GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/40

Question 40 (Textile Engineering & Fibre Science)

The diameter (mm) of a cotton yarn of 50 tex count and 0.45 packing density, assuming cotton fibre density to be 1.54 g/cm³, is __0.29 : 0.31__.

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Given in the question:

Count of the yarn=50 tex

Packing density=0.45

Density of the cotton fibre=1.54g/cm³
Diameter of yarn(D)=?

Formula:

$Dia of yarn(D)=3.57\times 10^-3(\sqrt\frac{tex}{Packing coefficient \times density of fibre(\rho_f)}) cm$

$Dia of yarn(D)=3.57\times 10^-3(\sqrt\frac{50}{0.45 \times 1.54}) cm$

$Dia of yarn(D)=3.57\times 10^-3(\sqrt72.15) cm$

$Dia of yarn(D)=3.57\times 10^-3 \times 8.49 cm$

$Dia of yarn(D)=3.57\times 10^-3 \times 8.49 cm$

$Dia of yarn(D)=30.32\times 10^-3 cm$

$Dia of yarn(D)=30.32\times 10^-3 \times cm$

$Dia of yarn(D)=30.32\times 10^-3 \times 10 mm$

$Dia of yarn(D)=30.32\times 10^-2 mm$

$Dia of yarn(D)=0.30 mm$ (Answer)

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