Question

a filter medium has:

\\(d_{10} = 0.30\text{ mm}\\)

\\(d_{60} = 0.42\text{ mm}\\)

the medium is most likely:

unsuitable for any filter
highly uniform
poorly graded
coarser than all rsf media

Explanation:

🆕 New Concept Discovered: Uniformity Coefficient
Measuring how uniform a granular material is.

Step 1: Calculate the Uniformity Coefficient

The uniformity coefficient \( U_c \) (or \( C_u \)) is a measure of how uniform the particle sizes are in a granular medium. It is calculated using the formula:

$$ U_c = \frac{D_{60}}{D_{10}} $$

Given:

• \( D_{10} = 0.30\text{ mm} \)
• \( D_{60} = 0.42\text{ mm} \)

$$ U_c = \frac{0.42}{0.30} = 1.4 $$

Step 2: Interpret the Uniformity Coefficient

A uniformity coefficient \( U_c \) close to \( 1.0 \) indicates that the particles are nearly all the same size (highly uniform).

• In water treatment filtration (such as rapid sand filters), a filter medium is considered highly uniform if \( U_c \) is typically less than \( 1.5 \) (often aiming for \( 1.3 \) to \( 1.5 \)).
• Since \( U_c = 1.4 \), the filter medium is highly uniform.

Answer:

Highly uniform