9. A cylindrical pressure vessel is subjected to an internal pressure  and the allowable tangential stress of the vessel is . The vessel has a wall thickness  in. The factor of safety is . a) What is the maximum inside diameter of the vessel? Then select a preferred diameter. b) If , , and  and  are independent, determine the probability of failure using the First Order Second Moment Method. Use the theory of thin-walled vessels.

Answer:  a) , ; b)