Question

From a sieve analysis test on a soil sample, the mean size of particles observed is 1 mm. The Lacey’s silt factor is

• A. 1.76
• B. 17.6
• C. 176
• D. 0.176

Hint:

Lacey’s silt factor is a key parameter in irrigation channel design, reflecting the soil’s grain size. The formula \( f = 1.76 \sqrt{d \) (where \( d \) is in mm) is empirical and widely used to estimate the silt factor for alluvial soils.

Answer 1

The Correct Option is A

Step 1: Identify the given data.
The mean particle size from a sieve analysis test is 1 mm. We need to find the Lacey’s silt factor (\( f \)). The options are:
(1) 1.76
(2) 17.6
(3) 176
(4) 0.176
Step 2: Recall the concept of Lacey’s silt factor.
Lacey’s silt factor (\( f \)) is used in the design of irrigation channels (Lacey’s regime theory) to account for the silt-carrying capacity of the flow. It depends on the mean particle size of the soil and is given by the empirical formula:
\[ f = 1.76 \sqrt{d} \] Where:
\( d \): Mean particle size (in mm)
\( f \): Lacey’s silt factor (dimensionless)
Step 3: Substitute the given value and calculate the silt factor.
The mean particle size is \( d = 1 \, \text{mm} \). Substituting into the formula:
\[ f = 1.76 \sqrt{1} = 1.76 \]
Step 4: Verify the result.
Lacey’s silt factor typically ranges from 0.5 to 2 for most soils:
Fine silt: \( f \approx 0.5 \) to 0.8
Medium sand: \( f \approx 1.0 \) to 1.5
Coarse sand: \( f \approx 1.5 \) to 2.0
A particle size of 1 mm corresponds to coarse sand, and \( f = 1.76 \) fits within the expected range.
Step 5: Select the correct option.
The Lacey’s silt factor is 1.76, which matches option (1).
\[ \boxed{1.76} \]