GATE (TF) Textile 2011 Question Paper Solution | GATE/2011/TF/39

Question 39 (Textile Engineering & Fibre Science)

For a plain woven fabric, the diameter of warp and weft yarns are 0.2 mm and 0.3 mm, respectively. The crimp in warp yarn is 9% and pick spacing is 0.4 mm. The fabric thickness in mm is

(A)	0.32
(B)	0.50
(C)	0.64
(D)	0.75

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Given in the question-

Dia of warp yarn( $d_1$ )=0.2mm

Crimp in warp yarn( $C_1$ )=9%

Pick spacing=0.4mm

Dia of weft yarn( $d_2$ )=0.3 mm

Fabric thickness(mm,t)=?

By formula:

Fabric thickness(t)=h1+d1

Where ,

h1(Warp crimp hieght)= $\frac{136\times \sqrt C_1}{1000 \times PPI}$ inch

given,
Pick spacing=0.4mm
=0.0004 meter

$PPM=\frac{1}{pick spacing}$

$PPM=\frac{1}{0.0004}$

PPM(picks per meter)=2500

PPI(picks per inch)=2500/39.34

PPI=63.5485

Now,

h1(Warp crimp hieght)= $\frac{136\times \sqrt C_1}{1000 \times PPI}$ inch

h1(Warp crimp hieght)= $\frac{136\times \sqrt 9}{1000 \times 63.5485}$ inch

h1(Warp crimp hieght)= $\frac{136\times 3}{1000 \times 63.5485}$ inch

h1(Warp crimp hieght)= $\frac{408}{63548.5}$ inch

h1(Warp crimp hieght)=0.00642 inch

h1(Warp crimp hieght)=0.00642 x 2.54 x 10 mm

h1(Warp crimp hieght)=0.163 mm

Now,

Fabric thickness(t)=0.163+0.2

Fabric thickness(t)=0.36 mm (Ans)

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