Mass balancing (Food engineering)

Question

Raw milk contains 12% solids is pasteurized to 70 degree Celsius before entering the evaporator for concentration. The concentrated milk leaving the evaporator contains 50% solids. During evaporation, 0.5% of heated raw milk is lost due to fouling in the evaporator. Concentrated milk leaves evaporator and enters spray dryer, where the milk powder containing 3% moisture is form.

Calculate the amount of milk powder collected for every kg of raw milk entering the pasteurizer.

Answer 1

You don't really say and I'm not an expert in this area so I'm not sure, but I'll assume the percentages are "percent by mass" as opposed to "percent by volume".

Let's say, to make it easy, that we start with 1000g of raw milk (1 kg). That means, since it is 12% solids, that we would have 120g of solids and 880g of water. We are also told that 0.5% gets lost in the process meaning that there would be 120(0.995) = 119.4 g of solids after that process and we are also told that the result is 50-50, therefore, we would also have 119.4 g of water left.

During the final step, additional water is lost but we would maintain the 119.4 g of solids. The final result has 3% water therefore, if we say that the total weight is "T", then:

T = amount of solids + amount of water

T = 119.4 + 0.03(T)

0.97T = 119.4

T = 119.4/0.97

T = 123.09 g

So for every 1 kg of raw milk, we can expect about 123 g of powdered milk.