GATE (TF) Textile 2020 Question Paper Solution | GATE/2020/TF/45

Question 45 (Textile Engineering & Fibre Science)

In wet spinning of acrylic filament yarn, the volumetric flow rate of the spinning dope per spinneret hole is 0.1 cm3/min. If the surface speed at the first take up roller is 1.5 m/min and the diameter of spinneret hole is 0.02 cm, then the jet stretch (rounded off to 2 decimal places) is __0.46 to 0.48__.

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Given in the question:
Volumetric flow rate of the spinning dope per spinneret hole(V)=0.1 cm3/min

Surface speed at first take up roller(Take up length,L2) =1.5 m/min

Diameter of spinneret hole(d) =0.02 cm
The jet stretch=?

Calculation:

Stretch=Take up length/Delivery length

Volumetric flow rate=0.1 cm3/min

Volume of fibre=\pi x d2 x L1/4 (v=\pi x r2 x h)

(Where d is the diameter of spinneret hole and L1 is the delivery length)

0.1 = \pi x (0.02)2 x L1/4 ,

0.1 = 3.14 x 0.0004 x L1/4 ,

L1 =318.47 cm/min ,

L1 =3.184 m/min

Now,

Stretch=Take up length(L2)/Delivery length(L1)

Stretch=1.5/3.184 ,

Jet Stretch=0.47 (Answer)

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