GATE (TF) Textile 2008 Question Paper Solution | GATE/2008/TF/72

Common Data Questions

A cotton fabric has 25 ends per cm, 28 picks per cm, warp count 30 tex, weft count 15 tex, warp crimp 12%. The diameter of the yarn is given by; 4.44 x 10-3 (yarn tex/fibre density)1/2

Question 72 (Textile Engineering & Fibre Science)

The crimp (%) in weft yarn is

[Show Answer]

Option C is correct.

Given in the question-

Ends per cm(EPCM)=25

Picks per cm(PPCM)=28

Warp count=30 tex

Weft count=15 tex

Warp crimp=12%

The ratio of warp way modular length to sum of thread diameter=?

Let the warp way modular length=l1

Sum of diameter=D

Sum of diameter(D)=Warp diameter(d1)+Weft diameter(d2)

d_1=4.44 \times 10^-3 \times \sqrt \frac{Warp count}{Density of cotton fibre} cm

d1=4.44 \times 10^-3 \times \sqrt \frac{30}{1.54}

d1=4.44 \times 10^-3 \times \sqrt 19.48

d1=4.44 \times 10^-3 \times 4.41

d1=19.58 \times 10^-3 cm


d_2=4.44 \times 10^-3 \times \sqrt \frac{Weft count}{Density of cotton fibre} cm

d_2=4.44 \times 10^-3 \times \sqrt \frac{15}{1.54} cm

d_2=4.44 \times 10^-3 \times \sqrt 9.74 cm

d_2=4.44 \times 10^-3 \times 3.12 cm

d_2=13.94\times 10^-3 cm

Sum of diameter(D)=Warp diameter(d1)+Weft diameter(d2)

D=19.58 \times 10^-3+13.94\times 10^-3 cm

D=33.52 \times 10^-3 cm

By formula-

Warp crimp%=(l1-P2) x 100/P2

P2 is the pick spacing=1/PPCM


By formula-


Where h is the crimp hieght

d_1+d_2=\frac{136 \times \sqrt Warp crimp percentage}{ppcm\times 2.54 \times 1000}  \times 2.54+\frac{136 \times \sqrt Weft crimp percentage}{epcm\times 2.54 \times 1000}\times 2.54

19.58 \times 10^-3+13.94\times 10^-3 =\frac{136 \times \sqrt 12}{28\times 2.54 \times 1000}\times 2.54+\frac{136 \times \sqrt Weft crimp percentage}{25\times 2.54 \times 1000}\times 2.54

33.52 \times 10^-3=0.01682+0.005440 \times \sqrt Weft crimp percentage

0.03352-0.01682=0.005440 \times \sqrt Weft crimp percentage

0.0167=0.005440 \times \sqrt Weft crimp percentage

{0.0167}{0.005440}=\sqrt Weft crimp percentage

\sqrt Weft crimp percentage=3.07

Weft crimp percentage=9.42

Weft crimp percentage=10 (Approx) (Ans)

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