Question

When the stream function \(\psi\) satisfies the Laplace equation \[ \nabla^2\psi=0, \] the flow is confirmed to be

• A. Rotational
• B. Irrotational
• C. Unsteady
• D. Three dimensional flow

Hint:

For incompressible flow, \[ \boxed{ \nabla^2\phi=0 \quad\text{and}\quad \nabla^2\psi=0 } \] indicate an \[ \boxed{\text{Irrotational flow}.} \]

Answer 1

The Correct Option is B

Step 1: Recall the property of the stream function. For a two-dimensional incompressible flow, \[ \nabla^2\psi=0 \] is Laplace's equation. This condition is satisfied when the flow is \[ \boxed{\text{Irrotational}.} \]

Step 2: Identify the correct flow type. If \[ \nabla^2\psi=0, \] then the vorticity is zero. Hence, \[ \boxed{\text{The flow is irrotational}.} \] Therefore, \[ \boxed{(B)} \] is the correct answer.