If the inside diameters of the cutting edge and sample tube are 68 mm & 70 mm respectively and 76 mm & 74 mm are the outside diameters of the cutting edge and sample tube respectively, then outside clearance of the sampler is _______.
2.7%
Calculating Soil Sampler Outside Clearance
This question asks us to calculate the outside clearance percentage for a soil sampler given its dimensions. The outside clearance is an important factor in soil sampling as it affects the disturbance caused to the soil sample during collection.
Understanding Soil Sampler Clearance
Soil samplers have specific dimensions for the cutting edge and the sample tube. Clearance refers to the difference in diameters between these parts. There are two main types of clearance:
- Inside Clearance: This is the difference between the inside diameter of the sample tube and the inside diameter of the cutting edge. A small inside clearance helps in reducing friction between the soil sample and the tube.
- Outside Clearance: This is the difference between the outside diameter of the cutting edge and the outside diameter of the sample tube. Outside clearance allows the sampler barrel to follow the cutting shoe without excessive friction or compressing the soil on the outside.
Given Dimensions of the Soil Sampler
Let's list the given dimensions:
- Inside diameter of cutting edge (\(D_c\)) = 68 mm
- Inside diameter of sample tube (\(D_t\)) = 70 mm
- Outside diameter of cutting edge (\(D_{oc}\)) = 76 mm
- Outside diameter of sample tube (\(D_{ot}\)) = 74 mm
Formula for Outside Clearance
The formula to calculate the outside clearance percentage is given by:
\[ \text{Outside Clearance (%) } = \frac{\text{Outside diameter of cutting edge} - \text{Outside diameter of sample tube}}{\text{Outside diameter of sample tube}} \times 100\% \]
Or, using the symbols:
\[ \text{Outside Clearance (%) } = \frac{D_{oc} - D_{ot}}{D_{ot}} \times 100\% \]
Step-by-Step Calculation
Now, let's substitute the given values into the formula and calculate the outside clearance:
\[ \text{Outside Clearance (%) } = \frac{76 \text{ mm} - 74 \text{ mm}}{74 \text{ mm}} \times 100\% \]
First, calculate the difference in outside diameters:
\[ 76 \text{ mm} - 74 \text{ mm} = 2 \text{ mm} \]
Now, divide this difference by the outside diameter of the sample tube:
\[ \frac{2 \text{ mm}}{74 \text{ mm}} \]
\[ \frac{2}{74} \approx 0.027027 \]
Finally, multiply by 100% to get the percentage:
\[ 0.027027 \times 100\% \approx 2.703\% \]
The calculated outside clearance is approximately 2.703%. Looking at the options provided, the value closest to this result is 2.7%.
Summary of Dimensions and Calculation
| Parameter | Value (mm) |
|---|---|
| Inside diameter of cutting edge (\(D_c\)) | 68 |
| Inside diameter of sample tube (\(D_t\)) | 70 |
| Outside diameter of cutting edge (\(D_{oc}\)) | 76 |
| Outside diameter of sample tube (\(D_{ot}\)) | 74 |
| Calculation Step | Value |
|---|---|
| Difference in outside diameters (\(D_{oc} - D_{ot}\)) | \(76 - 74 = 2 \text{ mm}\) |
| Ratio \(\frac{D_{oc} - D_{ot}}{D_{ot}}\) | \(\frac{2}{74} \approx 0.027027\) |
| Outside Clearance (%) | \(0.027027 \times 100 \approx 2.703\%\) |
The calculated outside clearance of the sampler is approximately 2.7%.
Important Questions from Site Investigation and Sub-Soil Exploration
In order to minimize sampling disturbance the area ratio A r,\(\left( {{{\rm{A}}_{\rm{r}}} = \frac{{{\rm{D}}_{\rm{e}}^2 - {\rm{D}}_{\rm{i}}^2}}{{{\rm{D}}_{\rm{i}}^2}}{\rm{\;}}} \right)\) should be
Shelby tube is one of the most widely used devices for:
Which one of the following is NOT a soil exploration technique?
If the sampler tube is pushed at the bottom of the bore hole to a distance of 585 mm with length of the sample recovered being 535 mm. Then the value of recovery ratio is ______.
The type of soil sample collected using wash boring technique is __________.
