GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/57

What will be the approximate crimp percentage for a square fabric if thread spacing is equal to the sum of the diameters of warp and weft threads ?

[Show Answer]

Option C is correct.

By crimp interchange equations-

h1+h2=d1+d2

h1+h2=D

Where, h1 & h2 are crimp height and D is the sum of diameter of warp and weft yarn

$h_1=\frac{4 \times P_2 \times \sqrt C_1}{3}$

$h_2=\frac{4 \times P_1\times \sqrt C_2}{3}$

Given,
If thread spacing=Sum of the diameter of yarn

P1=P2=D=P

h1+h2=D

Crimp=C1=C2=C

For square fabric.

$\frac{4 \times P_2 \times \sqrt C_1}{3}+\frac{4 \times P_1\times \sqrt C_2}{3}=D$

$\frac{4 \times P \times \sqrt C}{3}+\frac{4 \times P\times \sqrt C}{3}=P$

$\frac{4 \times \sqrt C}{3}+\frac{4\times \sqrt C}{3}=1$

$2 times \frac{4 \times \sqrt C}{3}=1$

$\frac{4 \times \sqrt C}{3}=\frac{1}{2}$

$\sqrt C=\frac{3}{8}$

$\sqrt C=0.375$

Square both side-

C=0.1406

C%=0.1406 x 100

C%=14.06 (Ans)