Standardization Problems

Here are the two examples of how to do milk standardization calculations:

1. If a dairy has 160 kg of 40% fat cream and wishes to standardize it to 32% fat cream, how much skimmilk (0% fat) must be added?

Mass Balance Approach

let x = kg skimmilk

y = kg of 32% cream

Mass Balance Equation (total mass into the process = total mass out of the process) 160 + x = y

Component Balance for Fat (fat into the process = fat out of the process)

.40 (160) = .32 (y) which says 40% of 160 kg comes in and 32% of y goes out
.40 (160) = .32(160+ x), substituting our equation for y
.32x = 64 - 51.2
x = 40 kg skimmilk

2. How much cream testing 35% fat must be added to 500 kg of milk testing 4% fat to obtain cream testing 10% fat?

Mass Balance Approach

let x = kg 35% cream

y = kg of 10% cream

Mass Balance x + 500 = y (mass in = mass out)

Component Balance for Fat

x (.35) + 500 (.04) = y (.10) again, fat in = fat out
x (.35) + 20 = x(.10) + 50
.25 x = 30
x = 120 kg of 35% cream

Note: if your algebra skills are not very good, I can highly recommend this website - I Do Maths.

 

Pearson square approach to above problem

A shortcut for 2-component mass balances
Place desired percentage in the centre of a rectangle
Place percentage composition of two available streams in left corners of rectangle
Cross subtract lower from higher numbers for right corners of triangle (higher number - lower number)
Use right corners as ratios of two streams

Using the above problem:

Component Mass
35     6
   10
4     25        500
      ___     ____
       31 

35% cream = (500 x 6)/25 = 120 kg
This will produce 620 kg cream at 10% fat. 

Check yur work - (620 x 0.10) = (120 x .35) + (500 x .04) - correct!