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The realisation of velocity potential in fluid flow indicates thatthe
- a)Flow must be irrotational
- b)Circulation around any closed curve must have a finite value
- c)Flow is rotational and satisfies the continuity equation
- d)Vorticity must be non-zero
Correct answer is option 'A'. Can you explain this answer?
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The realisation of velocity potential in fluid flow indicates thatthea...
Ans. (a) The realisation of velocity potential in fluid flow indicates that the flow must be irrotational.
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The realisation of velocity potential in fluid flow indicates thatthea...
Flow Must Be Irrotational:
In fluid dynamics, the velocity potential function is defined as the scalar field whose gradient gives the velocity field of a fluid flow. The existence of a velocity potential implies that the flow is irrotational. This means that the fluid particles do not experience any net angular velocity as they move along their paths.
Explanation:
- For an irrotational flow, the curl of the velocity field is zero. This condition is mathematically expressed as ∇ x V = 0, where V is the velocity vector field.
- The existence of a velocity potential φ implies that the velocity field can be expressed as the gradient of a scalar function, i.e., V = ∇φ.
- By taking the curl of the velocity field expressed in terms of the velocity potential, it can be shown that the curl of the gradient of any scalar field is always zero, thus proving that the flow is indeed irrotational.
Significance:
- Irrotational flows have important implications in fluid dynamics, as they satisfy the Laplace's equation and simplify the analysis of flow behavior.
- Many practical applications, such as aircraft aerodynamics and fluid machinery design, assume irrotational flow conditions to simplify calculations and understand flow phenomena.
Therefore, the realization of a velocity potential in fluid flow indicates that the flow must be irrotational, which is a fundamental property in fluid dynamics.
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The realisation of velocity potential in fluid flow indicates thatthea)Flow must be irrotationalb)Circulation around any closed curve must have a finite valuec)Flow is rotational and satisfies the continuity equationd)Vorticity must be non-zeroCorrect answer is option 'A'. Can you explain this answer?
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