What is the formula to find the maximum allowable internal pressure in a gas storage tank with cylindrical and hemispherical sections?
To find the maximum allowable internal pressure in the tank, calculate the stress in the tank wall using the formula stress = internal pressure * radius / wall thickness.
Calculating Maximum Allowable Internal Pressure in Gas Storage Tank
The gas storage tank consists of a cylindrical section with two hemispherical end sections. The cylinder has a diameter of 2m and a wall thickness of 15mm. If the allowable normal stress of the tank wall is 150MPa, we can determine the maximum allowable internal pressure.
Given Data:
- Cylinder diameter = 2m
- Wall thickness = 15mm
- Allowable normal stress (σ) = 150 MPa
Calculating Inner Diameter and Radius:
Inner diameter = Diameter - 2 * Wall thickness = 2000 mm - 2 * 15 mm = 1970 mm
Inner radius (r) = Inner diameter / 2 = 1970 mm / 2 = 985 mm
Calculating Hoop Stress (σ_h):
Hoop stress is the stress in the circumferential direction.
σ_h = Pressure * Inner diameter / (2 * Wall thickness)
Rearranging Formula for Pressure:
Pressure = (σ_h * 2 * Wall thickness) / Inner diameter
Substitute Values and Solve for Pressure:
Pressure = (150 MPa * 2 * 15 mm) / 1970 mm ≈ 2.28 MPa
For each hemispherical end section, the radius is also 1m. The stress in each end section is equal to the stress in the cylindrical section, so the maximum allowable internal pressure in each end section is also 10,000 kPa. Since there are two end sections, the total maximum allowable internal pressure in the tank is 20,000 kPa.