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A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with V. (ft) of warm milk at a temperature of T. (F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at T, ("F) is added at a volumetric flow rate of q (ft/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to Vị after all of the cows have been milked.

A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with V. (ft) of warm milk at a temperature of T. (F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at T, ("F) is added at a volumetric flow rate of q (ft/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to Vị after all of the cows have been milked.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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2. A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with V. (ft') of warm milk at a temperature of T. ('F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at T, ('F) is added at a volumetric flow rate of q (ft'/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to Vr after all of the cows have been milked. (a) Derive a dynamic model for the process so that the temperature of the milk can be determined as a function of time. (b) Perform a degrees of freedom analysis. Identify all of the model constants, input variables and output variables.
Transcribed Image Text:2. A milk storage tank on a dairy farm is equipped with a refrigeration compressor which removes Q (Btu/min) of heat from warm milk. The insulated and perfectly mixed tank is initially filled with V. (ft') of warm milk at a temperature of T. ('F). The compressor is then turned on and begins to chill down the milk at the same time that fresh warm milk at T, ('F) is added at a volumetric flow rate of q (ft'/min) through a pipeline from the milking parlor. The total volume of milk in the tank increases to Vr after all of the cows have been milked. (a) Derive a dynamic model for the process so that the temperature of the milk can be determined as a function of time. (b) Perform a degrees of freedom analysis. Identify all of the model constants, input variables and output variables.
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