A sample of sand, 5 cm in diameter and 15 cm long, was prepared at a porosity of 60% in a constant-head apparatus. The total head was kept constant at 30 cm and the amount of water collected in 5 seconds was 40 cm³. The test temperature was 20°C. What is the seepage velocity ?
- A0·21 cm/s
- B0·98 cm/s
- C0·67 cm/sCorrect
- D0·45 cm/s
Solution
Concept
Discharge velocity and seepage velocity
Formula
v = Q / A; vs = v / n
Step-by-step solution
1. Q = 40 / 5 = 8 cm³/s; A = π × 5² / 4 = 19.63 cm². 2. Discharge velocity v = 8 / 19.63 = 0.407 cm/s. 3. Seepage velocity vs = v / n = 0.407 / 0.60 = 0.68 cm/s ≈ 0.67 cm/s.
Explanation
The water actually flows only through the voids, so the seepage velocity is the discharge velocity divided by the porosity.
Why the other options are wrong
0.45 cm/s and 0.21 cm/s do not divide by the porosity correctly. 0.98 cm/s would need a porosity of about 0.42.
Shortcut
Seepage velocity = (Q/A)/n.
Common mistake
Reporting the discharge velocity 0.41 cm/s.
Correct answer: C) 0·67 cm/s