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?

import math

x=int(input("enter a number: "))

print (math.sqrt(math.fabs(

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

Answer:

the answer is d.

explanation: