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30 June, 23:53

Air is contained in a vertical piston-cylinder assembly such that the piston is in static equilibrium. the atmosphere exerts a pressure of 14.7 lbf/in2 on top of the 6-in-diameter piston. the absolute pressure of the air inside the cylinder is 16 lbf/in2. the local acceleration of gravity is g = 32.2 ft/s2. determine (a) the mass of the piston, in lb, and (b) the gage pressure of the air in the cylinder, in psig

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  1. 1 July, 00:20
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    Refer to the diagram shown.

    p₁ = 14.7 psia, atmospheric pressure

    p₂ = 16 psia, absolute pressure in the cylinder

    The weight of the piston is

    W = mg

    where m = mass of the piston.

    g = 32.2 ft/s² = 386.4 in/s²

    The area of the piston is

    A = (π/4) * (6 in) ² = 28.273 in²

    Part a:

    For equilibrium,

    (p₂ - p₁) A = W

    (16 - 14.7) * (28.273) = (386.4) * (m)

    m = 0.095 lb

    Answer: m = 0.095 lb

    Part b:

    The gage pressure in the cylinder is

    p₂ - p₁ = 16 - 14.7 = 1.3 lb/in²

    Answer: 1.3 lb/in²
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