# 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

Option C is correct.
Given in the question-

Fineness of polyester fibre=1.5 denier

Fibre density()=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

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)