Dupuit-Forchheimer Assumption: Flow Behavior
The Dupuit-Forchheimer theory provides a simplified approach to analyzing groundwater flow, especially towards subsurface drains. It relies on specific assumptions to make the complex flow patterns mathematically tractable.
Key Assumption Analysis
- Horizontal Streamlines: This is a fundamental assumption. It posits that the primary direction of groundwater flow towards the drain is horizontal. This simplification allows the hydraulic gradient driving the flow to be approximated based on the difference in water table elevation over the horizontal distance.
- Vertical Equipotential Lines: Correspondingly, equipotential lines (lines of constant hydraulic head) are assumed to be vertical.
- Negligible Vertical Flow: The assumption of horizontal streamlines implies that the vertical component of flow is negligible compared to the horizontal component.
- Homogeneous and Isotropic Medium: While often assumed for simplicity in application, the core assumption about the *flow behavior itself* relates to the directionality of streamlines. The theory works best in relatively homogeneous and isotropic conditions but is fundamentally about simplifying the flow geometry.
- Uniform Recharge: This relates to the input conditions (e.g., rainfall infiltration) and is not the primary assumption about the flow *path* or *behavior* within the medium as described by Dupuit-Forchheimer.
Conclusion on Flow Behavior
The assumption of horizontal streamlines is the most direct and defining characteristic of the Dupuit-Forchheimer model concerning the *behavior* of flow in the porous medium towards subsurface drains. This simplification is crucial for deriving the characteristic flow equations.
Important Questions from Groundwater Occurrence
An unconfined aquifer of areal extent $20 \text{ km} \times 20 \text{ km}$ has hydraulic conductivity of $4 \text{ m/day}$, porosity of $0.32$, and storage coefficient (specific yield) of $0.18$. If the initial saturated thickness of the aquifer is $30 \text{ m}$, and $4\times10^8 \text{ m}^3$ of water is extracted from the aquifer, then the decline in the saturated thickness is _____________ (rounded off to two decimal places) m.
An unconfined aquifer extends over an area of $1 \text{ km}^2$ and has hydraulic conductivity, total porosity and specific retention of $20 \text{ m per day}, 30\%$ and $10\%$, respectively. After pumping some groundwater from this aquifer, the water table dropped to a depth of $20 \text{ m}$ from the ground level. If the water table was initially at $14.5 \text{ m}$ below the ground level, the change in groundwater storage in million cubic meters would be_______
Match the following items between Column I and Column II with the most appropriate combinations:
Column I Column II P Properties of confined and semi- confined aquifers 1 Perched aquifer Q Property of an unconfined aquifer 2 Coefficient of storage R Property of semi-confined aquifer 3 Specific yield S A special case of an unconfined aquifer 4 Leakage factor A fully penetrating well is installed in a homogenous and isotropic confined aquifer. The aquifer has uniform thickness of 16 m and hydraulic conductivity of 25 m/d. Water is being pumped out from the well at a constant rate of $0.1 \text{ } m^3/s$ till steady state condition is reached. If a drawdown of 3.5 m is observed at a distance of 75 m from the well then the drawdown at a distance of 150 m from the well will be________ (in m, rounded off to two decimal places).
An underground hazardous waste storage tank is leaking. The contaminant concentration directly beneath the site is 0.5 mg/L. The contaminant is travelling at an effective rate of 0.4 m per day towards a water well which is 2 km away.
Assume that the degradation of the contaminant follows a first order reaction, and the initial concentration of the contaminant becomes half in 10 years.
In this case, the contaminant concentration expected at the well under steady state conditions is ________ mg/L (rounded off to two decimal places).
