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Dry cleaner's rocket

A few years ago, newspapers reported a peculiar accident that happened in a dry-cleaning store: steam contained in a pressurized tank escaped through a broken valve, turning the tank into a rocket that travelled some distance before falling through the roof onto the dinner table of some family in some other part of the city. Let us approximately reconstruct the initial stages of that accident. Consider a steam tank weighing 300 N, resting on a support on the floor, as shown in the figure. A malfunctioning valve at the bottom of the tank allows steam to escape vertically downwards. The steam is “choked”, which means that its speed is sonic, which may be taken as 494 m/s. The escaping steam density may be taken as 0.4 kg/m3.
a) Determine the maximum diameter of the valve opening for the tank to remain on its support.
b) Assuming that the valve opening has a diameter of 100 mm, calculate the initial acceleration of the tank.
c) Assuming that the valve is fully open and that the top of the tank is 4 m below the roof, calculate the speed of the tank when it hits the roof. Neglect friction with air and loss of steam mass during this time. At the end of your calculation, check whether the assumption of negligible mass loss is justified.


Contributed by Stavros Tavoularis, Department of Mechanical Engineering,
University of Ottawa, Ottawa, Canada.

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