Mass Balance In Juice Treatment(Sugar Processing Industry)

In Sugar Processing industry, after clarification in clarifier, mass balance commence(the first recycling scheme in sugar processing industry), when the juice remained in the mud/sediments are recycled to the fresh incoming juice in the mills section.
If 40,000 liters/hour of juice is charged in the process, and it is indicated that 90% of the juice overflows to the evaporators as clear juice from clarifier, and in the clarifier, 5% of clear juice overflow after addition of floculant. Now you are required to calculate the rate  flow of the recycled juice. That is juice that is recycled from rotatory vacuum filter to the mills.
For you to solve this problem, first you have to draw the diagram(if you can figure it in your head then it's ok) with all available information and unknown which in this case is the amount of juice recycled to the mills to be mixed with fresh mills for the next processing. Then calculate the amount of expected product to be formed(clear juice). Write equation containing unknown then equate it to the amount of the product formed, for you to determine the flow rate of the recycled juice. That is the procedure that should be followed in problem involving recycle scheme but in this case it is direct.
This how we solve this problem:

(90/100 + 5/100  X 40,000) lrs/hr = 38,000 lrs/hour will overflow to the evaporators.
This means that 2000lrs or 5% of juice remained in the sediments and it will be recycled; therefore to get recycled flow rate: We say 2000 lrs/hour will be recycled and there we are and that is the flow rate of recycled juice.

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