Determine the maximum allowable pressure, $\backslash ($ p$\_\{\backslash$mathrm$\{$c$\},\backslash$max $\}\backslash ),$ in the cylindrical pressure vessel.

Express your answer in psi to three significant figures.

Learning Goal:

To calculate the maximum allowable stresses in pressure vessels, compute the minimum allowable thickness of pressure vessels to meet certain constraints, and observe and compare properties of different pressure vessel shapes.

Engineers are considering two possible vessel shapes for storing fuel. One shape is cylindrical and the other is spherical. Each vessel would be constructed out of the same material such that its hoop stresses and longitudinal stresses would be no greater than $16\mathrm{.}0$ ksi $.$ The cylindrical pressure vessel has an inside diameter of $\backslash ($ d$\_\{$c$\}=30\mathrm{.}0\backslash )$ in and a thickness of $\backslash ($ t$\_\{$c$\}=0\mathrm{.}750\backslash$mathrm$\{$in$\}\backslash ).$ The spherical pressure vessel has an inside diameter of $\backslash ($ d$\_\{$s$\}=25\mathrm{.}0\backslash )$ in and a thickness of $\backslash ($ t$\_\{$s$\}=0\mathrm{.}500\backslash$mathrm$\{$in$\}\backslash ).$

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Part B $-$ Maximum allowable pressure in the spherical pressure vessel

Determine the maximum allowable pressure, $\backslash ($ p$\_\{\backslash$mathrm$\{$s$\},\backslash$max $\}\backslash ),$ in the spherical pressure vessel.

Express your answer in psi to three significant figures.

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Part C $-$ Required thickness of the cylindrical pressure vessel for maximum pressure equivalency

Determine the required thickness of the cylindrical pressure vessel, $\backslash ($ t$\_\{$r$\}\backslash ),$ if it is subjected to the maximum allowable pressure of the spherical pressure vessel that was calculated in Part B $.$ Express your answer to three significant figures and include appropriate units.

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t$\_\{$r$\}=$

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