GATE (TF) Textile 2007 Question Paper Solution | GATE/2007/TF/71

Five grams of 1.5 denier polyester fibre of density 1.39 g/cm3 is packed in a cylinder of 30 mm diameter with perforated ends to make a fibre plug of 20 mm length.

Question 71 (Textile Engineering & Fibre Science)

Percentage porosity of the plug would be approximately

(A)25
(B)50
(C)75
(D)100
[Show Answer]

Option C is correct.
Given in the question-

Fineness of polyester fibre=1.5 denier

Fibre density(d_f)=1.39 g/cm3

Total weight of fibre(m)=5gm

Packed in a cylinde,diameter(D)=30 mm

To make fibre plug,length(l)=20 mm

% Porosity of plug=?

As we know,

Mass=volume x density

Total weight of fibre=Volume of cylinder x density of cylinder

M=V X dy

5=Area of cylider x length of plug x dy

5=\pi \times (\frac{D}{2})^2 \times 20 \times 10^-3 \times dy

5=3.14 \times (\frac{30 \times 10^-3}{2})^2 \times 20 \times 10^-3 \times dy

5=0.014130 \times 10^-3 \times dy

\frac{5}{0.014130 \times 10^-3}=dy

dy=353.86 x 1000 g/m3

dy=353.86 x 1000/1000000 g/cm3

dy=0.354 g/cm3

By formula-

Porosity%=1-Packing coefficient

Packing coefficient=Density of cylinder(yarn)/density of fibre

Packing coefficient=dy/df

Packing coefficient=0.354/1.39

Packing coefficient=0.255

Now,

Porosity=1-0.255

Porosity=0.745

Percentage Porosity=74.5
=75 (Ans)

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