Question

A thin spherical pressure vessel is subjected to an internal pressure of 4 N/mm². The mass of the empty vessel should not exceed 125 kg. If the factor of safety is 3.0, design the pressure vessel with the objective of maximizing the gas storage capacity, out of the following materials : Material Ultimate Tensile Strength Mass Density Su N/mm² p, kg/m Low Alloy Steel - 15 Cr90 M055 500 7800 Aluminium Alloy - 74530 250 2800 Copper Alloy - Cu Ni31 Mnl Fe 420 8400

Answer 1

p=4 N/mm² {pressure} Analysis based upon Low alloy Steel - 15690 mo55 as the material for thin spherical pressure versel. pd < Sut Tind 4+ Sut where p= Pressure inside the versel = 4 N/mm² d = diameter of versel t - thickness of versel 500 N/mme for low alloy steel N = factor of safety = 3 Tind- underced tensile stres 43d E 500 4+t 500 max. capacity. 4-5 for 500 3 1 de d = 500 t 3 Mais of the versel made from alloy steel < 125 Pored + d²+ t < 125 78000 T (500 +)?+ 5125 + = 125+ 32 It = 5.684 mm extreme Conditions 500² T *7800

Copacity of this tank 4 xd - Ad 6 where t= 5.684mm V = 2670940171 mmo 2.671 m² { for alloy steel tank} V= 0.44 516 m² ] {correct valur? Analysis based upon Vessel Aluminium alloy- 74530 ed < Sut Tind: N 4E 4 *d 4+t 250 3 [(Sut) Az = 250 d 3 250 € d = 250t mais of the vessel - Pal* +d²x t = 125 - 2800 * * * * (2504)2 +=125

- 13 125*9 2800 x 2502 = 12.7 mr Capacity of aluminium based Wessel: = 4() Td² 6 T # ( 25o 4 tj? & [250 -12.7] 0.62067 m3 Analysis based upon Copper Alloy wessel: pd < Sut 4t N (sut cepper = 420 4*d s 420 4*t 420 of € 140t d=140t { for max. Capacity

Mas of the versel : Pau x d² x t = 125 [ for max. Capacity 84000 * T * (402)² = 125 t3 - 125 8400 * T * 1402 t- 6.2288 mm Capacity of Copper based sphersial vesel - Id² 6 T (140+)3 X (140* 6+2288)3 V=0.3472 m3 Capacity of Aleminium based vessel Capacity of Steel based Capacity of copper based 0.6 2067 7 0.44 516 7 0.3472 hence All Aluminum alloy-74530 should be used for spherical vessel having parameters as: de 250 x t = 250 x 12 Anywer x 12.7 = 1.0583m It= 12.7 mm
i have calculated capacity of vessel for all the materials listed based upon the strength and maximum mass criteria.I reached to the conclusion that aluminium alloy should be used for making the vessel of largest capcity among them.