Fall 2004 ICE Topics: Process Control by Design 10.492 Problem Set 1: Examining the Energy Balance For this problem set, I will accept submissions with one or two names. (1) Beginning with the simplified energy balance for the shower F c T = F h T h + T c F h + F F h + F c c fill in the missing steps to derive the linearized energy balance T F hr + T F T F hr + T F ⎤ hr hr cr cr F T = cr cr + ⎡ ⎢ T hr − ( F + F ) ⎥ ⎦ ( F − F hr )+ F hr ( T − T hr ) hr + F ⎣ F hr + F 2 h F hr + F h cr cr hr cr cr ⎡ T T F hr + T F ⎤ + ⎣ ⎢ F hr + cr F hr cr 2 cr c cr cr c cr − ( F + F ) ⎥ ⎦ ( F − F )+ F ( T − T ) F hr + F cr hr cr cr • (please use the nomenclature of the Lecture Notes) (2) Specify practical reference conditions for each of the variables in the energy balance. For example, we know that a shower is more than a trickle and less than a torrent – what is a reasonable flowrate? We will regard these reference values as the desired operating condition for our process, and thus they should satisfy the steady state M&EB. • (please use the nomenclature of the Lecture Notes)
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