"EES example - how to get the Mach number (inversely) from the temperature ratio equation, Rayleigh flow
J. M. Cimbala"
 
"Universal ideal gas constant:"
Ru                    = 8314 [J/(kmol*K)]
 
"Gas is air:"
gamma          = 1.40 [-]
MW               = 28.97 [kg/kmol]
R                   = Ru/MW
c_v                 = R/(gamma-1)
c_P                = R*gamma/(gamma-1)
 
"Given information:"
T_01                = 553.19 [K]
T_02                = 1598.5 [K]
 
"Example of forward calculation - for a given Mach number, calculate the temperature ratio:"
M_1                = 0.17018 [-]
T01byT0star     = (2+(gamma-1)*(M_1^2))*(gamma+1)*(M_1^2)/((1+gamma*(M_1^2))^2)
 
"Example of the inverse calculation - for a given temperature ratio, calculate Mach number:"
T02byT0star     = (T_02/T_01)*T01byT0star
T02byT0star     = (2+(gamma-1)*(M_2^2))*(gamma+1)*(M_2^2)/((1+gamma*(M_2^2))^2)