Question

Effective diameter of aquifer material is defined as the diameter of the grains such that x % of the grains are finer. x =

• A. 10
• B. 40
• C. 60
• D. 90

Hint:

Effective diameter is always $D_{10}$ ($10\%$ finer). Uniformity Coefficient $C_u = D_{60}/D_{10}$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Allen Hazen's classical particle size distribution parameter defines the effective grain diameter controlling permeability in porous granular media.
Key Formula or Approach:
\[ D_{10} = \text{Effective Grain Size (10\% finer by weight)} \]
\[ K = C \cdot (D_{10})^2 \quad \text{(Hazen's Hydraulic Conductivity Formula)} \]

Step 2: Detailed Explanation:
In hydrogeology, well screen design, and geotechnical engineering:
The effective size (or effective diameter) of a porous soil or aquifer material is universally denoted as \(D_{10}\).
This is defined as the sieve particle diameter such that exactly \(10\%\) of the soil particles by weight are smaller (finer) than this size, and \(90\%\) are coarser.
Hazen demonstrated that hydraulic permeability is primarily governed by this smallest 10% particle fraction.

Step 3: Final Answer:
Therefore, \(x = 10\), matching option (A).