Pressure Vessels: Radial & Hoop Stresses at Inner & Outer Surfaces

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In summary, the problem involves a cylinder with an internal diameter of 30mm and an external diameter of 50mm, subject to an internal pressure of 60MPa. The equations for radial and hoop stresses are given, but the value of "r" is unknown. The radius can be calculated as half the diameter, but the units should be consistent with MPa requiring meters instead of milimeters. Once the value of "r" is determined, the equations can be used to find the radial and hoop stresses at the inner and outer surfaces.
  • #1
tone999
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Homework Statement


A cylinder has an internal diameter of 30mm and an external diameter of 50mm and is subject to an internal pressure which is 60MPa above that in the air surrounding the cylinder. Determine the radial and hoop stresses at the inner and outer surfaces.

Homework Equations


Basically i know:
internal radius in know as r1
external radius is r2

radial stress: pr1 squared/r2squared-r1squared X (r squared - r2 squared/ r squared)

hoop stresses : pr1 squared/r2squared-r1squared X (r squared + r2 squared/ r squared)

I don't know if these two equations are correct hopefully somebody could clarify this for me because the working out should be simple when this is known.

The Attempt at a Solution


I don't know what "r" is?
If i knew that i could take a stab at the equations hopefully somebody could give me two answers and if the equations are correct and two answers and i will do it myself to check this. Thanks
 
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  • #2
tone999 said:
I don't know what "r" is?

Radius is half the diameter, which would be 15mm and 25mm. I don't know if your formula is correct but make sure you keep the units consistent; I think MPa requires that you work in meters (m), not milimeters (mm).
 
  • #3
Yeah I've got that. I mean "r" on its own in the equation. I know the values for r1 - 0.015m
r2 - 0.025m
Internal pressure - 60x10 to the power of 6 Nm2
 

1. What is a pressure vessel?

A pressure vessel is a container designed to hold a gas or liquid at a pressure significantly different from the surrounding pressure. Examples include gas cylinders, boilers, and storage tanks.

2. What are radial and hoop stresses in a pressure vessel?

Radial stress is the stress that acts perpendicular to the surface of the pressure vessel, while hoop stress is the stress that acts parallel to the surface. These stresses are caused by the pressure inside the vessel and are important factors in determining the vessel's structural integrity.

3. How are radial and hoop stresses calculated?

The radial and hoop stresses in a pressure vessel can be calculated using the formulas σr = pr/t and σh = pr/2t, where p is the internal pressure, r is the radius of the vessel, t is the thickness of the vessel's wall, and σr and σh are the radial and hoop stresses, respectively.

4. What is the significance of the stresses at the inner and outer surfaces of a pressure vessel?

The stresses at the inner and outer surfaces of a pressure vessel are important because they determine the maximum allowable pressure that the vessel can withstand without failing. The stresses are highest at the inner surface, so it is important to ensure that the vessel's design can withstand these stresses.

5. How can the radial and hoop stresses be reduced in a pressure vessel?

The radial and hoop stresses in a pressure vessel can be reduced by using a thicker wall, increasing the vessel's diameter, or decreasing the internal pressure. Other methods include using reinforcing rings or adding stiffening elements to the vessel's design.

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