There is an overpressure p inside the spherical pressure vessel. The wall thickness t of the...

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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. (1 p.) b) Determine the symbolic expression for the wall stress. (2 p.) c) How many percent larger is the volume of the pressurized sphere compared to the unpressurized one (coefficient of volumetric expansion is e)? Pressure p=3 MPa, wall thickness t=0.01 m, radius r = 1.6 m and Young's modulus E = 210000 MN/m (2 p.) Instructions for the part a: Draw the hemisphere and the pressure p and tension acting on it. P E 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. (1 p.) b) Determine the symbolic expression for the wall stress. (2 p.) c) How many percent larger is the volume of the pressurized sphere compared to the unpressurized one (coefficient of volumetric expansion is e)? Pressure p=3 MPa, wall thickness t=0.01 m, radius r = 1.6 m and Young's modulus E = 210000 MN/m (2 p.) Instructions for the part a: Draw the hemisphere and the pressure p and tension acting on it. P E