Since this vessel will be fully submerged, it is essential to analyze the hydrostatic forces acting on the outside of the vessel. Beginning with a hand calculation of the stresses building up in the main body PVC tubing, then calculating a factor of safety for different depths, up to the maximum depth of ten meters. The first thing that must be calculated is the change in pressure, which is computed by the following equation.
This will give us the change in pressure, depending on the depth. This change in pressure will be used to calculate the von mises stress. There are three principal stresses acting on the pressure vessel. The hoop stress, longitudinal stress, and thickness stress. The equations for these values are as follows.
Using these three principles stresses and plugging their equations onto the von mises stress and simplifying, we end up with the simple to understand equations of the following.
Which can then be simplified to
Equation 5 simplifies the von Mises stress for the entire system. Then the Factor of Safety (or Safety Factor) for the material under loading is found by comparing the von Mises equivalent stress to the yield stress of the material. If the von Mises stress is found to be greater than the material’s yield stress, the material will not be able to support the load
Factor of Safety
The Factor of Safety can be determined for a variety of depths. The material being analyzed is the size four PVC tubing. The figure below is a cross-sectional drawing in inches from McMaster-Carr.
Using a Microsoft Excel spreadsheet, the Factor of Safety for a variety of different depths was calculated. The depths analyzed are zero to fifteen meters. The maximum dive depth possible while using this material is estimated to be 215 meters.
The material we have selected is expected to perform at the operating depth with a large margin of safety. Since standard Schedule 40 PVC pipe is cheap and readily available, it is unnecessary to attempt optimization of the pipe wall thickness. Future teams using our design will be able to dive too much greater depths. As seen in the table above, the maximum Factor of Safety at operating depth is 33.30. The yield strength of PVC can be found in Appendix A. Below is a chart of how the Factor of Safety as determined by the von Mises stress changes with depth.
Now to verify our results we need to throw them in SolidWorks simulation. Due to constraining problems, it was impossible to apply the hydrostatic force to the entire vessel. This is because as the entire model shrinks it produces very unrealistic results on the constraints holding it back, for example, we were getting displacements of greater than fifty inches. So in order to verify our results we were able to place roller support on two ends of a pipe so therefore it could shrink and expand as pleased without affecting the simulation. We set the pipe properties to PVC rigid which again is in the appendix for the mechanical properties. Then we applied the changing pressure force to compensate for the atmospheric pressure inside the vessel in ran the simulation to see the von misses. As expected, our result came back within 10% of what we calculated, and our factor of safety was verified.