# Dupuit Equation for Steady-State Flow to a Trench in an Unconfined Aquifer (With Recharge)

Application: Geotechnics

## Summary

### Notes on Dupuit Equation for Steady-State Flow to a Trench in an Unconfined Aquifer (with Recharge)

- Select the required output, then set the other parameters to the required values.
- The Dupuit equation for horizontal flow can also be applied to flow to a river, but caution should be used when interpreting results as riverbed permeabilities can vary significantly from the surrounding aquifer material.
- The Dupuit equation for horizontal flow only applies if the water table in the aquifer and trench is constant.

For equations, assumptions and references see equations.

### Tool Parameters

Values displayed with a may be changed ... click on a value to display an entry form ... or use the arrows right of a value to select from a list.

### Tool Behaviour

This tool exhibits spreadsheet-like behaviour ... change a value and related values are re-calculated automatically.

### Dupuit Equation for Steady-State Flow to a Trench 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.

### Variable Recharge:

where:

*Q* = discharge per unit thickness (m^{2}/d)

*K* = hydraulic conductivity of aquifer (m/d)

*h _{2}*,

*h*= steady-state heads measured along flow path (m)

_{1}*L*= distance between steady-state head measurements (m)

*R*= net recharge (-ve for net evapotranspiration) (m/d)

### Assumptions^{2}:

- The aquifer is unconfined.
- The aquifer has an infinite areal extent.
- The trench is of infinite length (into the page).
- The aquifer is homogeneous, isotropic and of uniform thickness over the area influenced by the trench.
- Prior to trench dewatering, the water table is horizontal over the area influenced by the trench.
- The trench penetrates the entire saturated thickness of the aquifer.
- The flow to the trench 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 trench (cross-sectional flow).
^{1}

### References:

^{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.

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