Question

Material Balance Using Pearson Square

1. Let's say you are blending because you would like to lower the level of alcohol in our wine. We have some Merlot (A) that is 15% alcohol, and we would like to blend it with another Merlot (B) wine so we end up with a target alcohol of 12%. The other wine’s (B) alcoholic content is 11%. You are asked to produce 5,000 quarts of this blended wine (@ Sp. Gr. = 1.09)

2. After using the centrifuge for separation, you have skim milk at 0.5 % fat and cream at 40 % fat. You wish to produce a 500-kilogram batch of standardized milk with a final fat content of 3.5 % from skim milk and cream. How much of each component would you mix to obtain the desired product (in pounds)?

Answer 1

1. To produce 5000 quarts of this blended wine you need 1250 quarts of Wine A and 3750 quarts of Wine B.

2. To produce a 500 kg batch, you need 83.8 pounds of cream and 1018.5 pounds of skim milk.

Step-by-step explanation:

(a) Step 1. Draw the Pearson Square. The opposite corner is the substraction of the large value and the smaller value. For example, the upper-right corner is (12-11) = 1. The Lower right corner is (15-12)=3.

Wine A 15% 1 parts

12%

Wine B 11% 3 parts

Step 2. The total amount of "parts"is 1+3=4, which 1 part corresponds to Wine A and 3 parts to Wine B.

So, the blend has to be 1/4=0.25 parts of Wine A and 3/4=0.75 parts of Wine B.

We can verify the result

`Alcohol_(blend)=0.25*Alcohol_(A)+0.75*Alcohol_{B)\\Alcohol_(blend)=0.25*0.15+0.75*0.11 = 0.0375+0.0825=0.12`

To produce 5000 quarts of this blended wine you need 1250 quarts of Wine A and 3750 quarts of Wine B.

(b) Step 1. Draw the Pearson square

Cream 40% 3 parts

3.5%

Skim milk 0.5% 36.5 parts

% of Cream = 3/(3+36.5) = 0.076 = 7.6%

% of Skim milk = 36.5/(3+36.5) = 0.924 = 92.4%

`Fat_(StandardMilk) = 0.076*Fat_(cream)+0.924*Fat_(skimmilk)\\Fat_(StandardMilk) = 0.076*40+0.924*0.5= 3.04 + 0.46 = 3.5`

To produce a 500 kg batch, you need 500*0.076= 38 kgs of cream and 500*0.924= 462 kgs of skim milk. This is equivalent to 83.8 pounds of cream and 1018.5 pounds of skim milk (1 kg = 2.2 pounds).