Stream Function:
The stream function is a mathematical concept used to describe fluid flow in two-dimensional, incompressible flows. It is defined as a scalar function, denoted by Ψ, and is used to determine the flow patterns or streamlines of a fluid. The stream function is defined in such a way that the velocity components of the flow can be obtained by taking the derivatives of the stream function with respect to the coordinates.

Velocity Potential:
The velocity potential is another mathematical concept used to describe fluid flow. It is also a scalar function, denoted by φ, and is used to determine the velocity components of a fluid flow. The velocity potential is defined in such a way that the velocity components can be obtained by taking the derivatives of the velocity potential with respect to the coordinates.

Vorticity:
Vorticity is a vector quantity that describes the local spinning motion of a fluid element. It is defined as the curl of the velocity vector, denoted by ω. The vorticity vector is perpendicular to the plane of fluid flow and has a magnitude that represents the rate of rotation. In rotational flows, the vorticity is non-zero, indicating the presence of local spinning motion in the fluid.

Existence in Rotational and Irrotational Flows:
Among the given parameters, vorticity and stream function exist in both rotational and irrotational flows.

Vorticity:
In rotational flows, the vorticity is non-zero and represents the local spinning motion of the fluid. This spinning motion can be observed in flows such as swirling flows, vortex flows, or turbulent flows. In irrotational flows, the vorticity is zero, indicating no local spinning motion in the fluid. Irrotational flows are typically observed in laminar flows or flows around streamlined objects.

Stream Function:
The stream function is a mathematical concept used to describe fluid flow patterns in both rotational and irrotational flows. In rotational flows, the stream function can be used to determine the flow patterns or streamlines of the fluid. It provides a way to visualize and analyze the flow behavior. In irrotational flows, the stream function can also be used to determine the flow patterns, even though the vorticity is zero. It is a useful tool for understanding the flow behavior and the relationship between the velocity components.

Therefore, the correct answer is option 'B' - Both vorticity and stream function exist in both rotational and irrotational flows.