GATE (TF) Textile 2009 Question Paper Solution | GATE/2009/TF/53

Common Data Questions

Assume Peirce’s Geometry and circular yarn of 0.5 mm diameter. A square plain woven fabric with maximum sett would have

Thread spacing (mm) in the fabric as

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Given,

Peirce’s geometry

Diameter of circular yarn=0.5 mm

A square plain woven fabric with sett.

i.e ,

EPI=PPI

E=I

In case of jammed fabric-

$2\times \sqrt (1-(\frac{p}{d})^2)=1$

$\sqrt (1-(\frac{p}{d})^2)=\frac{1}{2}$

By doing square both side-

$(1-(\frac{p}{d})^2)=\frac{1}{4}$

$(1-\frac{1}{4})=(\frac{p}{d})^2$

$\frac{3}{4}=(\frac{p}{d})^2$

$\frac{\sqrt3}{2}=\frac{p}{d}$

$\frac{p}{d}=\frac{\sqrt3}{2}$

$p=\frac{\sqrt3}{2}\times d$

Where,

p=thread spacing and d is the diameter of circular yarn
d1+d2=d
where, d1=d2
$p=\frac{\sqrt3}{2}\times 2 \times d1$

$p=\frac{\sqrt3}{2}\times 2 \times 0.5$

$p=\frac{1.732}{2}\times 2 \times 0.5$

$p=1.732 \times 0.5$

Thread spacing(p)=0.866 mm (Ans)