GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/53

Question 53 (Textile Technology & Fibre Science)

A 50 tex yarn with mass CV of 12.5 % is produced from staple polyester fibres each of 4.5 denier fineness. The index of irregularity of the yarn, (rounded off to two decimal places), is __1.25__.

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Given:
Fineness of yarn=50 tex
=9*50 (Denier=9*Tex)
Fineness of yarn=450 denier

Mass CV(CV_effective)=12.5%
Polyester fibre fineness=4.5 denier

Formula:

Index of irregularity= $\frac{CV_{effective}}{CV_{limit}}$

Where, CV_limit= $\frac{100}{\sqrt{n}}$ (For polyester yarn)
Where, n is number of fibres in the yarn
n=count of yarn/count of fibre
n=450/4.5
n=100

CV_lim= $\frac{100}{\sqrt{n}}$
CV_lim= $\frac{100}{\sqrt{100}}$
CV_lim= $\frac{100}{10}$

CV_limit=10

Index of irregularity= $\frac{CV_{effective}}{CV_{limit}}$

= $\frac{12.5}{10}$

Index of irregularity(I)=1.25 (Answer)

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