# Mechanics - cylindrical steel pressure vessel

1. Dec 3, 2013

### designmind93

mechanics -- cylindrical steel pressure vessel

1. The problem statement, all variables and given/known data

A thin-walled, closed-end, cylindrical steel pressure vessel, internal diameter 500 mm and wall-thickness 10 mm, has an internal volume 0.5 cubic metres. Find the additional volume of a compressible fluid that must be pumped in at a pressure of 20 bar and fill the vessel completely. Take for steel: E = 210 GPa, Nu = 0.25 and for the fluid K = 2500 MPa. If the flat end plates are replaced by two thin-walled hemi-spheres of similar internal diameter, what should be the correct ratio of thickness between the sphere and cylinder? How much additional volume of fluid (due to the strain expansion of the vessel) is required to fill the vessel completely at the pressure of 20 bar?

2. Relevant equations

3pd/4tE (1- Nu) + pv/K + 638.1 x 10^-6

3. The attempt at a solution

Additional volume = 638.1 x 10^-6 m^3

ratio = 3/7

thickness of sphere = 4.29 mm

How do i go about solving the bit in bold?

My lecturer gave me the formula, but I cannot make the answer equal to 731.4 x 10^-6 m^3 which he says it will....

if anyone can solve this and show how they did it i would very much appreciate it!