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# ecm 3 soln - ECM 5 Winter 2009 Problem Set 3 Due This...

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ECM 5 Winter, 2009 Problem Set 3 Due 1/14/08 This problem gives students the opportunity to use their tank-draining data, to visualize a more complex system than was used in the laboratory and to relate it to the laboratory system, and to use graphical methods in problem solving. 1 . Consider three tanks that are identical to the one you used in the laboratory. Assume that two of the tanks are mounted directly above the third so that the flow from the upper two tanks goes directly into the lower tank. Also assume the following: the first upper tank (tank A) is initially filled to a height above the orifice of 50 cm; the second upper tank (tank B) is initially filled to a height above the orifice of 25 cm; the lower tank (tank C) is initially empty; the plug is removed from each of the two upper tanks at t = 0; the plug is removed from the lower tank when the liquid level above the orifice in the lower tank is 40 cm. Use graphical methods and the data that you obtained in the laboratory to determine the height of liquid in each tank above the orifice as a function of time t and show the results in a graph. The graph will have three lines; label them A, B, and C, respectively, for the two upper tanks and lower tank. Notes: The rate of tank draining is dependent on the height of liquid in the tank. As was observed in the lab, as the tank levels dropped, the rate of flow from the draining tank decreased. In the case of this assignment, two of the tanks simply drain. However, the lower tank (tank C) accumulates water by inflow from tanks B and C and does not lose water until the plug is removed. So for some period tank C is characterized by an increasing liquid height and for some period it is characterized by a decreasing liquid height. If you did not collect data in the laboratory, or something is wrong with the data you did collect, then send an email to the instructors or the TA’s and do the assignment with their data, which they will send you.

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