###### 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)=V _{L}/V_{o}**

D=V

_{L}/S

**V**

_{L}=D*S**Linear density(g/m)=Through put rate(m/min)/V**

_{L }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)**