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The existence of velocity potential in fluid-flow indicates that:
- a)The flow must be irrotational
- b)The flow is rotational and satisfies the continuity equation
- c)The vorticity must not be zero
- d)The circulation around any closed curve must have a finite value
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The existence of velocity potential in fluid-flow indicates that:a)The...
Velocity Potential function: These function is defined as a function of space and time in a flow such that the negative derivation of this function with respect to any direction gives the velocity of fluid in that direction.
If velocity potential (ϕ) exist, there will be a flow.
Now, Angular velocity is given by:
Therefore,
ωz = 0
i.e Flow is irrotational.
Therefore for existence of velocity potential function in a fluid flow, flow must be irrotational.
Vorticity is twice of angular velocity, hence it is also zero.
If velocity potential (ϕ) exist, there will be a flow.
Now, Angular velocity is given by:
Therefore,
ωz = 0
i.e Flow is irrotational.
Therefore for existence of velocity potential function in a fluid flow, flow must be irrotational.
Vorticity is twice of angular velocity, hence it is also zero.
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The existence of velocity potential in fluid-flow indicates that:a)The...
Explanation:
The existence of a velocity potential in fluid flow indicates that the flow must be irrotational. This means that option A is the correct answer.
Velocity Potential:
The velocity potential is a scalar field that is used to describe fluid flow in terms of a potential function. It is defined as the scalar field Φ, such that the velocity vector V can be expressed as the gradient of Φ.
Irrotational Flow:
An irrotational flow is a flow in which the fluid particles move along paths that are parallel to each other. In other words, the fluid particles do not rotate as they move. This can also be understood as the fluid having no vorticity.
Explanation of the Options:
Let's analyze the other options to understand why they are not correct.
Option B:
If the flow is rotational, it means that the fluid particles are rotating as they move. This contradicts the assumption of the existence of a velocity potential, which implies an irrotational flow. Additionally, satisfying the continuity equation does not necessarily indicate that the flow is rotational.
Option C:
The statement that the vorticity must not be zero is incorrect. Vorticity is a measure of the local rotation of fluid particles. In an irrotational flow, the vorticity is indeed zero.
Option D:
The statement that the circulation around any closed curve must have a finite value is incorrect. In an irrotational flow, the circulation around any closed curve is actually zero.
Conclusion:
In summary, the existence of a velocity potential in fluid flow indicates that the flow must be irrotational. This means that the correct answer is option A.
The existence of a velocity potential in fluid flow indicates that the flow must be irrotational. This means that option A is the correct answer.
Velocity Potential:
The velocity potential is a scalar field that is used to describe fluid flow in terms of a potential function. It is defined as the scalar field Φ, such that the velocity vector V can be expressed as the gradient of Φ.
Irrotational Flow:
An irrotational flow is a flow in which the fluid particles move along paths that are parallel to each other. In other words, the fluid particles do not rotate as they move. This can also be understood as the fluid having no vorticity.
Explanation of the Options:
Let's analyze the other options to understand why they are not correct.
Option B:
If the flow is rotational, it means that the fluid particles are rotating as they move. This contradicts the assumption of the existence of a velocity potential, which implies an irrotational flow. Additionally, satisfying the continuity equation does not necessarily indicate that the flow is rotational.
Option C:
The statement that the vorticity must not be zero is incorrect. Vorticity is a measure of the local rotation of fluid particles. In an irrotational flow, the vorticity is indeed zero.
Option D:
The statement that the circulation around any closed curve must have a finite value is incorrect. In an irrotational flow, the circulation around any closed curve is actually zero.
Conclusion:
In summary, the existence of a velocity potential in fluid flow indicates that the flow must be irrotational. This means that the correct answer is option A.
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The existence of velocity potential in fluid-flow indicates that:a)The flow must be irrotationalb)The flow is rotational and satisfies the continuity equationc)The vorticity must not be zerod)The circulation around any closed curve must have a finite valueCorrect answer is option 'A'. Can you explain this answer?
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