ANS:B - twice the angular velocity vector

The flow is considered rotational when the velocity normal to the plane of the area is equal to twice the angular velocity vector. In fluid mechanics, rotational flow refers to the type of flow where fluid particles move in circular or curved paths around a central axis. This type of flow is characterized by a non-zero curl of the velocity vector field. In rotational flow, the velocity of the fluid particle at any point in the flow field can be decomposed into two components:

1. Tangential velocity component: This component represents the velocity of the fluid particle tangent to the circular path or streamlines. It contributes to the rotational motion of the fluid.
2. Normal velocity component: This component represents the velocity of the fluid particle normal to the circular path or streamlines. It contributes to the radial motion of the fluid.

In rotational flow, the normal velocity component is twice the angular velocity vector, which describes the rate of rotation of the fluid around the central axis. Therefore, the flow is considered rotational if its normal velocity component is equal to twice the angular velocity vector.