Question

If \(\nabla \times \mathbf{V} = 0\), then the flow is

• A. Steady
• B. Continuous
• C. Rotational
• D. Irrotational

Hint:

In irrotational flow, fluid particles have no angular velocity about their center.

Answer 1

The Correct Option is D

In fluid dynamics, a vector field \(\mathbf{V}\) is referred to as having a certain property if its curl, denoted by \(\nabla \times \mathbf{V}\), satisfies specific conditions. The curl of a vector field is a measure of the rotation of the field around a point.

If \(\nabla \times \mathbf{V} = 0\), it implies that the vector field has no tendency to induce rotation or swirling motion at any point in the field. Such a field is called irrotational.

Therefore, when the curl of a vector field is zero, the flow is described as irrotational. This is because the absence of curl indicates a lack of angular momentum in the fluid particles, hence no rotational flow occurs.