Question

Consider two successive screen sizes in the Tyler standard screen scale, viz. 150 meshes per inch and 200 meshes per inch. Their linear sizes of the openings are L150 and L200, respectively. If the value of L200 is \(2.9 \times 10^{-3}\) inch, then the value of L150 (in inch) is \(\times 10^{-3}\) (rounded off to one decimal place).

Hint:

Successive Tyler standard sieves differ in opening size by a constant ratio of root 2, with the coarser (lower mesh number) screen having the larger opening.

Answer 1

Correct Answer: 4.1

Cross-check using the standard published Tyler sieve aperture table. The 200 mesh screen's opening is about $74\ \mu m$ (0.074 mm), and each successive coarser screen has an opening larger by the fixed factor $\sqrt{2}$. Converting $L_{200}=2.9\times10^{-3}$ inch to metric gives $73.7\ \mu m$, matching the standard value. The published table lists 150 mesh at about $104\ \mu m$; checking, $\sqrt2 \times 73.7 = 104.2\ \mu m$, agreeing with the table. Converting back to inches gives $4.10\times10^{-3}$ inch.\[ \boxed{L_{150} \approx 4.1\times10^{-3}\ \text{inch}} \]