• # question_answer An invicid irrotational flow field of free vortex motion has a circulation constant $\Omega \,.$ the tangential velocity at any point in the flow field is given by $\text{ }\!\!\Omega\!\!\text{ /r}$ where, r, is the radial distance from the centre. At the centre, there is a mathematical singularity which can be phiysically substituted by a forced vortex motion $(r={{r}_{c}}),$ the angular velocity E is given by: A) $\text{ }\!\!\Omega\!\!\text{ /(}{{\text{r}}_{c}}{{)}^{2}}$                    B) $\text{ }\!\!\Omega\!\!\text{ /}{{\text{r}}_{c}}$C) $\text{ }\!\!\Omega\!\!\text{ }\,{{\text{r}}_{c}}$                        D) $\text{ }\!\!\Omega\!\!\text{ }\,\text{r}_{c}^{2}$

At the interface of free and forced vortex, tangential velocities are equal.    $\frac{\Gamma }{2\pi {{r}_{c}}}=\omega {{r}_{c}}$ Or         $\omega =\frac{\Gamma }{2\pi }\times \frac{1}{r_{c}^{2}}=\frac{\Omega }{r_{c}^{2}}$ Where $\omega =\frac{\Gamma }{2\pi }$