After a day's hard work, you decide to take a relaxing, warm bath. So, you close the tube outlet of your bathtub and open the water tap. You need about 300 liters of water in your bath. The flow rate of water from the tap is 0.5L/s. You don't need Transport Phenomena to know that will take 600 seconds to fill your bath. But the question is: what if you use the concepts of transport phenomena? Please refer to Exercise 1.1. While relaxing in your bath, you start wondering: "what would have happened if I had forgotten to close the outlet of the bath"? You decide to make a rough estimate and assume the following: - your bath is rectangular, with a width of 0.5m, a length of 2m and a height of 0.5m; - the outflow is proportional to the height of the water present (not true, but that doesn't matter for this exercise); - the proportionality constant is 2.5103m2/s The flow rate of water from the tap is still 0.5L/s. (a) Make a sketch of the situation and draw only the relevant quantities. (b) Set up a mass balance for the water in your bath. (c) What is precisely the control volume you have chosen? Check the dimensions of all terms in your balance: are they all the same? Do they all reflect that you have set up a mass balance? (d) Find the steady state height of the water in your bath, without solving the complete mass balance from (b). (e) You obviously would have found out that the outlet is open when you come back to close the tap. Assume you were back after 8 minutes. Solve the mass balance and find the height of the water in your bath at t=480 seconds. Check the dimensions in your calculation