GATE (TF) Textile 2014 Question Paper Solution | GATE/2014/TF/33

Question 33 (Textile Engineering & Fibre Science)

A polypropylene yarn, melt spun at a throughput rate of W (g/s) and winding speed of S (m/min), was drawn to a draw ratio of D. The denier of this yarn is a function of W, S, D and a constant K. The Value of K, accurate to the nearest integer, is………………

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Given in the question

Through put rate(g/s)=W

Through put rate(g/min)=W*60

Winding speed(m/min)=S

Draw ratio=D

Denier of the yarn is a function of W,S,D and a constant K.

Value of K=?

Calculation:

Draw ratio(D)=VL/Vo

D=VL/S

VL=D*S

Linear density(g/m)=Through put rate(m/min)/VL speed(m/min)

Linear density(g/m)=60*W/(D*S)

By the definition of Denier-

Linear density(g/m)=W/(D*S)

i.e., D*S meter length have=60*W gm weight

1 meter length have=60*W/(D*S)

Then, 9000 meter length have=(60*W/(D*S))*9000

i.e., Denier=9000*60*(W/(D*S))
Denier=54000*(W/(D*S))

Hence, denier is a function of W,D & S,

So, the value of K=54000 (Answer)