In fluid dynamics, a Rankine oval is a potential flow pattern that involves the superimposition of a source and a sink at equal strength. The streamline representing the Rankine oval can be described using a stream function \(\psi\). The oval shape occurs at a specific value of \(\psi\).
The stream function for the Rankine oval is given by:
\(\psi = \frac{\Gamma}{2\pi}\left(\tan^{-1}\frac{y}{x-a}-\tan^{-1}\frac{y}{x+a}\right)\)
Where:
Setting \(\psi = 0\) solves for the shape of the Rankine oval with equal axes, because when \(\psi = 0\), it corresponds to the closed streamline that represents the boundary of the resulting oval.
Therefore, the correct substitution to find the shape of the Rankine oval of equal axes is:
\(\psi = 0\).