The temperature in a process unit is controlled by passing cooling water at a measured rate through
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 water flow rate ϕ (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 ϕ. Plots of T versus ϕ on rectangular and semilog coordinates are distinctly curved (ruling out T = aϕ + b and T = aebϕ as possible empirical functions), but a log plot appears as follows:
A line drawn through the data goes through the points (ϕ1 = 25 L/s, T1 = 210°C) and (ϕ2 = 40 L/s, T2 = 120°C).
(a) What is the empirical relationship between ϕ and T?
(b) Using your derived equation, estimate the cooling water flow rates needed to maintain the process unit temperature at 85°C, 175°C, and 290°C.
(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.
Step by Step Answer:
Elementary Principles of Chemical Processes
ISBN: 978-1119498759
4th edition
Authors: Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard