GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/50

Question 50 (Textile Technology & Fibre Science)

Cloth cover factor of a square plain jammed cotton fabric, accurate to one decimal place, is __22.8 to 23.1__.

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Given in the question–

The type of fabric=Square plain jammed cotton fabric

Calculation–

$Cloth cover factor(K)=K_1+K_2-\frac{K_1K_2}{28}$

$Warp cover factor(K_1)=\frac{d_1}{s_1}\times28$

$Weft cover factor(K_2)=\frac{d_1}{s_1}\times28$

Where, d₁ is the warp yarn diameter ,d₂is the weft yarn diameter and s₁is the end spacing ,s₂ is the pick spacing
For square jammed fabric:
d₁=d₂=d , s₁=s₂ =s

Spacing(s)=2dsin60
$s=2d*\frac{\sqrt3}{2}$

$s=d\times\sqrt{3}$
$Warp cover factor(K_1) =Weft cover factor(K_2)=\frac{d}{s}\times28$

= $\frac{d}{d\times\sqrt{3}}\times28$

= $\frac{1}{\sqrt3}\times28$

Then,
$Cloth cover factor(K)=K_1+K_2-\frac{K_1K_2}{28}$

$K=\frac{1}{\sqrt3}\times28+\frac{1}{\sqrt3}\times28-\frac{\frac{1}{\sqrt3}\times28\times\frac{1}{\sqrt3}\times28}{28}$

$K=16.16+16.16-9.33$

$K=32.32-9.33$

$Cloth cover factor(K)=22.99$ (Answer)

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