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MECHMAT 15: Thin-Walled Pressure Vessels – YOUTUBE PLAYLIST

Session 15.1 Thin-walled Pressure Vessels – Stresses in their Walls
This video describes and derives the relationship between the internal gauge pressure and stresses in the walls of thin-walled pressure vessels. We also discuss how bubbles are also pressure vessels with surface tension.

Session 15:Q1 Specify the Thickness of a Wall for a Thin Pressure Vessel
If we are designing a spherical pressure vessel with an internal volume of V, what thickness t would be necessary to support a pressure p if the maximum axial tolerable stress is S_y?

Session 15.2 Thin-walled Pressure Vessels – Some Examples
This video describes scenarios with pressure vessels that involve calculating stresses, strain, taking into account Poisson’s ratio, and change in radius.

Session 15:Q2 Thin-walled Pressure Vessels – Strain in Cylindrical Vessel
If the cylindrical pressure vessel has internal radius r, internal pressure p, thickness t, elastic modulus E, and Poisson’s ratio ν, what is ϵ_x where x is in the circumferential direction?

Session 15:Q3 Thin-walled Fuselage of an Airplane
You are taking a flight to a nice, warm place to get out of the snow that has engulfed New Jersey (not in the year 2023) for spring break. As you board the plane, you notice and learn a few things as you sit in the open cabin surfing the web on your phone.
a) The fuselage of the plane looks like a cylinder (some of you, say, “duh”). When the plane is 10,000 m above sea level, what is the relative difference in pressure between the inside and outside of the cabin (gauge pressure) in units of kPa, assuming the internal pressure of the cabin has a pressure equivalent to that at sea level? Hint: pressure above sea level in units of kPa is calculable by p=101e^{-0.00012 h} (kPa), where h is height at or above sea level.
b) The diameter of the cylindrical fuselage is about 5 m, and the thickness of the cylindrical shell is about 1 mm. Using the difference in pressure calculated in part (a), what is the hoop stress in the shell of the fuselage for the plane at 10,000 m above sea level?

Session 15: Q4 “Compound cylinder”
We have a “compound cylinder” with an inner cylinder of r₁, t₁, and E₁ with a gauge pressure inside this inner cylinder of p. An outer cylinder fitting snugly around the inner one has inner radius equal to r₁ +t₁, thickness t₂, and elastic modulus E₂. What is the hoop stress in the outer cylinder? You may want to look at Example 2.2.2 on Roylance’s page: 2.2: Pressure Vessels – Engineering LibreTexts

Session 15.3 Thin-walled Pressure Vessels: Optimal Wrap Angle
This video describes the classic derivation of the optimal wrap angle for a filament-based composite surrounding a cylindrical pressure vessel.

To be uploaded in the future.

Select Assignment Questions

Live MechMat Sessions

Mechanics of Materials – Session 15: Thin-walled Pressure Vessels
In-class problem-solving in small groups working to solve problems involving thin-walled pressure vessels.

Notes

Fa2024 Session 15: MechMat – Thin-walled Pressure Vessels – Instructional Slides
Session 15: MechMat – Thin-walled Pressure Vessels – Instructional Slides
Fa2023 In-class and Office Hours Notes
Su2023 In-class and Office Hours Notes
Sp2023 MechMat In-class Notes Starting from Session 9
Session 15: MechMat- Thin-walled Pressure Vessels – Colab IPython

Additional Video Content

Examples of Pressure Vessels (Thick and Thin)
This video shows some examples of thin-walled pressure vessels in the forms of hoses and a fire extinguisher.

https://www.youtube.com/watch?v=dTLE00qbH08?start=0amp;end=87

Thin-Walled Pressure Vessels
This video by Jeff Hanson describes hoop and longitudinal stresses in cylindrical and spherical pressure vessels.

Online Text

2.2: Pressure Vessels – Engineering LibreTexts
Pressure vessel – Wikipedia

For complementary information, see our YouTube Channel and the Wikibook.

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