Question

If 35,000kg of whole milk containing 4% fat is to be separated in a 6 hour period into skim milk with 0.45% fat and cream with 45% 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.)

(a) 5678 kg/hr

(b) 5368 kg/hr

(c) 2567 kg/hr

(d) 2578 kg/hr

This question was addressed to me during an interview.

This intriguing question comes from Energy Balance Numericals Without Reactions topic in portion Energy Balance of Bioprocess Engineering

Answer 1

Correct option is (b) 5368 kg/hr

For explanation I would say: Mass in: Total mass = 35000/6 = 5833 kg.

Fat = 5833 x 0.04 = 233 kg.

And so Water plus solids-not-fat = 5600 kg.

Mass out: Let the mass of cream be x kg then its total fat content is 0.45x. The mass of skim milk is (5833 – x) and its total fat content is 0.0045 (5833 – x).

Material balance on fat: Fat in = Fat out

5833 x 0.04 = 0.0045(5833 – x) + 0.45x. And so x = 465 kg.

So that the flow of cream is 465 kg / hr and skim milk (5833 – 465) = 5368 kg/hr.