Which one of the following statements is true to two-dimensional flow of ideal fluids?

Explanation:

Two-Dimensional Flow of Ideal Fluids

• In fluid mechanics, two-dimensional flow refers to a flow scenario where the velocity components are functions of only two spatial coordinates, typically x and y, and the flow parameters do not vary in the third coordinate (z). For an ideal fluid, which is incompressible and inviscid, the flow can be analyzed using mathematical tools such as the stream function and potential function.

Option 3: "Stream function will exist but potential function may or may not exist."

This statement is correct because, in the case of two-dimensional flow of ideal fluids:

1. Stream Function: The stream function (ψ) always exists for two-dimensional, incompressible flows. The stream function is a scalar function whose contours represent streamlines. It helps visualize the flow pattern and satisfies the condition for continuity in two-dimensional flow. For incompressible flow, the continuity equation ensures the existence of the stream function.
2. Potential Function: The potential function (φ) exists only if the flow is irrotational. For a flow to be irrotational, the vorticity (the curl of the velocity field) must be zero. Hence, while the stream function exists for all two-dimensional incompressible flows, the potential function may or may not exist depending on whether the flow is irrotational or not.