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For a vertical semicircular plate submerged in a homogeneous liquid with its diameter ‘d' at the free surface, the depth of centre of pressure from the free surface is
- a)
- b)
- c)
- d)
Correct answer is option 'A'. Can you explain this answer?
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Explanation:
Center of Pressure for a Submerged Vertical Semicircular Plate:
- The depth of the center of pressure from the free surface for a submerged vertical semicircular plate can be determined using the formula:
- Depth of center of pressure = 3πd/32
Derivation:
- The formula for the depth of the center of pressure for a submerged vertical semicircular plate is derived from the principle of hydrostatics.
- The center of pressure for a curved surface is located at a distance of 2r/3 from the free surface, where r is the radius of the curved surface.
- For a semicircular plate with diameter d, the radius r is d/2.
- Therefore, the depth of the center of pressure can be calculated as follows:
Depth of center of pressure = 2(d/2)/3
Depth of center of pressure = d/3
Depth of center of pressure = d/3 * π
Depth of center of pressure = 3d/3π
Depth of center of pressure = 3d/2π
Depth of center of pressure = 3πd/32
Conclusion:
- Therefore, the correct depth of the center of pressure from the free surface for a submerged vertical semicircular plate with diameter d is 3πd/32.
Center of Pressure for a Submerged Vertical Semicircular Plate:
- The depth of the center of pressure from the free surface for a submerged vertical semicircular plate can be determined using the formula:
- Depth of center of pressure = 3πd/32
Derivation:
- The formula for the depth of the center of pressure for a submerged vertical semicircular plate is derived from the principle of hydrostatics.
- The center of pressure for a curved surface is located at a distance of 2r/3 from the free surface, where r is the radius of the curved surface.
- For a semicircular plate with diameter d, the radius r is d/2.
- Therefore, the depth of the center of pressure can be calculated as follows:
Depth of center of pressure = 2(d/2)/3
Depth of center of pressure = d/3
Depth of center of pressure = d/3 * π
Depth of center of pressure = 3d/3π
Depth of center of pressure = 3d/2π
Depth of center of pressure = 3πd/32
Conclusion:
- Therefore, the correct depth of the center of pressure from the free surface for a submerged vertical semicircular plate with diameter d is 3πd/32.
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For a vertical semicircular plate submerged in a homogeneous liquid with its diameter ‘d atthe free surface, the depth of centre of pressure from the free surface isa)b)c)d)Correct answer is option 'A'. Can you explain this answer?
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