As illustrated in Fig. P6.38, a tornado can be approximated by a free vortex of strength (Gamma)

Question:

As illustrated in Fig. P6.38, a tornado can be approximated by a free vortex of strength $\Gamma$ for $r>R_{c}$, where $R_{c}$ is the radius of the core. Velocity measurements at points $A$ and $B$ indicate that $V_{A}=125 \mathrm{ft} / \mathrm{s}$ and $V_{B}=60 \mathrm{ft} / \mathrm{s}$. Determine the distance from point $A$ to the center of the tornado. Why can the free vortex model not be used to approximate the tornado throughout the flow field $(r \geq 0)$ ?

Figure P6.38