A thin walled cylindrical pressure vessel having a radius of 0.5 m and...
Understanding the Problem
To find the hoop stress in a thin-walled cylindrical pressure vessel, we can use the formula for hoop stress (σ_h):
σ_h = (P * r) / t
Where:
- P = Internal Pressure
- r = Radius of the cylinder
- t = Wall Thickness
Given values:
- P = 700 kPa = 700,000 Pa
- r = 0.5 m = 500 mm
- t = 25 mm = 0.025 m
Calculating the Hoop Stress
1. Convert Units:
- Ensure all dimensions are in meters for consistency:
- P = 700,000 Pa
- r = 0.5 m
- t = 0.025 m
2. Substitute Values into the Formula:
- σ_h = (700,000 * 0.5) / 0.025
3. Perform the Calculation:
- σ_h = (350,000) / 0.025
- σ_h = 14,000,000 Pa
Final Result
- Convert the stress into MPa for easier interpretation:
- 14,000,000 Pa = 14 MPa
Thus, the hoop stress developed in the thin-walled cylindrical pressure vessel is:
Answer: 14 MPa (Option A)
Conclusion
- This result indicates a significant amount of stress in the vessel's walls due to the internal pressure.
- Understanding hoop stress is essential in designing safe pressure vessels to prevent failure.