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Present each part of your solution in the following format:


  • Assemble                                                                              
    • State what needs to be found (identify the extensive property to be counted).
    • Diagram the set-up/situation with a brief description
  • Analyze                                                                         
    • List assumptions
    • Identify given (pertinent) information from the problem statement
    • Provide extra data necessary ( if applicable)
    • Identify a basis for your solution
    • Describe the system
    • Write the governing equation for the situations you wish to solve identifying terms which will cancel or stay
  • Calculate                                                                      
    • State governing equation in reduced form with extensive properties of interest
    • Calculate answers – SHOW ALL WORK/STEPS/CONVERSIONS
  • Finalize                                                                     
    • Formally state your answer with correct units
    • Draw appropriate conclusions about your answer

Problem Statements

1. To generate the biodegradable polymer, poly-L-lactic acid (PLA), a continuous production method is used. The monomer, lactic acid (LA), is reacted with a catalyst in the presence of water to generate PLA. One unit of this multi-unit process is a mixer. Streams 1, 2, and 3 are inlets to this mixer; stream 4 is an outlet. Stream 1 contains water and catalyst. The mass fraction of catalyst in stream 1 is 0.30. Stream 2 contains water and LA. Stream 3 is a recycle stream from further down the operation coming back into the mixer and contains water, LA, catalyst, and PLA. In stream 3, the mass fraction of PLA is 0.08, the mass fraction of catalyst is 0.03, and the mass fraction of LA is 0.250. The contents of the 3 streams are well-mixed and leave in stream 4. In stream 4, the mass fraction of catalyst is 0.15 and the mass fraction of PLA is 0.02. The mass flow rate of LA in stream 2 is ten times the mass flow rate of LA in stream 3.

                             a) Write a mass conservation equation for each of the four constituents (water, LA, catalyst, and PLA) in the system.

                             b) Determine the flow rate of each of the four streams.

                             c) Determine the mass fraction of each of the constituents (water, LA, catalyst, and PLA, as appropriate) in streams 2 and 4.

2. You are an entrepreneur starting a company to sell vitamin supplements. In manufacturing you have a bioreactor that has three input streams and one output stream. Each input vessel is carring two vitamins in varying proportions. The first input stream is a slurry of Vitamins A and B12 in water. Stream 2 is a slurry of Vitamins B12 and C in water. Stream 3 is a slurry of Vitamins C and D in water. The output stream is a slurry with all 4 vitamins that goes down stream in your production to be formed into gel caplets. Each slurry input is 1 part the first vitamin, 1 part the second vitamin, and 1 part water. If the downstream processes in your manufacturing can only handle up to 100 gm/hr of the output flow, determine the flow rates of the input streams that will maximize production if your output needs to be (10+E)% Vitamin D and (20+F)% Vitamin C. What percentages of your output slurry would be Vitamin A and Vitamin B12? 

Note: EFGH are the last 4 digits of your student id.  If the leading digit in any given value is 0 use 10 instead.

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