A) \[\text{ }\!\!\Omega\!\!\text{ /(}{{\text{r}}_{c}}{{)}^{2}}\]
B) \[\text{ }\!\!\Omega\!\!\text{ /}{{\text{r}}_{c}}\]
C) \[\text{ }\!\!\Omega\!\!\text{ }\,{{\text{r}}_{c}}\]
D) \[\text{ }\!\!\Omega\!\!\text{ }\,\text{r}_{c}^{2}\]
Correct Answer: A
Solution :
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 \[\omega =\frac{\Gamma }{2\pi }\]You need to login to perform this action.
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