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Sampler clearances and area ratio (59 mm)

Short answer

Inside clearance Ci=1.69%, outside clearance Co=1.61%, area ratio Ar=14.02%. Clearances acceptable but Ar > 10% indicates slight disturbance.

A sampler has the following dimensions: inside diameter of cutting edge = 59 mm; outside diameter of cutting edge = 63 mm; inside diameter of sampling tube = 60 mm and outside diameter of sampling tube = 62 mm. Calculate (i) area ratio (ii) inside clearance (iii) outside clearance.

Given: D1=59D_1 = 59 mm (cutting edge inside), D3=63D_3 = 63 mm (cutting edge outside), D2=60D_2 = 60 mm (tube inside), D4=62D_4 = 62 mm (tube outside).

(i) Area ratio

Ar=D32−D12D12×100=632−592592×100=4883481×100=14.02%A_r = \frac{D_3^2-D_1^2}{D_1^2}\times100 = \frac{63^2-59^2}{59^2}\times100 = \frac{488}{3481}\times100 = 14.02\%

(ii) Inside clearance

Ci=D2−D1D1×100=60−5959×100=1.69%C_i = \frac{D_2-D_1}{D_1}\times100 = \frac{60-59}{59}\times100 = 1.69\%

(iii) Outside clearance

Co=D3−D4D4×100=63−6262×100=1.61%C_o = \frac{D_3-D_4}{D_4}\times100 = \frac{63-62}{62}\times100 = 1.61\%

Answer: Ar=14.02%A_r = 14.02\%, Ci=1.69%C_i = 1.69\%, Co=1.61%C_o = 1.61\%. (The clearances are acceptable, but Ar>10%A_r > 10\%, so the sample would be slightly disturbed.)

✓ Answer checked by Claude Sonnet 5.5

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