Question

A 60 cm diameter well completely penetrates a confined aquifer of permeability \( 5 \times 10^{-4} \, {m/s} \). The length of the strainer (spanning the entire thickness of the aquifer) is 10 m. The drawdown at the well under steady state pumping is 1.0 m. Assume that the radius of influence for this pumping is 300 m.
The discharge from the well (in litres per minute) is ......... (round off to the nearest integer).

Hint:

When calculating discharge from a well in a confined aquifer, ensure to account for the radius of influence, permeability, thickness of the aquifer, and the well radius. Always convert the discharge to the desired units, such as litres per minute.

Answer 1

We use the formula for discharge from a well in a confined aquifer: \[ Q = \frac{2 \pi k b s_w \log_e \left( \frac{R}{r_w} \right)}{ \log_e \left( \frac{R}{r_w} \right)} \] Where: - \( k = 5 \times 10^{-4} \, {m/s} \) (permeability)
- \( b = 10 \, {m} \) (thickness of the aquifer)
- \( R = 300 \, {m} \) (radius of influence)
- \( r_w = 0.3 \, {m} \) (radius of well)
- \( s_w = 1 \, {m} \) (drawdown) Substituting the values: \[ Q = \frac{2 \pi \times 5 \times 10^{-4} \times 10 \times 1 \times \log_e \left( \frac{300}{0.3} \right)}{\log_e \left( \frac{300}{0.3} \right)} = 4.54 \times 10^{-3} \, {m}^3/{s} \] Convert to litres per minute: \[ Q = 4.54 \times 10^{-3} \times 60 \, {lit/min} = 272.87 \, {lit/min} \approx 273 \, {lit/min} \] Thus, the discharge from the well is \( 273 \, {lit/min} \).