Methanol is added to a storage tank at a rate of 1200 kg/h and is simultaneously

Chapter 10, Problem 10.3

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Methanol is added to a storage tank at a rate of 1200 kg/h and is simultaneously withdrawn at a rate m_ wtkg/h that increases linearly with time. At t 0 the tank contains 750 kg of the liquid and m_ w 750 kg/h. Five hours later m_ w equals 1000 kg/h. (a) Calculate an expression for m_ wt, letting t 0 signify the time at which m_ w 750 kg/h, and incorporate it into a differential methanol balance, letting Mkg be the mass of methanol in the tank at any time. 591 WEBC10 06/04/2015 22:56:56 Page 592 (b) Integrate the balance equation to obtain an expression for Mt and check the solution two ways. (See Example 10.2-1.) For now, assume that the tank has an infinite capacity. (c) Calculate how long it will take for the mass of methanol in the tank to reach its maximum value, and calculate that value. Then calculate the time it will take to empty the tank. (d) Now suppose the tank volume is 3.40 m3 . Draw a plot of M versus t, covering the period from t 0 to an hour after the tank is empty. Write expressions for Mt in each time range when the function changes.