (m)
L = distance between steady-state head measurements (m)
R = net recharge (-ve for net evapotranspiration) (m/d)

Assumptions2:
  1. The aquifer is unconfined.
  2. The aquifer has an infinite areal extent.
  3. The trench is of infinite length (into the page).
  4. The aquifer is homogeneous, isotropic and of uniform thickness over the area influenced by the trench.
  5. Prior to trench dewatering, the water table is horizontal over the area influenced by the trench.
  6. The trench penetrates the entire saturated thickness of the aquifer.
  7. The flow to the trench 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 trench (cross-sectional flow).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.