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10 May, 07:01

If 36 000 kg of full cream 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?

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  1. 10 May, 07:24
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    B=5522.33kg/h

    C=478.11kg/h

    Explanation:

    Hi! It's a mass balance. First we have to determine the inflow.

    mass flow rate = 36000kg / 6h = 6000kg / h

    We define the input variable

    - input flow (A) = 6000kg / h

    -XgA = percentage of fat in A = 0.04

    We define output variables.

    - skim milk (B)

    -creme (C)

    -XgB = fat percentage at B = 0.0045

    -XgC = percentage of fat in C = 0.45

    Then we can start with the balance.

    As a general rule, the mass balance is:

    Input = Output

    Balance sheet

    1) A = B + C

    Fat balance

    2) A * XgA = B * XgB + C * XgC

    Now we can solve.

    We replace and clear B in equation 2

    6000kg / h * 0.04 = B * 0.0045 + C * 0.45

    B = (240kg / h) / 0.045-C*0.45/0.0045

    3) B = 53333.33kg / h-C * 100

    We replace equation 3 in 1 and clear C

    A = B + C

    6000kg / h = 53333.33kg / h-C * 100 + C

    C = (6000kg/h-53333.33kg/h) / (-99)

    C=478.11kg/h

    We replace C in equation 3 and calculate B

    B = 53333.33kg / h-478.11kg/h * 100

    B=5522.33kg/h

    Then we have the values of the outflows.

    C=478.11kg/h

    B=5522.33kg/h
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