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. \[\text{ }\!\!\Omega\!\!\text{ }\,\text{r}_{c}^{2}\]