Emulsion:
A mixture of some lubricating agents is applied on jute fiber to make the fiber soften and flexible. Here, mathematics problems of emulsion in jute spinning are discussed below.
An emulsion is an intimate mixture of two immiscible liquids where one is dispersed in small globules on the other and the addition of a third substance brings stability. The emulsion is made by splitting up oil into minute drops which are prevented from reuniting in water.
General recipe of emulsion:
- Water- 73%
- Oil-25.4%
- Emulsifier- 1.6%
Mathematics Problems and Solutions of Emulsion in Jute Spinning
Problem-(01):
If raw jute receives an application of 20% emulsion of which 15% is absorbed. Find out the weight of a batch of 12 bales of raw jute. (4000lbs = 1bale)
Solution:
Wt of 12 bales = 4000× 12 = 48000lbs
100 lbs raw jute after batching wt = 115 lbs
1 lbs raw jute after batching wt= 115/100 lbs
…………………………………………………………115 X 48000
48000 lbs raw jute after batching wt = …………………….
………………………………………………………………..100
= 55200lbs (ANS)
Problem-(02):
If an emulsion is prepared as follows: Oil = 24%, Water =74.5%, Emulsifier =15%. If raw jute receives an application of 20% emulsion of which 15% absorbed. Find out the absorbed amount oil, water and emulsifier of raw jute (A batch containing 12bales, 4000lbs/bale)
Solution:
Oil:
Wt of 12 bales = 4000×12 = 48000 lbs.
100 lbs emulsion contains = 24lbs oil
1lbs emulsion contains = 24/100 lbs oil
……………………………………….24 X 15
15 lbs emulsion contains = ………….… = 3. 6 lbs oil
………………………………………….100
100 lbs raw jute absorbs =3.6 lbs
1 raw jute absorbs = 36/100 lbs
………………………………………….3.6 X 48000
48000 lbs raw jute absorbs = …………………
………………………………………………..100
=172.8 lbs oil (ANS)
Water:
100 lbs emulsion contains =74.5 lbs water
…………………………………..74.5
1 lbs emulsion contain =………lbs water
…………………………………..100
……………………………………74.5 X 15
15 lbs emulsion contain =…………… = 11.175 lbs
………………………………………100
100 lbs jute absorbs =11.175 lbs
1lb jute absorbs= 11.175/100 lbs
……………………………………..11.175 X 48000
48000 lbs jute absorbs = ………………………..
……………………………………………..100
=536.4 lbs
= 536.4/9 gallon
= 59.6 gallons (ANS)
Emulsion:
100 lbs emulsion contains =1.5 lbs emulsifier
…………………………………….1.5
1 lbs emulsion contain = ……… lbs emulsifier
……………………………………100
……………………………………1.5 X 15
15 lbs emulsion contain =…………. = 3.225lb emulsifier
……………………………………….100
100 lbs raw jute absorbs = 3.225 lb emulsifier
………………………………….3.225
1 lb raw jute absorbs = …………… lb emulsifier
……………………………………100
………………………………………….3.225 X 48000
48000 lbs raw jute absorbs = ……………………..
…………………………………………………..100
= 10.8 lb emulsifier, (ANS)