Chaplygin's equation

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In mathematics, Chaplygin's equation, named after Sergei Alekseevich Chaplygin, is a partial differential equation useful in the study of transonic flow.^[1] It is

$\Psi _{{\theta \theta }}+{\frac {v^{2}}{1-{\frac {v^{2}}{c^{2}}}}}\Psi _{{vv}}+v\Psi _{v}=0.$

Here, $c=c(v)$ is the speed of sound, determined by the equation of state of the fluid and Bernoulli's principle.

References

↑ Landau, L. D.; Lifshitz, E. M. (1982). Fluid Mechanics (2 ed.). Pergamon Press. p. 432.

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