Question

Which of the following statements regarding well discharge are true?
A. It increases with drawdown
B. It increases with well diameter
C. It is affected by diameter but not drawdown
D. It decreases with drawdown
Choose the correct answer from the options given below:

• A. C only
• B. A and B only
• C. B and D only
• D. B and C only

Hint:

- Discharge is directly proportional to drawdown (\(Q \propto s\)).
- Discharge is logarithmically proportional to well radius (\(Q \propto 1/\ln(R/r_w)\)).
Therefore, increasing the drawdown is much more effective at increasing yield than digging a wider well.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Well discharge is the volume of water pumped from a well per unit of time.
In steady-state groundwater hydraulics, well discharge is modeled using Dupuit's equilibrium equation.
Key Formula or Approach:
For a confined aquifer under steady-state conditions, the discharge (\(Q\)) is given by: \[ Q = \frac{2\pi \cdot T \cdot s}{\ln(R/r_w)} \] where:
- \(T\) is the aquifer transmissivity.
- \(s\) is the drawdown (\(H - h_w\)).
- \(r_w\) is the radius (or diameter) of the well.
- \(R\) is the radius of influence of the well.

Step 2: Detailed Explanation:
Let us analyze each statement based on the discharge equation:
- Statement A and D:
Drawdown (\(s\)) is the drop in the water level inside the well during pumping.
Looking at the equation, discharge \(Q\) is directly proportional to drawdown \(s\).
Therefore, as you increase the drawdown by pumping harder, the discharge increases.
Thus, Statement A is correct, and Statement D is incorrect.
- Statement B:
The well radius (or diameter) \(r_w\) appears in the denominator as a logarithmic term (\(\ln(R/r_w)\)).
Increasing the well diameter decreases this denominator, which increases the discharge \(Q\).
However, because this is a logarithmic relationship, doubling the well diameter only increases the discharge by a small percentage (typically \(10%\) to \(15%\)).
Nevertheless, the physical trend is that discharge does increase with well diameter.
Thus, Statement B is correct.
- Statement C:
Since discharge is highly dependent on both well diameter and drawdown, this statement is incorrect.

Step 3: Final Answer:
The correct statements are A and B only.