Question:

The shape of Rankine oval of equal axes can be found out by substituting

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\(\psi = 0\) corresponds to the dividing streamline in Rankine bodies.
Updated On: July 22, 2025
  • \(\psi = 0\)
  • \(\psi = 1\)
  • \(U = 0\)
  • \(U = 1\)
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The Correct Option is A

Solution and Explanation

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:

  • \(\Gamma\) is the circulation strength of the source/sink pair.
  • \(a\) is the distance from the origin to each source or sink along the x-axis.

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:

\(\psi = 0\).

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