# Extension of the Dupuit–Forchheimer Model for Non-Hydrostatic Flows in Unconfined Aquifers

## Abstract

**:**

## 1. Introduction

## 2. Governing Equations

## 3. Seepage Flows with a Phreatic Surface

#### 3.1. Rectangular Profile Dam

#### 3.2. Trapezoidal Profile Dam

## 4. Recharge-Induced Curvilinear Groundwater Flows

#### 4.1. Unconfined Flow over Sloping Planar Bedrock

#### 4.2. Unconfined Flow over Curved Bedrock

## 5. Unconfined Flow to Drains

## 6. Concluding Remarks

## Acknowledgments

## Conflicts of Interest

## Appendix A

## References

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**Figure 1.**Definition sketch, showing a Cartesian coordinate system for a non-hydrostatic groundwater flow.

**Figure 2.**Definition sketch for seepage flow through a dam with vertical upstream and downstream faces.

**Figure 5.**Unconfined seepage flows through homogeneous trapezoidal profile dams: (

**a**) an asymmetrical dam with a vertical upstream face and a 45° downstream face slope ($q/K{H}_{u}=0.47$); and (

**b**) a symmetrical dam with faces sloping at 45° ($q/K{H}_{u}=0.20$).

**Figure 6.**Recharge-induced unconfined groundwater flows over planar bedrock: (

**a**) horizontal bedrock; and (

**b**) bedrock slope = 2.03°.

**Figure 7.**Recharge-induced unconfined groundwater flows in a sloping aquifer (bedrock slope = 21.8°).

**Figure 8.**Recharge-induced curvilinear groundwater flows with a phreatic surface: (

**a**) $P/K=0.0740$; and (

**b**) $P/K=0.0274$.

**Figure 10.**Section of a saturated aquifer drained by a toe drain overlying horizontal impermeable bedrock at the downstream end ($j=m$).

**Figure 11.**(

**a**) Phreatic-surface profile for unconfined flow to a wide flat drain overlying impermeable bedrock. The corresponding vertical distributions of the piezometric head of the flow at various locations: (

**b**) $x/L=0.25$; (

**c**) $x/L=0.50$; and (

**d**) $x/L=0.75$.

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Zerihun, Y.T.
Extension of the Dupuit–Forchheimer Model for Non-Hydrostatic Flows in Unconfined Aquifers. *Fluids* **2018**, *3*, 42.
https://doi.org/10.3390/fluids3020042

**AMA Style**

Zerihun YT.
Extension of the Dupuit–Forchheimer Model for Non-Hydrostatic Flows in Unconfined Aquifers. *Fluids*. 2018; 3(2):42.
https://doi.org/10.3390/fluids3020042

**Chicago/Turabian Style**

Zerihun, Yebegaeshet T.
2018. "Extension of the Dupuit–Forchheimer Model for Non-Hydrostatic Flows in Unconfined Aquifers" *Fluids* 3, no. 2: 42.
https://doi.org/10.3390/fluids3020042