Question: a. Question 2 Consider an inverted conical tank (with radius R and height It) as shown in the Cure below. The tani tank is being

a. Question 2 Consider an inverted conical tank (with radius R and height It) as shown in the Cure below. The tani tank is being filled with water and inlet now rate is 100 ml/min and the initial height of the war in the carlet at the top and an outlet at the bottom. The tank has a height (11) of 40 cm and a radius () of 10 cm. (ha) is 10 cm. Water is also being drawn out of the bottom of the tank at an outlet flow rate of 50 mm Starting from a general mass balance equation for the conical tank, derive the appropriate datterential equation for the mass balance of the system. The differential equation should only be a function of the outlet flow rates. (8 marks) height of the liquid in the tank (h), the height of the tank (1), the radius of the tank (R) and the wler and b. Solve the differential equation from part a) to get the correct expression for the liquid level in the tank as a function of time (i.e. h(t)). (4 marks) For safety, the tank has a level alarm which will be turned on when the water reaches 90% of the total height of the tank. How long will it take for the alarm to be triggered? (2 marks) C. R H a. Question 2 Consider an inverted conical tank (with radius R and height It) as shown in the Cure below. The tani tank is being filled with water and inlet now rate is 100 ml/min and the initial height of the war in the carlet at the top and an outlet at the bottom. The tank has a height (11) of 40 cm and a radius () of 10 cm. (ha) is 10 cm. Water is also being drawn out of the bottom of the tank at an outlet flow rate of 50 mm Starting from a general mass balance equation for the conical tank, derive the appropriate datterential equation for the mass balance of the system. The differential equation should only be a function of the outlet flow rates. (8 marks) height of the liquid in the tank (h), the height of the tank (1), the radius of the tank (R) and the wler and b. Solve the differential equation from part a) to get the correct expression for the liquid level in the tank as a function of time (i.e. h(t)). (4 marks) For safety, the tank has a level alarm which will be turned on when the water reaches 90% of the total height of the tank. How long will it take for the alarm to be triggered? (2 marks) C. R H

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