A2. Pressure vessels Consider the two pressure vessel geometries shown below. Both are thin-walled vessels made of titanium 6A1-4V; both are to be pressurized from 0 to the same pressure, p: and both have the same internal volume. V}, (the v-DIMe of the internal cavityi not the volume of wall material). The rst is a spherical vessel with radius r,. The second is a cylindrical vessel with hemispherical end caps of radius re, and in between, a cylindrical portion with length L = 81C. The vessel initial volumes. pressures, and titanium mechanical properties (Young's modulus, Poisson's ratio. yield stress and density) are: Vb: 0.639 1113, p = 30 MPa. E = 114 GPa, u= 0.34, cry: 880 MPa, p= 4.43 g/cm3 8.) Find the respective constant wall thicknesses, is or tc, needed for each vessel type to supporl pressure, p, with a factor of safety against yielding of l. 1)) Find the resulting weight of each vessel, W, or WC, when empty. c) When the pressure is increased from 0 to p, calculate the thickness change, Ala or Arc, observed in each vessel type and where it occurs. d) Find the volume change, AV, or AVE, in each vessel when pressurized from 0 to p. e) In comparison to the mult obtained in part (b), how much weight can be saved in the cylindrical vessel supporting pressure p, by allowing a reduction in the material thickness in locations where the maximum stress (whether hoop or axial) happens to be signicantly less than the yields stress, cry= 880 MPa. Note: \\Ve ignore any effects of the small transition region in the cylindrical vessel where the end caps join the cylindrical middle