Question

In a flow, if velocity potential (\(\phi\)) exists, then the flow is said to be

• A. Rotational
• B. Irrotational
• C. Laminar
• D. Real flow

Hint:

Velocity potential is a scalar function whose gradient gives velocity in irrotational flow.

Answer 1

The Correct Option is B

In fluid dynamics, when a velocity potential (\(\phi\)) exists, the flow is described as irrotational. This is because the existence of a velocity potential implies that the flow is conservative, allowing us to define a scalar function whose gradient gives the velocity field. For a flow to be irrotational, the curl of the velocity vector field must be zero:

\(\nabla \times \mathbf{V} = 0\)

Since \(\mathbf{V} = \nabla \phi\), the curl of a gradient is always zero, i.e.,

\(\nabla \times \nabla \phi = 0\)

Thus, the presence of a velocity potential (\(\phi\)) indicates an irrotational flow, aligning with the properties of potential flow where no vortices are present.