$2.(20$ points$)$ The hydrant valve shown below carries pressurized water in a pipe network. The valve cover is secured using six $\backslash (3/4-10\backslash )$ UNC SAE grade $5$ bolts and must withstand a maximum internal pressure of $500$ psi. The local municipal code requires that the stress in the bolts not exceed one third of the proof strength. A rubber gasket with the dimensions shown is installed between the valve cover and pipe section below. To provide proper sealing, the gasket must be compressed with a pressure of $\backslash (300\backslash$mathrm$\{$psi$\}+/-10\backslash \%\backslash )$ at all times. The stiffness of the bolts is $9$ times greater than that of the gasket.

a$)(4$ points$)$ What bolt torque $($inch lbs$)$ would produce the maximum gasket clamping pressure?

b$)(8$ points$)$ Is the stress in the bolts acceptable at the maximum internal pressure?

c$)(6$ points$)$ Is the gasket clamping pressure acceptable at the maximum internal pressure?

d$)(2$ points$)$ Is this an optimally sized bolt for the application? Would the stress in the next size smaller bolt still be acceptable? Assume the gasket would not change in this case.

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