GATE (TF) Textile 2017 Question Paper Solution | GATE/2017/TF/36

Question 36 (Textile Engineering & Fibre Science)

If the distance between two adjacent fibres of circular cross-section in a hexagonally packed yarn is equal to the radius of the fibre, then the packing density of yarn, accurate to three decimal places, is __0.380 to 0.420__.

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Given in the question:

a=d/2

In hexagonally packing

If, distance between two adjacent fibres of circular cross-section= a

And dia of fibres=d

i.e., Radius of fibres=d/2

By formula–

$Packing density of yarn(P.C)=\frac{\pi d^2}{2 \sqrt{3} (a+d)^2}$

$Packing density of yarn(P.C)=\frac{3.14 d^2}{2 \sqrt{3} (d/2+d)^2}$

$Packing density of yarn(P.C)=\frac{3.14 d^2}{2 \sqrt{3} (3d/2)^2}$

Packing density of yarn(P.C)=0.385 (Answer)

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