Find the dimensions R, t, and L of the pressure vessel such that its weight is minimized. The pressure vessel is made of steel with a volume V = 50 m³ and an internal pressure P = 50 Atm. The allowable stress is σ = 800 Atm.
Added by Brian G.
Close
Step 1
We need to find the dimensions R, t, and L of the pressure vessel. Let's assume that the pressure vessel is cylindrical in shape. Show more…
Show all steps
Your feedback will help us improve your experience
Hafiz Shahzaib and 63 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The spherical pressure vessel has an inner diameter of $2 \mathrm{m}$ and a thickness of $10 \mathrm{mm} .$ A strain gauge having a length of $20 \mathrm{mm}$ is attached to it, and it is observed to increase in length by $0.012 \mathrm{mm}$ when the vessel is pressurized. Determine the pressure causing this deformation, and find the maximum in-plane shear stress, and the absolute maximum shear stress at a point on the outer surface of the vessel. The material is steel, for which $E_{\mathrm{st}}=200 \mathrm{GPa}$ and $\nu_{\mathrm{st}}=0.3$.
The thin-walled cylindrical pressure vessel of inner radius $r$ and thickness $t$ is subjected to an internal pressure $p .$ If the material constants are $E$ and $\nu,$ determine the strains in the circumferential and longitudinal directions. Using these results, compute the increase in both the diameter and the length of a steel pressure vessel filled with air and having an internal gauge pressure of 15 MPa. The vessel is $3 \mathrm{m}$ long, and has an inner radius of $0.5 \mathrm{m}$ and a thickness of $10 \mathrm{mm} . E_{\mathrm{st}}=200 \mathrm{GPa}, \nu_{\mathrm{st}}=0.3$.
The thin-walled cylindrical pressure vessel of inner radius $r$ and thickness $t$ is subjected to an internal pressure $p .$ If the material constants are $E$ and $\nu,$ determine the strains in the circumferential and longitudinal directions. Using these results, calculate the increase in both the diameter and the length of a steel pressure vessel filled with air and having an internal gage pressure of 15 MPa. The vessel is $3 \mathrm{m}$ long, and has an inner radius of $0.5 \mathrm{m}$ and a thickness of $10 \mathrm{mm} . E_{\mathrm{st}}=200 \mathrm{GPa}, \nu_{\mathrm{st}}=0.3$
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD