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Question: The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that encloses the unit. The exact relationship between the unit temperature T(?C) and the cooling flow water flow rate F (L/s) is extremely complex, and it is desired to derive a simple empirical formula to approximate this relationship over a limited range of flow rates and temperatures. Data are taken for T versus F. Plots of T versus F on rectangular and semi log coordinates are distinctly curved (ruling out T = aF + b and T = aebF as possible empirical (functions), but a log plot appears as follows: A line drawn through the data goes through the points (F1 = 25, T1 = 210) and (F2 = 40. T2 = 120)
(a) What is the empirical relationship between F and T?
(b) Using your derived equation, estimate the cooling water flow rates needed to maintain the process unit temperature at 85oC, 175oC, and 290oC.
(c) In which of the three estimates in part (b) would you have the most confidence and in which would you have the least confidence? Explain your reasoning.
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