3. During the design of spherical pressure vessel for space programs, a primary criterion is the mass of the vessel (which determines how much it costs to put it into the orbit). Given the stress in a thin walled spherical vessel is tensile and given by: Pr 2t where P is the pressure in the vessel, r is the radius and t is the wall thickness. For safety, materials will experience stress smaller that yield stress by a safety factor N. 10-1 Show that the minimum mass of the pressure vessel will be m = 2NT Pr³ P where p is the density of material. ys
3. During the design of spherical pressure vessel for space programs, a primary criterion is the mass of the vessel (which determines how much it costs to put it into the orbit). Given the stress in a thin walled spherical vessel is tensile and given by: Pr 2t where P is the pressure in the vessel, r is the radius and t is the wall thickness. For safety, materials will experience stress smaller that yield stress by a safety factor N. 10-1 Show that the minimum mass of the pressure vessel will be m = 2NT Pr³ P where p is the density of material. ys
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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![**Design of Spherical Pressure Vessels for Space Programs**
A critical factor in designing spherical pressure vessels for space programs is their mass, which influences the cost of launching them into orbit. The tensile stress in a thin-walled spherical vessel is calculated using the formula:
\[ \sigma = \frac{Pr}{2t} \]
where:
- \( P \) is the pressure inside the vessel.
- \( r \) is the radius of the vessel.
- \( t \) is the wall thickness.
For safety, materials used must endure stress levels below the yield stress, reduced by a safety factor \( N \).
**Minimum Mass Calculation**
To determine the minimum mass (\( m \)) of the pressure vessel, the following formula is used:
\[ m = \frac{2N\pi Pr^3 \rho}{\sigma_{ys}} \]
where:
- \( \rho \) is the material's density.
- \( \sigma_{ys} \) is the yield stress of the material.
**Material Selection for Pressure Vessels**
Based on data from Appendices B1 and B4, select the material from the table below that results in the lightest possible pressure vessel. For brittle materials, the yield strength is equivalent to the tensile stress.
| Material |
|-----------------------------------|
| Steel 4340 Q&T |
| Al 7075-T6 |
| Ti-6-4, aged |
| ZrO3+Y2O3 |
| Nylon 6,6 |
| Composite, Aramid fibers in epoxy |
| Composite: CFRE |
Choose the most suitable material considering both weight and safety requirements for effective design.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3b63b44-9302-458a-a5f0-5e786e8527ac%2Fc3f6c969-cd5e-4613-9605-f4fe3435ebd1%2F8j2j2ud_processed.png&w=3840&q=75)
Transcribed Image Text:**Design of Spherical Pressure Vessels for Space Programs**
A critical factor in designing spherical pressure vessels for space programs is their mass, which influences the cost of launching them into orbit. The tensile stress in a thin-walled spherical vessel is calculated using the formula:
\[ \sigma = \frac{Pr}{2t} \]
where:
- \( P \) is the pressure inside the vessel.
- \( r \) is the radius of the vessel.
- \( t \) is the wall thickness.
For safety, materials used must endure stress levels below the yield stress, reduced by a safety factor \( N \).
**Minimum Mass Calculation**
To determine the minimum mass (\( m \)) of the pressure vessel, the following formula is used:
\[ m = \frac{2N\pi Pr^3 \rho}{\sigma_{ys}} \]
where:
- \( \rho \) is the material's density.
- \( \sigma_{ys} \) is the yield stress of the material.
**Material Selection for Pressure Vessels**
Based on data from Appendices B1 and B4, select the material from the table below that results in the lightest possible pressure vessel. For brittle materials, the yield strength is equivalent to the tensile stress.
| Material |
|-----------------------------------|
| Steel 4340 Q&T |
| Al 7075-T6 |
| Ti-6-4, aged |
| ZrO3+Y2O3 |
| Nylon 6,6 |
| Composite, Aramid fibers in epoxy |
| Composite: CFRE |
Choose the most suitable material considering both weight and safety requirements for effective design.
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