GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/46

Question 46 (Textile Engineering & Fibre Science)

If the specific volume of yarn is increased by 21% the percentage increase in yarn diameter would be

[Show Answer]

Let, the initial specific volume of yarn=V1

Then , final specific volume of yarn(V2)=V1+V1 x 21%
V2=V1+0.21 V1
V2=1.21 V1

Let, initial dia of yarn=d1

Final dia of yarn=d2

Now, by formula-

Dia of yarn=0.990 \times \sqrt \frac {Specific volume}{840 \times Ne}

d=0.990 \times \sqrt \frac {V}{840 \times Ne}

i.e. Diameter of yarn is directly proportional to the sqaure root of the specific volume of yarn.

d \alpha  \sqrt V

\frac{d_1}{d_2}=\frac{\sqrt V_1}{\sqrt V_2}

\frac{d_1}{d_2}=\frac{\sqrt V_1}{\sqrt 1.21 \times V_1}

\frac{d_1}{d_2}=\frac{1}{\sqrt 1.21}


Reverse the whole equations-




(\frac{d_2}{d_1}-1)\times 100=0.1 \times 100

(\frac{d_2}{d_1}-1)\times 100=10


The percentage increase in yarn diameter=10 (Ans)

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