An exact exit condition for multiphase critical flow

It is well known that the zero of the determinant of the coefficient matrix of the gradient vector of the multiphase equation set defines the critical flow plane at steady state. I show that this zero is expressible as a very simple relation. Evaluation of this relation shows a significant dependence on phasic superheat. The result provides an exact closure equation for system codes for break and relief valve flow. Further, the time derivatives of the dependent variables do not diverge at the critical plane and the steady state critical condition is also valid during a transient (i.e. the determinant of the coefficient matrix of the vector of time derivatives is never zero)