Question

The inside diameter of a sampler tube is 50 mm. The inside diameter of the cutting edge is kept such that the Inside Clearance Ratio (ICR) is 1.0% to minimize the friction on the sample as the sampler tube enters into the soil. The inside diameter (in mm) of the cutting edge is _________ (round off to two decimal places).

Hint:

The inside clearance ratio is used to determine the optimum size for cutting edges to reduce friction during sample collection.

Answer 1

Correct Answer: 49.49

The Inside Clearance Ratio (ICR) is the difference between the inside diameter of the sampler tube and the cutting edge, expressed as a percentage of the sampler tube's inside diameter: \[ ICR = \frac{d_{\text{tube}} - d_{\text{cutting}}}{d_{\text{tube}}} \times 100 \] Where:
- \( d_{\text{tube}} = 50 \ \text{mm} \) (inside diameter of the sampler tube),
- \( d_{\text{cutting}} \) is the inside diameter of the cutting edge.
Substituting the given ICR value of 1.0%: \[ 1.0 = \frac{50 - d_{\text{cutting}}}{50} \times 100 \] Solving for \( d_{\text{cutting}} \): \[ 1.0 = \frac{50 - d_{\text{cutting}}}{0.5} \] \[ 50 - d_{\text{cutting}} = 0.5 \] \[ d_{\text{cutting}} = 49.5 \ \text{mm} \] Thus, the inside diameter of the cutting edge is: \[ \boxed{49.5~\text{mm}} \]