Question #95077

. If 60,000 kg of whole milk containing 4% fat is to be separated in a 6 hour period into skim milk with 0.4% fat and cream with 35% fat, what are the flow rates of the two output streams from a continuous centrifuge which accomplishes this separation? Basis: 1 hour's flow of whole milk.

Expert's answer

For 1hour whole milk feed = (60,000 /6 )Kg=10,000Kg

So that the flow rate of whole milk feed = 10,000 kg/hr

Mass of whole milk=10,000 kg

Mass of cream = x kg

Mass of skim milk=(1-x)

Mass balance equation is

Whole milk= skim milk + cream

10,000kg=skim milk + x kg

So, skim milk = (10,000-x) kg

Material balance on fat is

10,000kg×0.04 = (10,000-x)×0.004 + x

On solving the above equation we get the value of x

So, x=361.44 kg

So that the flow rate of cream = x= 361.44kg/hr

and mass of skim milk= (10,000-x)=(10,000-361.44)kg

= 9,638.56 kg

So that the flow rate of skim milk = 9,638.56 kg/hr.

For checking

(Whole milk) flow rate = (skim milk + cream) flow rate

10,000 kg/hr = (9,638.56 + 361.44) kg/hr

10,000 kg/hr = 10,000 kg/hr

Hence it is proved.

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