Determining Hoop and Longitudinal Stress in a Compressed-Air Tank
What are the hoop stress and longitudinal stress in the cylindrical body of a compressed-air tank with specific dimensions and internal pressure?
Calculating Hoop Stress:
Hoop Stress = (Pressure × Diameter) / (2 × Thickness)
Given:
Internal gage pressure: 180 psi
Cylindrical body outer diameter: 30 inches
Thickness of the steel plate: 3/8 inch
Substituting the given values into the formula, we get:
Hoop Stress = (180 psi × 30 inches) / (2 × 3/8 inch)
Hoop Stress = 180 × 30 × 8 / (2 × 3)
Hoop Stress = 7200 psi
Therefore, the hoop stress in the cylindrical body of the compressed-air tank is approximately 7200 psi.
Calculating Longitudinal Stress:
The longitudinal stress in the cylindrical body of the compressed-air tank can be determined using the formula:Longitudinal Stress = (Pressure × Diameter) / (4 × Thickness)
Substituting the given values into the formula, we get:
Longitudinal Stress = (180 psi × 30 inches) / (4 × 3/8 inch) Longitudinal Stress = 180 × 30 × 8 / (4 × 3) Longitudinal Stress = 4800 psi
Therefore, the longitudinal stress in the cylindrical body of the compressed-air tank is approximately 4800 psi.
Understanding Hoop and Longitudinal Stress in Compressed-Air Tanks
When a compressed-air tank is subjected to internal pressure, it experiences stress in different directions. The hoop stress is the stress acting circumferentially around the cylindrical body of the tank, while the longitudinal stress is the stress acting along the length of the tank.In the given scenario, the hoop stress was calculated to be 7200 psi, indicating the maximum stress experienced by the tank's cylindrical body due to the internal pressure. On the other hand, the longitudinal stress was determined to be 4800 psi, representing the stress along the length of the tank.
It is essential to calculate and understand these stress values to ensure the structural integrity and safety of the compressed-air tank. By analyzing the hoop and longitudinal stresses, engineers can design tanks that can withstand the pressure requirements and prevent any potential failure.