Question

For an irrotational flow, the velocity potential lines and the streamlines are always:

• A. {Parallel to each other}
• B. {Coplanar}
• C. {Orthogonal to each other}
• D. {Inclined to horizontal}

Hint:

For irrotational flow, streamlines and equipotential lines intersect at right angles.

Answer 1

The Correct Option is C

Step 1: In an irrotational flow, the velocity potential \( \phi \) and the stream function \( \psi \) satisfy the Cauchy-Riemann equations. Step 2: The gradients of \( \phi \) and \( \psi \) are perpendicular at every point, making their respective lines orthogonal. Thus, the correct answer is Orthogonal to each other.