Imagining you have 1 m3 cubed container made out of steel and inside the container is 5 bar. What will the force be felt on the container if the pressure inside suddenly drops to 1 bar? Temperature can be omitted if needed.
Trying to design a yield limit for pressure-drop resistant materials through tensile/compressive measurements.
The force acting on the walls of the container due to the pressure inside can be calculated using the formula:
F = P * A
where:
- F is the force,
- P is the pressure, and
- A is the area.
Given a cubical container with an edge length of 1 m, one side's surface area (A) is 1 m^2. Since a cube has six faces, the total surface area is 6 m^2.
When the pressure inside the container drops from 5 bar to 1 bar, the pressure change (ΔP) is -4 bar. Converting this to pascals (since 1 bar equals 100,000 Pa), the pressure change is -400,000 Pa or -400,000 N/m^2.
So, the total force change experienced by the walls of the container is:
ΔF = ΔP * A ΔF = -400,000 N/m^2 * 6 m^2 ΔF = -2,400,000 N
The negative sign indicates that the force has decreased due to the pressure drop.
The stress on the walls of the container is the force divided by the area over which the force is distributed. In this case, the change in stress on the walls is equal to the change in pressure because the area cancels out:
Δσ = ΔF / A Δσ = -400,000 N/m^2
This means the stress on the walls of the container decreases by 400,000 N/m^2 due to the pressure drop. This stress is what your material must be able to withstand. The yield limit of your material, obtained through tensile or compressive tests, should be higher than this value to prevent deformation.
Please note that this calculation assumes that the stress is evenly distributed over the walls of the container, and ignores other potential factors such as strain hardening, material defects, or localized stresses due to design features (like welds, or changes in thickness). A more detailed analysis using mechanical engineering and material science principles would be needed for a thorough safety assessment.
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