Question

A spherical pressure vessel is formed using 20 gauge (0.0359 inch) cold drawn AISI 1020 steel sheet, Syield-57,000 psi, Sultimate 68,000 psi. density 0.282 lb/cubic inch Temperature is 75 F. mine the maximum pressure in the tank for an inner diameter of 15 inches using yield Deter Volume of sphere 4/3*pi*radius cubed Surface area of a sphere -4*pi'r squared. Calculate the minimum tank weight in lbm using a 15% factor for weld thickness and fittings. strength with a factor of safety of four. How much air can the tank hold in Ibm? R- 53.35 ft-lbf/lbmRPvmT P .15 t 0.03694 ut 37 Sy 57000 =1136.6 81 57,600 loy.5P = 1167 in

Answer 1

SOLUTION Given: Spherical pressure Vessel At inner watt of the vessel , in x and y direction , the stresses are eaud Ox-Gy σ , but the stess in the z-dive ction is not zero and itis equal to Pressuy P in comprssio n c leaty, the element is n Tiaxial stress Pd The maximum out -of -plane shear stress 4t 2 We have, ', Syidd: 57000 psi Factor of sakty, Fs 4 t=0.0359 tnch d=15inch using yled sternth yield stergth in sheas Fom 4 ) max = (allowable Syield 2*4 57000 Sy ield ree) _ = 135,126 psi 1 5 | P = 135-126 Psi

Calculatron of Tank weght Volume of sphere material = 4ㅈ(Ht)3-3113 2 2 V= 25.497g inch o+t) T-14 inch Density, p = 0.282 lb/cubic inch 2 Mass = PV =0.282×25.4979 ヲ | Mass = 7.19 lbm

Now taking 15. factos for weld thicknes fittiry Total weght 1-15% 7.13 = 8.2685 bm Cal culation of aix Vi1767.145 ubic inch (4767.145 x 1 639 xl5 cubic mehe V;28.96 351 l-3 cublc mebe T75 F297.64 Kelvin P 135-126 Psi 931.66 КРа Using idel gas eq uation %28 . 96 351 x1D-3 mx 0.28 7 x 257.04 - g31.66 m 0.31 65 3 m (0-31653 x 2.2046) tbm