Determine the enhance in volume of the vessel, Mechanical Engineering

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/mm2. Determine the enhance in volume of the vessel, taking E = 2 × 105 N/mm2 and v = 0.3.

Solution

Diameter of the vessel, d = 800 mm.

Thickness, t = 6 mm.

Internal pressure, p = 1.5 N/mm2.

 ∴ Hoop stress, σh  = pd /4t = 1.5 × 800 / (4 × 6 )= 50 N/mm2

∴ Hoop strain, ε  = (σh /E)(1 - v) =(50/2 × 105) (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× 8003 /6= 2.6808 × 108  mm3

∴ Increase in volume, δV = εv × V

= 5.25 × 10- 4  × 2.6808 × 108  = 140743 mm3

Posted Date: 1/21/2013 2:07:42 AM | Location : United States







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