A tank contains 2 m3 of water. A stream of brine containing 20kg/m3 of salt is...

 

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A tank contains 2 m3 of water. A stream of brine containing 20kg/m3 of salt is fed into the tank at a rate of 0.02m3/s. Liquid flows from the tank at a rate of 0.01 m3/s. The tank is well agitated. Your task is to find the salt concentration for a given volume in the tank, the amount of salt in the tank at any given time, and the time elapsed to obtain a given amount of salt in the tank, as stated below. A. Using the above information: (1) Draw a simple sketch of the system (6 points) (2) Write down all conservation rate equations applicable to the system (4 points) (3) List and justify all simplifying assumptions (9 points) (4) Using the simplifying assumptions derive the final forms of all the applicable conservation rate equations (26 points) B. From the final forms of the applicable rate equations obtained in A(4) above set up the appropriate differential equations and: (1) Calculate the salt concentration in the tank when the tank contains 4 m3 of brine (40 points) (2) The amount of salt in the tank at any time t, from B.1 (7 points), and (3) The elapsed time when the amount of salt in the tank is 30 kg, from B.2. A tank contains 2 m3 of water. A stream of brine containing 20kg/m3 of salt is fed into the tank at a rate of 0.02m3/s. Liquid flows from the tank at a rate of 0.01 m3/s. The tank is well agitated. Your task is to find the salt concentration for a given volume in the tank, the amount of salt in the tank at any given time, and the time elapsed to obtain a given amount of salt in the tank, as stated below. A. Using the above information: (1) Draw a simple sketch of the system (6 points) (2) Write down all conservation rate equations applicable to the system (4 points) (3) List and justify all simplifying assumptions (9 points) (4) Using the simplifying assumptions derive the final forms of all the applicable conservation rate equations (26 points) B. From the final forms of the applicable rate equations obtained in A(4) above set up the appropriate differential equations and: (1) Calculate the salt concentration in the tank when the tank contains 4 m3 of brine (40 points) (2) The amount of salt in the tank at any time t, from B.1 (7 points), and (3) The elapsed time when the amount of salt in the tank is 30 kg, from B.2.