If the flow of an incompressible fluid is irrotational as well as steady, then it is known as:
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Link the word "Irrotational" directly to "Potential." In fluid mechanics, you cannot have a Velocity Potential if the fluid is spinning (rotating). So, Irrotational + Incompressible = Potential Flow.
Potential flow (also known as ideal flow) refers to a flow field where the velocity can be expressed as the gradient of a scalar function called the
velocity potential ($\phi$).
2. Required Conditions:
• Irrotational: The curl of the velocity vector is zero ($\nabla \times \vec{V} = 0$). This means individual fluid particles do not rotate about their own axes as they move. A velocity potential $\phi$
only exists if the flow is irrotational.
• Incompressible: The density is constant. This leads to the continuity equation $\nabla \cdot \vec{V} = 0$.
• Steady: Properties at any point do not change with time ($\partial/\partial t = 0$).
3. Mathematical Outcome: When these conditions are met, the flow satisfies
Laplace's Equation:
$$\nabla^2\phi = 0$$
This is the cornerstone of classical aerodynamics and hydrodynamics, used to model flow around airfoils and cylinders where viscosity can be neglected.