Determine the enhance in volume of the vessel:
A thin spherical vessel of diameter 800 mm and thickness 6 mm is filled through a liquid at an internal pressure of 1.5 N/mm^{2}. Determine the enhance in volume of the vessel, taking E = 2 × 105 N/mm^{2} and v = 0.3.
Solution
Diameter of the vessel, d = 800 mm.
Thickness, t = 6 mm.
Internal pressure, p = 1.5 N/mm^{2}.
∴ Hoop stress, σ_{h} = pd /4t = 1.5 × 800 / (4 × 6 )= 50 N/mm^{2}
∴ Hoop strain, ε = (σ_{h} /E)(1 - v) =(50/2 × 10^{5}) (1 - 0.3) = 1.75 × 10^{- 4}
∴ Volumetric strain, εv = 3 × εh
= 3 × (1.75 × 10- 4 ) = 5.25 × 10^{- 4}
∴ Original volume, V = π d ^{3} / 6
= π× 800^{3 }/6= 2.6808 × 10^{8 } mm^{3}
∴ Increase in volume, δV = ε_{v} × V
= 5.25 × 10^{- 4} × 2.6808 × 10^{8} = 140743 mm^{3}