Question

If the flow of an incompressible fluid is irrotational as well as steady, then it is known as:

• A. Non-uniform flow
• B. Uniform flow
• C. Potential flow
• D. Laminar flow

Hint:

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.

Answer 1

The Correct Option is C

Fluid flows are categorized based on several mathematical and physical criteria. When a flow satisfies specific conditions of being steady, incompressible, and irrotational, it allows for a simplified mathematical treatment. 1. Defining 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.

4. Other Flow Types:

• Laminar Flow: Smooth, orderly flow in layers (dominated by viscosity).

• Uniform Flow: Velocity does not change with respect to space (location).