SAPO Fluids 8.1.png - The force acting on a circular...

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Unformatted text preview: The force acting on a circular surface ct radius r due to a gas with pressure P is: F= PA = Pip-2 Since there is air an both the Upper and IWEr sides cf the cylinder, the total pressure flame acting on the cylinder I5: FL - F“ = {PL — 1*")an The sign convention here is selected such that "up" is the positive direction the pressure in the lower rt of the tithe would act to push the cylinder up+ and the pressure In the upper part the tube 1llleuld act to pus the cylinder eel-m}. Greylty also acts to pull the cylinder downward, so the total force acting on the cylinder is: Fuel = [PL - Pei”: — mg Ely Newton's 2nd law. this is equal to the cylinder's rnass times its acceleration. When the cylinder is initially at rest (before the plunger is pushefih its acceleration is zeror so the pressure in the Ll errand lower portions of the tube must not be the same. ile the upper portion of the pipe is open [and let erefore at ambient pressure equal to 1 atmes here}, the Inner portion ofthe Pipe is not. The air in the lawyer porticn of the pipe has been the compressed by presence of the cytinder unti pressure imbalance became large enough to balance the farce of gravity. Setting the net force equal to ears and solving ferthe presstre in the lower region gives: ...
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