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Found the Solution I would like to thank everyone, especially @Baluncore for their responses. It is great to see people interested in the same topic. I was able to get the correct solution even though I still do not understand the compressed liquid water tables. The solution is found by...

There is no air in the tank. I first pull a perfect vacuum and pump water into the tank. This is a thought experiment so I can do things like pull a perfect vacuum. Also, there are no temperature changes. As I stated in the problem the process is isothermal. I am not being inconsistent. I...

Correction I forgot to square the stress so the expression for the total strain energy was incorrect. It should be U=\frac{V}{2E} \left(\sigma_\theta^2+\sigma_z^2\right)≈\frac{1.25rtL}{E}\frac{p^2r^2}{t^2}, which then has the correct units of force times distance.

Your response does not answer the question and is misleading. Of course, as much air as possible should be evacuated. However, to say that little energy is stored in the liquid or vessel walls is wrong and dangerous. It all depends on the situation. Just look at the strain energy for a long...

How is potential energy normally calculated I am defining the potential energy as the difference between the total internal energy U2 at (Pmax, Tam) and U1 at (Tatm, Patm). Pmax is the maximum pressure, Tatm is the atmospheric temperature, and Patm is the atmospheric pressure. My first...

I have a pressure vessel of volume V= 1 m^3 . The atmospheric pressure Patm = 101 kPa and Tatm = 22 C. I slowly pump liquid water into the pressure vessel until the internal pressure reaches P1 = 15 MPa. Also, the process is isothermal because the water was pumped in slowly and heat is exchange...

Answer There is a typo in my post above because (1+b) should be (1+v) in the denominator of the expression for P. The mistake I made was using the lame's equations for plain stress, while the problem wanted to plane strain solution. The expression for P matches the given result by making the...

Homework Statement A long, hollow, thick elastic cylinder (E , v) is surrounded by a thin elastic band of thickness t made of a different material (E_2 , v_2). The fit is ideal, such that neither a gap nor a pressure exists. An internal pressure p is then applied at the inside radius (r=a) of...