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From a design point of view, spherical pressure vessels are preferred over cylindrical pressure vessels become they
- a)Are cost-effective in fabrication
- b)Have uniform higher circumferential stress
- c)Uniform lower circumferential stress
- d)Have a large volume for the same quantity
Correct answer is option 'D'. Can you explain this answer?
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From a design point of view, spherical pressure vessels are preferred...
From a design point of view, spherical pressure vessels are preferred over cylindrical pressure vessels become they have a large volume for the same quantity.
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From a design point of view, spherical pressure vessels are preferred...
Spherical pressure vessels are preferred over cylindrical pressure vessels because they have a large volume for the same quantity. This can be explained in detail as follows:
1. Spherical vessels have a larger volume:
- The volume of a spherical pressure vessel is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
- On the other hand, the volume of a cylindrical pressure vessel is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
- Since the radius of a sphere is constant, a spherical vessel will have a larger volume compared to a cylindrical vessel with the same radius and height.
- This means that a spherical vessel can hold a larger quantity of material compared to a cylindrical vessel of the same size.
2. Cost-effectiveness in fabrication:
- Spherical pressure vessels are more cost-effective in fabrication compared to cylindrical pressure vessels.
- The fabrication of a spherical vessel involves less material and welding compared to a cylindrical vessel.
- The reduction in material and welding requirements leads to cost savings in terms of labor, time, and materials.
3. Uniform stress distribution:
- Spherical pressure vessels have a uniform stress distribution compared to cylindrical pressure vessels.
- In a spherical vessel, the stress is distributed evenly along the surface, resulting in uniform circumferential stress.
- On the other hand, cylindrical vessels have higher circumferential stress at the top and bottom, which can lead to weak points and potential failure.
- The uniform stress distribution in spherical vessels makes them more structurally stable and less prone to failure under pressure.
In conclusion, spherical pressure vessels are preferred over cylindrical pressure vessels because they have a larger volume for the same quantity. Additionally, they are more cost-effective in fabrication and have a uniform stress distribution, making them structurally stable.
1. Spherical vessels have a larger volume:
- The volume of a spherical pressure vessel is given by the formula V = (4/3)πr^3, where r is the radius of the sphere.
- On the other hand, the volume of a cylindrical pressure vessel is given by the formula V = πr^2h, where r is the radius of the base and h is the height of the cylinder.
- Since the radius of a sphere is constant, a spherical vessel will have a larger volume compared to a cylindrical vessel with the same radius and height.
- This means that a spherical vessel can hold a larger quantity of material compared to a cylindrical vessel of the same size.
2. Cost-effectiveness in fabrication:
- Spherical pressure vessels are more cost-effective in fabrication compared to cylindrical pressure vessels.
- The fabrication of a spherical vessel involves less material and welding compared to a cylindrical vessel.
- The reduction in material and welding requirements leads to cost savings in terms of labor, time, and materials.
3. Uniform stress distribution:
- Spherical pressure vessels have a uniform stress distribution compared to cylindrical pressure vessels.
- In a spherical vessel, the stress is distributed evenly along the surface, resulting in uniform circumferential stress.
- On the other hand, cylindrical vessels have higher circumferential stress at the top and bottom, which can lead to weak points and potential failure.
- The uniform stress distribution in spherical vessels makes them more structurally stable and less prone to failure under pressure.
In conclusion, spherical pressure vessels are preferred over cylindrical pressure vessels because they have a larger volume for the same quantity. Additionally, they are more cost-effective in fabrication and have a uniform stress distribution, making them structurally stable.
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From a design point of view, spherical pressure vessels are preferred over cylindrical pressure vessels become theya)Are cost-effective in fabricationb)Have uniform higher circumferential stressc)Uniform lower circumferential stressd)Have a large volume for the same quantityCorrect answer is option 'D'. Can you explain this answer?
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