2.42. WP The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that encloses the unit. Cooling water PROCESS UNIT ROTAMETER p(liters/s) T(°C) Jacket The exact relationship between the unit temperature T(°C) and the water flow rate o (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 ø. Plots of T versus ø on rectangular and semilog coordinates are distinctly curved (ruling out T = aø + b and T = aebó as possible empirical functions), but a log plot appears as follows: 300 T(°C) 200 100 10 100 p(L/s) A line drawn through the data goes through the points (ø1 = 25 L/s, T = 210°C) and (ø2 = 40 L/s, T, = 120°C). a. What is the empirical relationship between o and T? Answer 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.
2.42. WP The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that encloses the unit. Cooling water PROCESS UNIT ROTAMETER p(liters/s) T(°C) Jacket The exact relationship between the unit temperature T(°C) and the water flow rate o (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 ø. Plots of T versus ø on rectangular and semilog coordinates are distinctly curved (ruling out T = aø + b and T = aebó as possible empirical functions), but a log plot appears as follows: 300 T(°C) 200 100 10 100 p(L/s) A line drawn through the data goes through the points (ø1 = 25 L/s, T = 210°C) and (ø2 = 40 L/s, T, = 120°C). a. What is the empirical relationship between o and T? Answer 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.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Transcribed Image Text:2.42. WP The temperature in a process unit is controlled by passing cooling water at a measured rate through a jacket that
encloses the unit.
Cooling water
PROCESS
UNIT
ROTAMETER
p(liters/s)
T(°C)
Jacket
The exact relationship between the unit temperature T(°C) and the water flow rate o (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 ø. Plots of T versus ø on rectangular and semilog coordinates are distinctly curved (ruling out T = aø + b and
T = aebó as possible empirical functions), but a log plot appears as follows:
300
T(°C) 200
100
10
100
p(L/s)
A line drawn through the data goes through the points (ø1 = 25 L/s, T = 210°C) and (ø2 = 40 L/s, T, = 120°C).
a. What is the empirical relationship between o and T?
Answer
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.
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