Question

A source of strength \(\Gamma\) is placed in a uniform flow \(V_{\infty}\), the distance of the stagnation point from the source is

• A. \(\dfrac{\Gamma}{2\pi V_{\infty}}\)
• B. \(\dfrac{\Gamma}{3\pi V_{\infty}}\)
• C. \(\dfrac{\Gamma}{4\pi V_{\infty}}\)
• D. \(\dfrac{\Gamma}{5\pi V_{\infty}}\)

Hint:

For a source of strength \(\Gamma\) in a uniform flow, \[ \boxed{ r_s=\frac{\Gamma}{2\pi V_{\infty}} } \] where \(r_s\) is the stagnation point distance from the source.

Answer 1

The Correct Option is A

Step 1: Write the velocity due to a source. The radial velocity produced by a source of strength \(\Gamma\) is \[ V_r=\frac{\Gamma}{2\pi r}. \]

Step 2: Apply the stagnation condition. At the stagnation point, the velocity due to the source balances the uniform flow. Hence, \[ V_{\infty} = \frac{\Gamma}{2\pi r}. \] Solving for \(r\), \[ r = \frac{\Gamma}{2\pi V_{\infty}}. \] Therefore, \[ \boxed{ \frac{\Gamma}{2\pi V_{\infty}} } \] is the distance of the stagnation point from the source. Thus, \[ \boxed{(A)} \] is the correct answer.