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Which one of the statements is correct for a forced vortex?
- a)Turns in an opposite direction to a free vortex
- b)Always occurs in conjunction with a free vortex
- c)Has the linear velocity directly proportional to the radius
- d)Has the linear velocity inversely proportional to the radius
Correct answer is option 'C'. Can you explain this answer?
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Which one of the statements is correct for a forced vortex?a)Turns in ...
Ans. (c) Forced vortex flow: Forced vortex flow is one in which the fluid mass is made to rotate by means of some external agency. Where (v) = ω × r As ω is constant linear velocity (v) is directly proportional to the radius (r).
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Which one of the statements is correct for a forced vortex?a)Turns in ...
Forced Vortex
A forced vortex is a type of fluid flow where the fluid rotates around a central axis due to an external force or torque. This external force can be applied by a mechanical device, such as a pump or a mixer, or by other means.
Linear Velocity and Radius Relationship
In a forced vortex, the linear velocity of the fluid is directly proportional to the radius. This means that as the radius increases, the linear velocity of the fluid also increases, and as the radius decreases, the linear velocity decreases.
Explanation
The linear velocity of a fluid in a forced vortex is directly proportional to the radius. This relationship can be explained using the principle of conservation of angular momentum.
When a force is applied to a fluid, it creates a torque that causes the fluid to rotate. As the fluid rotates, the angular momentum is conserved, which means that the product of the moment of inertia and the angular velocity remains constant.
In a forced vortex, the moment of inertia is directly proportional to the square of the radius. This is because the moment of inertia depends on the distribution of mass around the central axis, and in a forced vortex, the mass is concentrated at larger radii.
Since the moment of inertia is directly proportional to the square of the radius, and the angular momentum is constant, the angular velocity is inversely proportional to the radius.
The linear velocity of the fluid is related to the angular velocity by the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius. Since the angular velocity is inversely proportional to the radius, the linear velocity is directly proportional to the radius.
Therefore, the correct statement for a forced vortex is that the linear velocity is directly proportional to the radius (option C).
A forced vortex is a type of fluid flow where the fluid rotates around a central axis due to an external force or torque. This external force can be applied by a mechanical device, such as a pump or a mixer, or by other means.
Linear Velocity and Radius Relationship
In a forced vortex, the linear velocity of the fluid is directly proportional to the radius. This means that as the radius increases, the linear velocity of the fluid also increases, and as the radius decreases, the linear velocity decreases.
Explanation
The linear velocity of a fluid in a forced vortex is directly proportional to the radius. This relationship can be explained using the principle of conservation of angular momentum.
When a force is applied to a fluid, it creates a torque that causes the fluid to rotate. As the fluid rotates, the angular momentum is conserved, which means that the product of the moment of inertia and the angular velocity remains constant.
In a forced vortex, the moment of inertia is directly proportional to the square of the radius. This is because the moment of inertia depends on the distribution of mass around the central axis, and in a forced vortex, the mass is concentrated at larger radii.
Since the moment of inertia is directly proportional to the square of the radius, and the angular momentum is constant, the angular velocity is inversely proportional to the radius.
The linear velocity of the fluid is related to the angular velocity by the equation v = ωr, where v is the linear velocity, ω is the angular velocity, and r is the radius. Since the angular velocity is inversely proportional to the radius, the linear velocity is directly proportional to the radius.
Therefore, the correct statement for a forced vortex is that the linear velocity is directly proportional to the radius (option C).
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Which one of the statements is correct for a forced vortex?a)Turns in an opposite direction to a free vortexb)Always occurs in conjunction with a free vortexc)Has the linear velocity directly proportional to the radiusd)Has the linear velocity inversely proportional to the radiusCorrect answer is option 'C'. Can you explain this answer?
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