Alight pressure vessel is made of 2024-t3 aluminum alloy tubing with suitable end closures. this cylinder has a 90mm od,

Alight pressure vessel is made of 2024-t3 aluminum alloy tubing with suitable end closures. this cylinder has a 90mm od, a 1.65mm wall thickness, and poisson's ratio 0.334. the purchase order specifies a minimum yield strength pf 320 mpa. what is the factor of safety if the pressure-release valve is set at 3.5 mpa?

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  1. Given:

    Outer Diameter, OD = 90 mm

    thickness, t = 0.1656 mm

    Poisson's ratio, [tex]\mu[/tex] = 0.334

    Strength = 320 MPa

    Pressure, P =3.5 MPa

    Formula Used:

    1).  [tex]Axial Stress_{max}[/tex] = [tex]P[\frac{r_{o}^{2} + r_{i}^{2}}{r_{o}^{2} - r_{i}^{2}}][/tex]

    2). factor of safety, m = [tex]\frac{strength}{stress_{max}}[/tex]

    Explanation:

    Now, for Inner Diameter of cylinder, ID = OD - 2t

    ID = 90 - 2(1.65) = 86.7 mm

    Outer radius,  [tex]r_{o}[/tex] = 45mm

    Inner radius,  [tex]r_{i}[/tex] = 43.35 mm

    Now by using the given formula (1)

      [tex]Axial Stress_{max}[/tex] = [tex]3.5[\frac{45^{2} + 43.35^{2}}{45^{2} - 43.35^{2}}][/tex]

      [tex]Axial Stress_{max}[/tex] = [tex]3.5\times 26.78[/tex] =93.74 MPa

    Now, Using formula (2)

    factor of safety, m = \frac{320}{93.74} = 3.414

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