What is the longitudinal stress induced in a thin cylinder under internal pressure?
Calculating Longitudinal Stress in a Thin Cylinder
Longitudinal stress in a thin-walled cylinder under internal pressure can be determined using the formula:
σ = Pr / (2t)
Where:
- σ is the longitudinal stress
- P is the internal pressure
- r is the radius of the cylinder
- t is the thickness of the wall
Given values for the thin cylinder:
- Internal pressure (P) = 2 MPa
- Internal diameter (d) = 1.8 m (convert to radius = 0.9 m)
- Wall thickness (t) = 18 mm = 0.018 m
By substituting these values into the formula, we can calculate the longitudinal stress induced in the cylinder.
Calculation for the Longitudinal Stress
Given:
- Internal pressure (P) = 2 MPa = 2 x 10^6 Pa
- Radius (r) = 0.9 m
- Wall thickness (t) = 0.018 m
Substitute these values into the formula:
σ = (2 x 10^6 Pa * 0.9 m) / (2 * 0.018 m)
σ = 50 x 10^6 Pa = 50 MPa
Therefore, the longitudinal stress induced in the cylinder is 50 MPa.