Question

Consider a two-dimensional potential flow over a cylinder. If the freestream speed is $U_{\infty}$, the maximum speed on the cylinder surface is

• A. $\dfrac{U_{\infty}}{2}$
• B. $\dfrac{3U_{\infty}}{2}$
• C. $2U_{\infty}$
• D. $\dfrac{4U_{\infty}}{3}$

Hint:

In potential flow theory, a cylinder doubles the local velocity at its stagnation belt due to flow acceleration around the curved surface.

Answer 1

The Correct Option is C

In a two-dimensional inviscid, incompressible, irrotational flow over a circular cylinder, the flow can be described using potential flow theory.
The velocity distribution on the surface of the cylinder is given by:
\[ V(\theta) = 2U_{\infty}\,\sin\theta \]
The maximum value of $\sin\theta$ is 1, occurring at $\theta = 90^\circ$ and $270^\circ$. Therefore, the maximum speed on the cylinder surface becomes:
\[ V_{\max} = 2U_{\infty} \]
Thus, the correct answer is the freestream velocity multiplied by 2, which matches option (C).