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

(A)	1.03
(B)	6.26
(C)	10.26
(D)	12.26

[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

Similarily-

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

Where,
P2 is the pick spacing=1/PPCM

P2=1/28

By formula-

$d_1+d_2=h_1+h_2$

Where h is the crimp hieght

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

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