In a constant head permeameter with cross-section area of 10 cm², when the flow was taking place under a hydraulic gradient of 0.5, the amount of water collected in 90 seconds is 900 cm³. The permeability of the soil is
- A0.002 cm/sec
- B0.02 cm/sec
- C0.2 cm/sec
- D2.0 cm/secCorrect
Solution
Concept
Darcy's law applied to constant head test
Formula
Q = k · i · A, k = Q / (i · A · t) = V / (i · A · t)
Step-by-step solution
1. V = 900 cm³, t = 90 s, so Q = 10 cm³/s. 2. A = 10 cm², i = 0.5. 3. k = Q / (i A) = 10 / (0.5 × 10) = 2.0 cm/s.
Explanation
In the constant head test the discharge is measured for a known head. Darcy's law gives k = Q/(iA). With Q = 10 cm³/s, A = 10 cm² and i = 0.5, k = 2 cm/s.
Shortcut
k = V / (i · A · t): 900 / (0.5 × 10 × 90) = 2.
Common mistake
Using 900 cm³ as discharge without dividing by time.
Correct answer: D) 2.0 cm/sec