GATE (TF) Textile 2006 Question Paper Solution | GATE/2006/TF/30

An idealized hexagonal closed packed yarn has seven layers of 1.2 dtex fibres. The approximate count (Ne) of yarn is

[Show Answer]

Option B is correct.

Given –

Hexagonal close packing

No.of layers=7

Fibre count=1.2 dtex
=0.12 tex

By formula-

Total no of fibres= $3\times n^2-3\times n+1$

Where n is the no. of layers

Total no of fibres= $3\times 7^2-3\times 7+1$

Total no of fibres=147-21+1

Total no of fibres=127

Yarn count=No. of fibres x Fibre count

Yarn count=127 x 0.12

Yarn count=15.24 tex

By relationship-

Ne=590.5/tex

Ne=590.5/15.24

Ne=38.74

Yarn count(Ne)=39 (Ans)