Empirical equation of the Mach number as a function of the stagnation pressure ratio for a quasi-one-dimensional compressible flow

In the present work for a quasi-one-dimensional isentropic compressible flow model, an empirical equation of Mach number is constructed as function stagnation pressure ratio analytical that algebraic procedures cannot invert. The Excel 2019 Solver tool was applied to calibrate coefficients and exponents during its construction range from 1 10 5. A specific heat 1.1 1.67 generalized reduced gradient iterative method were used minimize sum squared error, which set objective function. results show 10, error less than 0.063% obtained, 5, 0.00988% obtained. It concluded obtained mathematical model reproduces trajectories inverted curves studied.