Question 38 (Textile Engineering & Fibre Science)
100 kg of 67/33 polyester/cotton blended yarn with 4% moisture content is shipped. The standard moisture regain values of polyester and cotton are 0.4% and 8.5% respectively. The correct invoice weight is approximately
| (A) | 92 kg |
| (B) | 96 kg |
| (C) | 99 kg |
| (D) | 104 kg |
[Show Answer]
Given in the question-
Weight of 67/33 polyester/cotton blended yarn=100 kg
Moisture content of blended yarn=4%
Moisture regain value of polyester yarn=0.4%
Moisture regain value of cotton yarn=8.5%
The correct invoice weight(W+D)=?
Where,
D=Oven dry weight of blend yarn
W=Weight of water present
Blend yarn weight=Oven dry weight of blend yarn+Oven dry weight of blend yarn x Moisture content%
100=D+D x 4/100
100=D+D x 0.04
100=1.04 D
D=100/1.04
Oven dry weight of yarn(D)=96.15 kg
Now,
Moisutre regain of blend yarn(M.R)=Weight % of polyester x Moisture regain value of polyester yarn+Weight % of cotton x Moisture regain value of cotton yarn/(Weight % of polyester+Weight % of cotton)
Moisutre regain of blend yarn(M.R)=67 x 0.4%+33 x 8.5% / (67+33)
Moisutre regain of blend yarn(M.R)=67 x 0.4%+33 x 8.5% / (67+33)
Moisutre regain of blend yarn(M.R)=0.268+2.805/ (100)
Moisutre regain of blend yarn(M.R)=3.073/ 100
Moisutre regain of blend yarn(M.R%)=(3.073/ 100) x 100
Moisutre regain of blend yarn(M.R%)=3.073 %
By formula-
Moisture regain%=W x 100/D
3.073=W x 100/96.15
W=3.073 x 96.15/100
W=295.47/100
W=2.95 kg
Now,
The correct invoice weight=(W+D)
=96.15+2.95
The correct invoice weight=99.10 kg (Ans)