User:Butakun~enwiki/Taylor-Maccoll equation

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

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.
• $\theta$ is the semivertex angle.