There is an overpressure p inside the spherical pressure vessel. The wall thickness t of the vessel can be assumed to be small compared to the radius r of the sphere. The radius is measured at the center of the vessel wall. The Young's modulus of the wall material is E.

a) Draw the free-body diagram and solve the symbolic expression for the wall stress.

b) How many percent larger is the volume of the pressurized ball in comparison to unpressurized (coefficient of volume expansion e)?

Values for b):

Overpressure inside the pressure vessel p = 3 MPa

Wall thickness t = 0.01 m

Radius r = 2 m

The Young's modulus E = 210000 MN/m²

P r E