Q25: A loose uniform sand with rounded grains has effective grains size of 0.05 cm. Co-efficient of permeability of the sand is:
📝 Detailed Explanation
Allen Hazen’s empirical formula provides a quick, practical estimate of a coarse-grained soil’s permeability directly from its effective size (D10), without needing a full permeability test.
Given: effective size D10 = 0.05 cm (loose, uniform, rounded sand grains).
✅ Why “0.25 cm/sec” Is Correct
Using Allen Hazen’s formula, K = 100·D10² (with D10 in cm, K in cm/s): K = 100 × (0.05)² = 100 × 0.0025 = 0.25 cm/sec.
🔑 Key Point
Hazen’s formula requires D10 to be SQUARED, not used directly — a very small effective size like 0.05 cm becomes an even smaller number once squared (0.0025), which is easy to get wrong under time pressure.
💡 Key Concepts for Students
- See Q36 for the general form of Hazen’s formula, K = C·D10², with C given as a constant typically between 100 and 150 depending on soil uniformity.
- Hazen’s formula is only valid for a specific range of soil particle sizes (roughly 0.1 mm to 3 mm, i.e., 0.01 cm to 0.3 cm) — outside that range it becomes unreliable.
- D10 (effective size) is the same quantity defined and used extensively in the Classification of Soil topic (see D10/D30/D60 and Cu/Cc calculations there).
- Hazen’s formula is an empirical approximation, not a first-principles derivation — useful for quick estimates, but a full permeability test (constant/falling head) remains more accurate for design purposes.
📚 Going Deeper: Allen Hazen's Empirical Permeability Formula
Allen Hazen’s formula offers a convenient shortcut for estimating a coarse-grained soil’s permeability directly from a single grain-size parameter — the effective size, D10 — without needing to run a full constant-head or falling-head laboratory test.
K = C · (D10)²
| Symbol | Meaning | Typical Value/Range |
|---|---|---|
| K | Coefficient of permeability | Result, in cm/s (when D10 is in cm) |
| D10 | Effective size (particle size at 10% finer) | Valid for roughly 0.01 cm to 0.3 cm (0.1 mm to 3 mm) |
| C | Empirical constant | Typically 100 to 150, depending on soil uniformity |
Because K depends on the SQUARE of D10, this formula is extremely sensitive to the effective size — a soil with twice the D10 of another will, all else equal, have roughly four times the permeability, according to this relationship. This strong sensitivity is a big part of why particle size (specifically the finer end of the distribution, captured by D10) dominates permeability so heavily compared to other grain-size measures like D50 or D60.