Question:
In deriving the equations for confined and unconfined aquifers, which of the following assumptions are used?
A. Change in the drawdown with respect to time is negligible.
B. The well penetrates the entire aquifer.
C. The flow is vertical and uniform everywhere in the horizontal section.
D. The flow is laminar.
Choose the correct answer from the options given below:
In deriving the equations for confined and unconfined aquifers, which of the following assumptions are used?
A. Change in the drawdown with respect to time is negligible.
B. The well penetrates the entire aquifer.
C. The flow is vertical and uniform everywhere in the horizontal section.
D. The flow is laminar.
Choose the correct answer from the options given below:
A. Change in the drawdown with respect to time is negligible.
B. The well penetrates the entire aquifer.
C. The flow is vertical and uniform everywhere in the horizontal section.
D. The flow is laminar.
Choose the correct answer from the options given below:
Show Hint
The key Dupuit-Thiem assumptions are: 1. Steady-state flow (\(\Delta h/\Delta t = 0\)). 2. Aquifer is homogeneous and isotropic. 3. Flow is horizontal (radial). 4. Darcy's Law is valid (laminar flow). 5. The well is fully penetrating.
Updated On: Sep 25, 2025
- A, B and D only
- A,B,C only
- A,B,C,D
- B,C and D only
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The Correct Option is B
Solution and Explanation
Step 1: Recall the Dupuit-Thiem assumptions for well hydraulics.
These are a set of simplifying assumptions used to derive the steady-state equations for flow to a well.
Step 2: Evaluate each statement against the standard assumptions.
- A. Change in the drawdown with respect to time is negligible: This is the definition of steady-state flow, where conditions are not changing over time. This assumption is used for the Thiem equation. It is a valid assumption.
- B. The well penetrates the entire aquifer: This is the assumption of a "fully penetrating" well, which simplifies the flow to being purely radial. It is a standard assumption.
- C. The flow is vertical and uniform everywhere in the horizontal section: This is incorrect. The Dupuit assumption states that the flow is horizontal and that the hydraulic gradient is equal to the slope of the water table and is constant with depth. Flow is not vertical. This statement is false.
- D. The flow is laminar: This means Darcy's Law is valid, which is a fundamental requirement for the derivation of these equations. This is a valid assumption.
Step 3: Conclude the correct combination.
Statements A, B, and D are standard assumptions used in deriving steady-state well equations. Statement C incorrectly describes the flow.
Therefore, the correct combination is A, B, and D.
These are a set of simplifying assumptions used to derive the steady-state equations for flow to a well.
Step 2: Evaluate each statement against the standard assumptions.
- A. Change in the drawdown with respect to time is negligible: This is the definition of steady-state flow, where conditions are not changing over time. This assumption is used for the Thiem equation. It is a valid assumption.
- B. The well penetrates the entire aquifer: This is the assumption of a "fully penetrating" well, which simplifies the flow to being purely radial. It is a standard assumption.
- C. The flow is vertical and uniform everywhere in the horizontal section: This is incorrect. The Dupuit assumption states that the flow is horizontal and that the hydraulic gradient is equal to the slope of the water table and is constant with depth. Flow is not vertical. This statement is false.
- D. The flow is laminar: This means Darcy's Law is valid, which is a fundamental requirement for the derivation of these equations. This is a valid assumption.
Step 3: Conclude the correct combination.
Statements A, B, and D are standard assumptions used in deriving steady-state well equations. Statement C incorrectly describes the flow.
Therefore, the correct combination is A, B, and D.
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