Standardization Problems


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

Mass Balance Approach


	let x = kg skimmilk

	    y = kg of  32% cream

Mass Balance  (mass into the process = 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
Pearson square approach to above problem
  1. A shortcut for 2-component mass balances
  2. Place desired percentage in the centre of a rectangle
  3. Place percentage composition of two available streams in left corners of rectangle
  4. Cross subtract lower from higher numbers for right corners of triangle (higher number - lower number)
  5. 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  =  120 kg
				_______
			  	  25

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