User:Butakun/Taylor-Maccoll equation

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In fluid dynamics, Taylor-Maccoll equation is the governing equation for supersonic conical flow, written as

$\left(1 - \frac{v^2}{a^2}\right) \frac{d^2 u}{d\theta^2} + \cot\theta\frac{du}{d\theta} + \left(2 - \frac{v^2}{a^2}\right) u = 0$

$v = \frac{du}{d\theta}$

Coordinate system, where the dotted line depicts conical shock

Coordinate system, where the dotted line depicts conical shock

where

$u$ is the velocity component in $\hat{e}_r$ .
$v$ is the velocity component in $\hat{e}_{\theta}$ .
$a$ is the speed of sound.
$θ$ is the semivertex angle.

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