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