A confined aquifer of thickness 5 m gives a steady discharge of 20 litre/sec through a well of 0.3 m radius. The height of water in the well dropped from 10 to 8 m after pumping. What is the coefficient of permeability when the radius of influence is taken as 300 m?
- A0.0001 × loge1000/π
- B0.101 × loge1000/π
- C0.011 × loge1000/π
- D0.001 × loge1000/πCorrect
Solution
Concept
Steady flow to a well in a confined aquifer
Formula
k = Q ln(R/r)/(2π b s)
Step-by-step solution
1. Q = 20 L/s = 0.02 m³/s, b = 5 m, s = 10 − 8 = 2 m, R/r = 300/0.3 = 1000. 2. k = 0.02 ln1000/(2π × 5 × 2) = 0.001 ln1000/π m/s.
Explanation
Thiem equation for a confined aquifer.
Why the other options are wrong
Other coefficients differ by factors of 10.
Shortcut
k = Q ln(R/r)/(2π b s).
Correct answer: D) 0.001 × log_e1000/π