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When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure
- a)varies as the square of the radial distance
- b)decreases as the square of the radial distance
- c)increases linearly as the radial distance
- d)varies inversely as the elevation along any vertical line
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
When a liquid rotates at a constant angular velocity about a vertical ...
A fluid is rotating at constant angular velocity ω about the central vertical axis of a cylindrical container. The variation of pressure in the radial direction is given by
It is given that the pressure at the axis of rotation is Pc.
Therefore, the required pressure at any point r is
Most Upvoted Answer
When a liquid rotates at a constant angular velocity about a vertical ...
Explanation:
When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure varies as the square of the radial distance. This phenomenon is known as the centrifugal effect.
Centrifugal Force:
Centrifugal force is a fictitious force that arises in a rotating reference frame. It is the force that appears to push objects away from the center of rotation. In the case of a liquid rotating about a vertical axis, centrifugal force is responsible for the pressure variation.
Pressure Variation:
The pressure variation in a rotating liquid can be explained by the centrifugal force acting on the fluid particles. As the liquid rotates, the centrifugal force acting on each fluid particle increases with its distance from the axis of rotation. As a result, the pressure on the fluid particles also increases with their distance from the axis of rotation.
Mathematical Expression:
The pressure variation in a rotating liquid can be expressed as:
ΔP = ρω²r²/2
Where ΔP is the pressure difference between two points, ρ is the density of the liquid, ω is the angular velocity of rotation, and r is the radial distance from the axis of rotation.
From the above expression, it can be observed that the pressure varies as the square of the radial distance. Hence, option A is the correct answer.
Conclusion:
When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure varies as the square of the radial distance. This phenomenon can be explained by the centrifugal force acting on the fluid particles.
When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure varies as the square of the radial distance. This phenomenon is known as the centrifugal effect.
Centrifugal Force:
Centrifugal force is a fictitious force that arises in a rotating reference frame. It is the force that appears to push objects away from the center of rotation. In the case of a liquid rotating about a vertical axis, centrifugal force is responsible for the pressure variation.
Pressure Variation:
The pressure variation in a rotating liquid can be explained by the centrifugal force acting on the fluid particles. As the liquid rotates, the centrifugal force acting on each fluid particle increases with its distance from the axis of rotation. As a result, the pressure on the fluid particles also increases with their distance from the axis of rotation.
Mathematical Expression:
The pressure variation in a rotating liquid can be expressed as:
ΔP = ρω²r²/2
Where ΔP is the pressure difference between two points, ρ is the density of the liquid, ω is the angular velocity of rotation, and r is the radial distance from the axis of rotation.
From the above expression, it can be observed that the pressure varies as the square of the radial distance. Hence, option A is the correct answer.
Conclusion:
When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressure varies as the square of the radial distance. This phenomenon can be explained by the centrifugal force acting on the fluid particles.
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When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressurea)varies as the square of the radial distanceb)decreases as the square of the radial distancec)increases linearly as the radial distanced)varies inversely as the elevation along any vertical lineCorrect answer is option 'A'. Can you explain this answer?
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When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressurea)varies as the square of the radial distanceb)decreases as the square of the radial distancec)increases linearly as the radial distanced)varies inversely as the elevation along any vertical lineCorrect answer is option 'A'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressurea)varies as the square of the radial distanceb)decreases as the square of the radial distancec)increases linearly as the radial distanced)varies inversely as the elevation along any vertical lineCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for When a liquid rotates at a constant angular velocity about a vertical axis as a rigid body, the pressurea)varies as the square of the radial distanceb)decreases as the square of the radial distancec)increases linearly as the radial distanced)varies inversely as the elevation along any vertical lineCorrect answer is option 'A'. Can you explain this answer?.
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