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Charles Link said:You need to write ## dW=(P_2-P_1)A \,dr=S \, dA' ##, where ## A=(2 \pi r) \, L ## and ## A'=2 \, ( 2 \pi r) \, L ##. Does that seem logical? ## \\ ##
Chestermiller said:If you slit the cylinder in half lengthwise and do a force balance on one of the halves, you have the following:
Pressure force on the half cylinder = ##\Delta P (2RL)##
Surface force on the half cylinder = ##4SL##
## A ## is the surface area of the sphere or cylinder. ## A' ## is the surface area that forms the surface tension. For a spherical droplet ## A =A' ##, but for a soap bubble with two surfaces,(inside and outside), and also for this cylindrical bubble that has two surfaces, ## A'=2 A ##.Jahnavi said:What is A' and dA' ?
Yes.Jahnavi said:In the expression for dW , A would be the outer surface area of the bubble , the one that is exposed to atmospheric pressure . Right ?
They were just trying to try to avoid the effects of putting end faces on it. It really doesn't need to be long. It can be a cylindrical bubble contained between two metal discs as @haruspex points out above. I agree with his input that otherwise, a cylindrical bubble is very hypothetical and simply does not occur in the real world. In many ways, these equations could be describing a cylindrical (elongated) balloon though, so it can be worthwhile to perform the computation as it may have other real world applications. (The tension in a balloon will increase with increasing dimensions, so I am only making a loose comparison here).Jahnavi said:Why do you think the cylinder has to be "very long " ?
Charles Link said:They were just trying to try to avoid the effects of putting end faces on it. It really doesn't need to be long. It can be a cylindrical bubble contained between two metal discs as @haruspex points out above. I agree with his input that otherwise, a cylindrical bubble is very hypothetical and simply does not occur in the real world. In many ways, these equations could be describing a cylindrical (elongated) balloon though, so it can be worthwhile to perform the computation as it may have other real world applications. (The tension in a balloon will increase with increasing dimensions, so I am only making a loose comparison here).