A spherical pressure vessel is required to contain 1.5 m3 of compressed natural gas at 22 MPa . If the tank is made of A516 grade 60 steel with a maximum normal stress 150 MPa , what is the required thickness of the tank wall?
Accepted Solution
A:
Answer:The required thickness of the tank wall is 87.7668 mm.Step-by-step explanation:Given : Volume of vessel is V=1.5 m³.A spherical pressure vessel is of compressed natural gas at P=22 MPa. If the tank is made of A516 grade 60 steel with a maximum normal stress 150 MPa.i.e. [tex]\sigma_{max}=150\ Mpa[/tex]To find : What is the required thickness of the tank wall?Solution : The diameter of the vessel is given by,[tex]\frac{d}{2}=\sqrt{\frac{3V}{4\pi} }[/tex][tex]\frac{d}{2}=\sqrt{\frac{3\times 1.5}{4\times 3.14}}[/tex][tex]\frac{d}{2}=\sqrt{\frac{4.5}{12.56}}[/tex][tex]\frac{d}{2}=\sqrt{0.358}[/tex][tex]\frac{d}{2}=0.598[/tex][tex]d=1.196\ m[/tex]Convert into mm,[tex]d=1.196\times 1000=1196.82\ mm[/tex]The thickness of the wall tank is given by,[tex]t=\frac{Pd}{2\sigma}[/tex][tex]t=\frac{22\times 1196.82}{2\times 150}[/tex][tex]t=\frac{26330.04}{300}[/tex][tex]t=87.7668[/tex]Therefore, the required thickness of the tank wall is 87.7668 mm.