diff --git a/IF97.h b/IF97.h index 864f3a0..4e6cab5 100644 --- a/IF97.h +++ b/IF97.h @@ -52,7 +52,7 @@ namespace IF97 // IF97 Constants const double Tcrit = 647.096; // K const double Pcrit = 22.064*p_fact; // MPa* - const double Rhocrit = 322.0; // kg/m³ + const double Rhocrit = 322.0; // kg/m^3 const double Scrit = 4.41202148223476*R_fact; // kJ*/kg-K (needed for backward eqn. in Region 3(a)(b) const double Ttrip = 273.16; // K const double Ptrip = 0.000611656*p_fact; // MPa* @@ -2394,7 +2394,7 @@ namespace IF97 // The equation is rearranged to solve for rho and turned // into functions f(T,P,rho0) and f'(T,P,rho0) for the // Newton-Raphson technique. Functions for - // dphi/ddelta and d²phi/ddelta² were also required. These + // dphi/ddelta and d^2phi/ddelta^2 were also required. These // additional Taylor functions are defined above. // double f(double T, double p, double rho0) const{ @@ -4172,7 +4172,7 @@ namespace IF97 return RegionOutput( IF97_HMASS,RegionOutputBackward(Pmax,s,IF97_SMASS),Pmax, NONE); else { // Determining H(s) along Tmax is difficult because there is no direct p(T,s) formulation. - // This linear combination fit h(s)=a*ln(s)+b/s+c/s²+d is not perfect, but it's close + // This linear combination fit h(s)=a*ln(s)+b/s+c/s^2+d is not perfect, but it's close // and can serve as a limit along that Tmax boundary. Coefficients in HTmaxdata above. // There is a better way to do this using Newton-Raphson on Tmax = T(p,s), but it is iterative and slow. double ETA = Hmax_n[0]*log(sigma) + Hmax_n[1]/sigma + Hmax_n[2]/pow(sigma,2) +Hmax_n[3]; @@ -4323,14 +4323,14 @@ namespace IF97 inline double cvmass_Tp(double T, double p){ return RegionOutput( IF97_CVMASS, T, p, NONE); }; /// Get the speed of sound [m/s] as a function of T [K] and p [Pa] inline double speed_sound_Tp(double T, double p){ return RegionOutput( IF97_W, T, p, NONE); }; - /// Get the [d(rho)/d(p)]T [kg/m³/Pa] as a function of T [K] and p [Pa] + /// Get the [d(rho)/d(p)]T [kg/m^3/Pa] as a function of T [K] and p [Pa] inline double drhodp_Tp(double T, double p){ return RegionOutput( IF97_DRHODP, T, p, NONE); }; // ******************************************************************************** // // Transport Properties // // ******************************************************************************** // - /// Get the viscosity [Pa-s] as a function of T [K] and Rho [kg/m³] + /// Get the viscosity [Pa-s] as a function of T [K] and Rho [kg/m^3] inline double visc_TRho(double T, double rho) { // Since we have density, we don't need to determine the region for viscosity. static Region1 R1; // All regions use base region equations for visc(T,rho).