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In the bubble

An inflatable “bubble” is used to cover a tennis court during winter. The covered ground area is circular with a diameter D and the material of the bubble is flexible plastic with a weight W and a density ρ.

a) Assume that the inflated bubble has a hemispherical shape. Determine the minimum absolute pressure inside the bubble that can sustain it from collapsing. Do not neglect buoyancy but neglect hydrostatic pressure differences in air. Explain your solution in detail, justifying all assumptions and statements and providing appropriate sketches indicating the different forces.

b) Now assume that the inflated bubble has a cylindrical shape, with the flat side on top. The weight and density of the bubble remain the same as in (a). Describe whether the minimum pressure required to sustain this bubble from collapsing would be higher, lower, or equal to the one for the hemispherical bubble.

c) Assume that the pressure inside the hemispherical bubble is 10% higher than that found in (a). Determine the force on the ground supports that hold the bubble down.

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

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