Topic: Fluid Mechanics
The velocity potential function $\phi$ satisfy the Laplace equation: $\frac{\partial^{2}\phi}{\partial x^{2}}+\frac{\partial^{2}\phi}{\partial y^{2}}+\frac{\partial^{2}\phi}{\partial z^{2}}=0$. Then the flow is
- A. Unsteady, incompressible, rotational
- B. Steady, compressible, rotational
- C. Steady, incompressible, irrotational
- D. Unsteady, compressible, irrotational
Answer: C. Steady, incompressible, irrotational
Explanation: A velocity potential function $\phi$ automatically satisfies the condition for irrotational flow. When it also satisfies the Laplace equation, it meets the requirement of the 3-D continuity equation for an incompressible fluid: $\frac{\partial u}{\partial x}+\frac{\partial v}{\partial y}+\frac{\partial w}{\partial z}=0$. Therefore, the flow is steady, incompressible, and irrotational.