GATE (TF) Textile 2016 Question Paper Solution | GATE/2016/TF/46

Question 46 (Textile Engineering & Fibre Science)

The surface area per unit volume (mm-1) of a circular polyester fibre of 1.5 denier fineness and 1.38 g/cm3 density, ignoring the fibre ends, is __322 : 323__.

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Given in the question:
Fineness of polyester fibre=1.5 denier

Density of fibre=1.38 g/cm3

Surface area per unit volume=?


Volume of cylinder(fibre,V)=\pi \times r^2 \times h

Where, r is the radius of the cylinder and h is the height of the cylinder

Surface area of fibre(S)= 2\pi\times r \times h

Surface area per unit volume=\frac {Surface area of fibre}{Volume of fibre}

Surface area per unit volume=\frac {2\pi\times r \times h}{\pi \times r^2 \times h}

Surface area per unit volume=\frac {2}{r}


By formula:

Denier=\pi r^2\times 9000\times100\times density of fibre

Denier=3.14 \times r^2 \times 9\times10^5 \times 1.38

1.5=3.14 \times r^2 \times 9\times10^5 \times 1.38

1.5=38.99\times10^5 \times r^2

\frac{1.5\times 10^-5}{38.99}= r^2

0.0385\times 10^-5= r^2

0.00385\times 10^-4= r^2

\sqrt 0.00385\times 10^-2= r


r=0.062\times10^-2 cm

r=0.062\times10^-1 mm

r=0.0062 mm

Surface area per unit volume=\frac {2}{r}

=322.58 mm

Surface area per unit volume=322.58 mm-1 (Answer)

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