A process control engineer has decided to install an automated shower control system in a bathroom of hr mansion. The design calls for a system that can deliver 3 gpm of water at 110°F by mixing hot water at 170oF, with colder water at 80oF, Flow and temperature transmitters are available along with control valves for adjusting the hot and cold water flow rates.
(a) Calculate the required flow rates of hot and cold water, assuming that the density acid heat capacity of water are constant.
(b) Calculate the relative gain array for the system and recommend a pairing of controlled and manipulated variables