- Aerodynamics

V = ∇?

V = ∇ × ?

V = -∇ × V

V = (∇ × V)?

Correct Answer :

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If the Laplace equation is satisfied by the velocity potential, then the fluid flows.

True

False

Can Not Say

None of the above

Correct Answer : Option (A) : True

Explanation : For the fluid to flow, it is essential for the velocity potential ? to satisfy the Laplace equation. If the condition is not met, the fluid does not flow and has zero velocity.

Thus, the condition for the fluid to flow is :

What is the nature of the flow having a velocity potential?

Viscous

Inviscid

Rotational

Irrotational

Correct Answer : Option (D) : Irrotational

Explanation : For irrotational flow, curl of velocity vector yields zero. In case the curl of any vector is zero i.e.∇ × V = 0, where V is a vector, it is also expressed in the form of ∇ζ where ζ is a scalar function. In case of irrotational flow, velocity potential ? is the scalar function. Hence if the flow has a velocity potential, it automatically implies that it is irrotational.