Suppose that you were asked to select a material for a spherical pressure vessel to be used in an aerospace application. The stress in the vessel wall is =2tpr where p is the internal pressure, r is the outer radius of the sphere, and t is the wall thickness. The mass of the vessel is m=4r2t where is the material density. The operating stress of the vessel will always be SY.S where S is a safety factor. (a) Show that the minimum mass of the pressure vessel will be m=2Spr3Y.S (b) Given Table 6.1 and the following data, select the alloy that will produce the lightest vessel. "Alloy designations and associated properties cited in this table and Tubles 63 and 6.10 are from Matals Hasdlook, Sth ef, Vol, 1 , and 9 th ed., Volk. 1-3,American Society for Metals, Metals Park, OH, 1961, 1978, 1979, and 1980. (c) Given Table 6.1 and the data in the preceding table, select the alloy that will produce the minimum cost vessel. Suppose that you were asked to select a material for a spherical pressure vessel to be used in an aerospace application. The stress in the vessel wall is =2tpr where p is the internal pressure, r is the outer radius of the sphere, and t is the wall thickness. The mass of the vessel is m=4r2t where is the material density. The operating stress of the vessel will always be SY.S where S is a safety factor. (a) Show that the minimum mass of the pressure vessel will be m=2Spr3Y.S (b) Given Table 6.1 and the following data, select the alloy that will produce the lightest vessel. "Alloy designations and associated properties cited in this table and Tubles 63 and 6.10 are from Matals Hasdlook, Sth ef, Vol, 1 , and 9 th ed., Volk. 1-3,American Society for Metals, Metals Park, OH, 1961, 1978, 1979, and 1980. (c) Given Table 6.1 and the data in the preceding table, select the alloy that will produce the minimum cost vessel