Respuesta :
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.
