Thin wall Pressure Vessel(cylinder)

In summary, when calculating the normal stress along the radial direction of a cylindrical pressure vessel, it is assumed that the stress is equal to the inner pressure P on both the negative and positive radial directions. For the outer wall, the normal stresses in the radial direction are assumed to be zero. This results in a linear decrease in normal stress from P to 0 along the thin wall. However, the shear force that should compensate for this decrease in pressure is neglected due to its small magnitude compared to the pressure stresses. This force is not neglected in the thick wall solution, which can be reduced to the thin wall solution when the thickness to radius ratio decreases. It is important to understand and analyze all stress components at different locations by playing with the
  • #1
MotoPayton
96
0
cylindrical pressure vessel with inner pressure P.

Take a infinitesimal cube on the inner-wall of the vessel. When calculating the normal stress along the radial direction it is assumed that that it is equal to P on the both the negative [itex]\widehat{r}[/itex] and positive [itex]\widehat{r}[/itex] directions.

For an outer wall infinitesimal cube it is assumed that the normal stresses in radial directions are zero.

I was told in class that the normal stress in the radial direction will decrease linearly from P to 0 along the thin wall.

My question is this: If the pressure is slowly decreasing in radial direction shouldn't there be a shear force to compensate for the fact that that normal stress is decreasing. So for the infinitesimal cube on the inner wall I picture the face in negative [itex]\widehat{r}[/itex] direction to have Pressure P and the face on the positive [itex]\widehat{r}[/itex] direction to have pressure P-dP. This change in pressure should cause a shearing force on the 4 faces normal to the [itex]\widehat{r}[/itex] direction in the negative [itex]\widehat{r}[/itex] direction.

Why is this shear force neglected. If it is because it is so small compared to the pressure stresses so it is neglected then can someone explain to me why it is small. It can't reason why this force would be of such small magnitude when the shear forces must compensate for this Pressure over the small distance of the thin wall.
 
Engineering news on Phys.org
  • #2
It is not neglected in the thick wall solution, so look up the thick wall solution and see how it reduces to the thin wall solution when the ratio of the thickness to the radius decreases. From the thick wall solution, you can calculate all the stress components at all locations. Play with the results.

chet
 

1. What is a thin wall pressure vessel?

A thin wall pressure vessel, also known as a thin-walled cylinder, is a type of container that is designed to store and distribute fluids under high pressure. It is typically made of a strong and lightweight material, such as steel, and has a wall thickness that is significantly smaller than its radius.

2. How does a thin wall pressure vessel work?

A thin wall pressure vessel works by using the principle of Pascal's law, which states that pressure applied to a confined fluid will be transmitted equally in all directions. This means that the thin walls of the cylinder are able to withstand the high internal pressure, distributing it evenly throughout the container.

3. What are the applications of thin wall pressure vessels?

Thin wall pressure vessels have a wide range of applications, including in industries such as oil and gas, chemical processing, and aerospace. They are commonly used to store and transport compressed gases, as well as for industrial processes that require high pressures, such as hydraulic systems.

4. How are thin wall pressure vessels designed and manufactured?

The design and manufacturing of thin wall pressure vessels require careful consideration of factors such as material selection, wall thickness, and structural integrity. Engineers use mathematical calculations and computer simulations to ensure that the vessel can withstand the expected pressure and any potential external forces.

5. What safety precautions should be taken when working with thin wall pressure vessels?

When working with thin wall pressure vessels, it is important to follow proper safety precautions to prevent accidents and injuries. These include regular inspection and maintenance of the vessel, proper handling and storage of compressed gases, and following all safety guidelines and regulations set by relevant authorities.

Similar threads

  • Mechanical Engineering
Replies
6
Views
2K
  • Mechanical Engineering
Replies
1
Views
2K
Replies
2
Views
1K
  • Biology and Medical
Replies
10
Views
2K
Replies
69
Views
2K
  • Engineering and Comp Sci Homework Help
Replies
2
Views
881
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
Replies
7
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
8
Views
3K
  • Engineering and Comp Sci Homework Help
Replies
9
Views
2K
Back
Top