Explanation:
Boundary Layer:
The boundary layer is the thin layer of fluid adjacent to a solid surface where the flow velocity changes from 0 at the surface to the free-stream velocity away from the surface. It is characterized by a region of high velocity gradient.

Flow:
In fluid mechanics, flow refers to the motion of a fluid. It can be either rotational or irrotational, depending on the behavior of the fluid particles.

Rotational Flow:
Rotational flow refers to the motion of fluid particles in which the velocity vectors have both magnitude and direction. The fluid particles move in a circular or spiral path, and there is a swirling motion present.

Irrotational Flow:
Irrotational flow refers to the motion of fluid particles in which the velocity vectors have magnitude but no direction. The fluid particles move in straight lines and there is no swirling motion present.

Analyzing the Options:
Let's analyze each option to determine which one is true.

a) Flow is rotational inside the boundary layer and irrotational outside.
This option suggests that the flow is rotational within the boundary layer and irrotational outside of it. This is true because within the boundary layer, the fluid particles experience a high velocity gradient, resulting in a swirling motion. Outside of the boundary layer, the flow is smoother, and the fluid particles move in straight lines.

b) Flow is irrotational inside the boundary layer and rotational outside.
This option suggests the opposite of option a, stating that the flow is irrotational within the boundary layer and rotational outside. This is incorrect because the boundary layer is characterized by a high velocity gradient, causing the fluid particles to move in a swirling motion.

c) Flow is rotational both inside and outside of the boundary layer.
This option suggests that the flow is rotational both within and outside of the boundary layer. This is incorrect because outside of the boundary layer, the flow is smoother and the fluid particles move in straight lines.

d) Flow is irrotational both inside and outside of the boundary layer.
This option suggests that the flow is irrotational both within and outside of the boundary layer. This is incorrect because within the boundary layer, the fluid particles experience a high velocity gradient, resulting in a swirling motion.

Conclusion:
Based on the analysis, the correct answer is option a) Flow is rotational inside the boundary layer and irrotational outside. Within the boundary layer, the flow is characterized by a swirling motion due to the high velocity gradient, while outside of the boundary layer, the flow is smoother and the fluid particles move in straight lines.