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Mathinline body \sigma_{hoop} = \frac{pR}{t}
Given Aluminum 6061-T6 as the material, which typically has a tensile yield strength of approximately 276 MPA (this analysis neglects the internal temperature of the piston due to the combustion of black powder, because we assume the temperature effects will be transient).
Resources:
The following resources are useful materials for learning about pressure vessel and piston theory:
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