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Consider a stirred tank heating process with constant holdup as depicted beiow Ti Wi Heater A liquid enters and leaves the tank at a mass flow rate of 200 lb/min. The feed and exit temperatures are 60°F and 100°F at steady state. The feed flow rate and temperature are possible disturbances while the heating rate Q is a potential manipulated variable. Assume the liquid has a density of 60 lb„/ft' and a heat capacity of 1.0 Btu/I.°F, and the iquid volume in the tank is 50 ft'. You can also assume that the heat loss to the surroundings through the walls of the tank is negligible. (a) Derive the dynamic model for the process. (b) Linearize the model and obtain three transfer functions relating the effluent temperature to the feed temperature, feed flow rate, and heating rate. Calculate the numerical values of the time constants and gains in the transfer functions.

Consider a stirred tank heating process with constant holdup as depicted beiow Ti Wi Heater A liquid enters and leaves the tank at a mass flow rate of 200 lb/min. The feed and exit temperatures are 60°F and 100°F at steady state. The feed flow rate and temperature are possible disturbances while the heating rate Q is a potential manipulated variable. Assume the liquid has a density of 60 lb„/ft' and a heat capacity of 1.0 Btu/I.°F, and the iquid volume in the tank is 50 ft'. You can also assume that the heat loss to the surroundings through the walls of the tank is negligible. (a) Derive the dynamic model for the process. (b) Linearize the model and obtain three transfer functions relating the effluent temperature to the feed temperature, feed flow rate, and heating rate. Calculate the numerical values of the time constants and gains in the transfer functions.

Introduction to Chemical Engineering Thermodynamics
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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Consider a stirred tank heating process with constant holdup as depicted beiow Wi V. lelllll Heater A liquid enters and leaves the tank at a mass flow rate of 200 lb/min. The feed and exit temperatures are 60°F and 100°F at steady state. The feed flow rate and temperature are possible disturbances while the heating rate Q is a potential manipulated variable. Assume the liquid has a density of 60 lb„/ft' and a heat capacity of 1.0 Btu/lb°F, and the liquid volume in the tank is 50 ft. You can also assume that the heat loss to the surroundings through the walls of the tank is negligible. (a) Derive the dynamic model for the process. (b) Linearize the model and obtain three transfer functions relating the effluent temperature to the feed temperature, feed flow rate, and heating rate. Calculate the numerical values of the time constants and gains in the transfer functions.
Transcribed Image Text:Consider a stirred tank heating process with constant holdup as depicted beiow Wi V. lelllll Heater A liquid enters and leaves the tank at a mass flow rate of 200 lb/min. The feed and exit temperatures are 60°F and 100°F at steady state. The feed flow rate and temperature are possible disturbances while the heating rate Q is a potential manipulated variable. Assume the liquid has a density of 60 lb„/ft' and a heat capacity of 1.0 Btu/lb°F, and the liquid volume in the tank is 50 ft. You can also assume that the heat loss to the surroundings through the walls of the tank is negligible. (a) Derive the dynamic model for the process. (b) Linearize the model and obtain three transfer functions relating the effluent temperature to the feed temperature, feed flow rate, and heating rate. Calculate the numerical values of the time constants and gains in the transfer functions.
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