Question

Consider a thin-walled cylindrical tube having a radius of 65 mm that is to be used to transport pressurized gas. (a) (10 points) If inside and outside tube pressures are 11 and 1.0 MPa, respectively, compute the minimum required thickness for a steel pressure vessel with a yield strength of 1000 MPa. Assume a factor of safety of 3.5.

Answer 1

Answer:

The minimum required thickness for a steel pressure vessel (t) is 2.275 mm

Explanation:

Minimum required thickness is the thickness of a material without corrosion allowance for each component  based on the appropriate design that consider pressure, mechanical and structural loading.

Given that:

radius (r) = 65 mm = 65 × 10⁻³ m

Factor of safety (N) = 3.5

Inside presssure ($P_{in}$) = 11 MPa

Outside pressure ($P_{out}$) = 1 MPa

Yield strength ($\sigma_y$) = 1000 MPa

Therefore:

$\sigma_y =\frac{\sigma_y}{N}$, Substituting values,

$\sigma_y =\frac{\sigma_y}{N}=\frac{1000}{3.5}=285.714 MPa$

The minimum required thickness for a steel pressure vessel (t) is given by the equation:

$t=\frac{r.(P_{in}-P_{out})}{\sigma_y}$. Substituting values

$t=\frac{r.(P_{in}-P_{out})}{\sigma_y}=\frac{65*10^{-3} *(11-1)10^{6} }{285.714*10^{6} } =2.275*10^{-3} =2.275 mm$

The minimum required thickness for a steel pressure vessel (t) is 2.275 mm