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………………
[Show Answer]
Write Here
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)