Identity component

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

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