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

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