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Sampler clearances and area ratio (69 mm)

Short answer

Inside clearance Ci=1.45%, outside clearance Co=1.39%, area ratio Ar=11.93%. Clearances are within limits, but Ar is marginally above 10%.

A soil sampler has the following dimensions: inside diameter of the cutting edge = 69 mm; outside diameter of cutting edge = 73 mm; inside diameter of the sampling tube = 70 mm and outside diameter of the sampling tube = 72 mm. Calculate: (i) inside clearance (ii) outside clearance and (iii) area ratio of the sampler.

Given: D1=69D_1 = 69 mm, D3=73D_3 = 73 mm (cutting edge inside/outside), D2=70D_2 = 70 mm, D4=72D_4 = 72 mm (tube inside/outside).

(i) Inside clearance

Ci=D2−D1D1×100=70−6969×100=1.45%C_i = \frac{D_2-D_1}{D_1}\times100 = \frac{70-69}{69}\times100 = 1.45\%

(ii) Outside clearance

Co=D3−D4D4×100=73−7272×100=1.39%C_o = \frac{D_3-D_4}{D_4}\times100 = \frac{73-72}{72}\times100 = 1.39\%

(iii) Area ratio

Ar=D32−D12D12×100=732−692692×100=5684761×100=11.93%A_r = \frac{D_3^2-D_1^2}{D_1^2}\times100 = \frac{73^2-69^2}{69^2}\times100 = \frac{568}{4761}\times100 = 11.93\%

Answer: Ci=1.45%C_i = 1.45\%, Co=1.39%C_o = 1.39\%, Ar=11.93%A_r = 11.93\%. Both clearances are within limits; the area ratio is a little over the 10% limit for a good undisturbed sample.

✓ Answer checked by Claude Sonnet 5.5

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