ANS:A - irrotational

The existence of a velocity potential implies that the fluid is irrotational. In fluid mechanics, an irrotational flow is one in which the fluid particles do not undergo any rotation as they move. Mathematically, this condition is expressed by the curl of the velocity field being zero, which is equivalent to the velocity field being the gradient of a scalar function known as the velocity potential. In irrotational flow, the velocity potential exists and can be used to describe the flow field. However, the existence of a velocity potential does not necessarily imply that the fluid is ideal, compressible, or in continuum. These properties are separate characteristics of fluid flow:

• Ideal vs. Non-ideal: Ideal fluids are assumed to be inviscid (having no viscosity) and incompressible, while real fluids exhibit viscosity and may also be compressible. The presence of a velocity potential does not determine whether a fluid is ideal or real; it only indicates the absence of rotation in the flow.
• Compressible vs. Incompressible: Compressibility refers to the change in density of a fluid under the influence of pressure. Incompressible fluids have negligible density changes under pressure variations, while compressible fluids experience significant changes in density. The presence of a velocity potential does not provide information about the compressibility of the fluid; additional considerations, such as the equation of state, are required to determine compressibility.
• Continuum vs. Non-continuum: Continuum mechanics describes fluid flow at macroscopic scales, assuming that the fluid is continuous and divisible into infinitesimally small fluid elements. Non-continuum flows, such as rarefied gas flows, involve discrete particles and require specialized models beyond continuum mechanics. The existence of a velocity potential does not specify whether the fluid is in continuum or non-continuum state; this depends on factors such as fluid density and mean free path.

Therefore, while the existence of a velocity potential indicates irrotational flow, other properties of the fluid, such as its ideal or real behavior, compressibility, and continuum assumptions, must be determined separately based on the specific characteristics of the fluid and the flow conditions.