Bernoulli's equation works beautifully at low speed — until the flow gets close to Mach 1. Then the physics changes qualitatively, not just quantitatively, and a shock wave appears.
At low speed, air is remarkably forgiving to model: treat its density as constant and standard incompressible aerodynamics — simple Bernoulli, in particular — gets you close enough for most purposes. That approximation holds up well below roughly Mach 0.3. Push the flow faster, and it stops holding. As local flow speed approaches and passes the local speed of sound, density changes become large enough that they can no longer be ignored, and the flow starts doing something incompressible theory has no way to describe at all: forming a shock wave.