Based on Allen-Hazen's experiments, the co-efficient of permeability k (cm/s) is related to the effective size of soil D₁₀ (cm) as _____ (where C is a constant with a value between 100 and 150).
- Ak = C / D₁₀²
- Bk = D₁₀ / C²
- Ck = C D₁₀²Correct
- Dk = C² D₁₀
Solution
Concept
For clean uniform sands, Hazen found k is proportional to the square of the effective size D10.
Formula
k = C D102 (k in cm/s, D10 in cm, C = 100 to 150)
Step-by-step solution
1. Hazen's formula is for clean, loose, uniform sands. 2. Permeability increases when pore size increases. 3. Pore size depends on the fine fraction, i.e. D10. 4. Hazen's relation: k = C D102, with C = 100 to 150 when k is in cm/s and D10 is in cm. 5. So the answer is (C).
Explanation
Allen Hazen showed that the permeability of clean sand depends mainly on its effective size D10. k varies with the square of D10, multiplied by a constant C. Bigger grains give bigger pores, so water flows more easily.
Why the other options are wrong
A: k would fall as grain size grows, which is wrong. B: Wrong power of D10, and C should not be in the denominator. D: k depends on D10 squared, not on C squared.
Shortcut
Bigger grains give more flow, so k = C × D102.
Common mistake
Using D10 in mm with C = 100 to 150; D10 must be in cm to get k in cm/s.
Correct answer: C) k = C D₁₀²