I'm studying Aerodynamics and I'm thinking about the Bernoulli Equation Statement.
Ignoring gravity contributes, it states that, in a potential fluid, the sum of static pressure and kinetic energy (per unit of mass) is a constant:
Typically, to solve the pressure distribution around an aerofoil (in order to calculate lift) in the context of a potential fluid, we can solve the Divergence problem about the velocity field:
$$\nabla \cdot V =0$$
Once the velocity field has been determined, we can use the Bernoulli equation to find the static pressure value in every point of the fluid field.
So my question is:
If the velocity would be too large in some points of the field, may we find there a negative static pressure? Algebraically speaking the answer is yes, because the Bernoulli Equation may "mathematically" lead to this result. But negative (absolute) pressure has no physical meaning, so how can we know if the Bernoulli Equation application will lead to robust results? A negative pressure would represent an "exhaustion" of static pressure to convert in kinetic energy, so in these conditions the velocity field cannot be realized and the Bernoulli equation would be violated. As I know, if we are dealing with liquid, the occurrence of a negative pressure would lead to cavitation and boiling, but in aerodynamics we deal with air (a gas).
So, How can we deal with an aerodynamic problem in which such a circumstance occurs, and what are the conditions to garantee negative pressure not to happen?