之前有点问题，最终如下
\par $C_p$采用4次多项式分段拟合
\begin{equation}\label{equ:NS_Cp}
C_p(T)=a_1+a_2T+a_3T^2+a_4T^3+a_5T^4
\end{equation}
\par静焓
\begin{equation}\label{equ:NS_H}
H(T)=\int_{T_{0}}^{T_{x}}C_p(T)dT=a_1T+\frac{a_2}{2}T^2+\frac{a_3}{3}T^3+\frac{a_4}{4}T^4+\frac{a_5}{5}T^5+a_6
\end{equation}
\par熵
\begin{equation}\label{equ:NS_S}
S(T)=\int_{T_{0}}^{T_{x}}C_p(T)\frac{dT}{T}=a_1\ln{T}+a_2T+\frac{a_3}{2}T^2+\frac{a_4}{3}T^3+\frac{a_5}{4}T^4+a_7
\end{equation}
\par$\bullet$求解静温(已知总温和马赫数)
\begin{equation}\label{equNSUs}
U_s^2=2\left(H(T_{tot})-H(T_{sta})\right)
\end{equation}
\begin{equation}\label{equNSmach}
Mach^2=\frac{U^2}{\gamma(T)R_gT}=\frac{U^2}{\frac{C_p(T)}{C_p(T)-R_g}R_gT}
\end{equation}
\par由(\ref{equ:NSmach})和(\ref{equ:NSUs})得
\begin{equation}\label{equNSTsta}
T_{sta}=\frac{2\left(H(T_{tot})-H(T_{sta})\right)}{Mach^2\frac{C_p(T_{sta})R_g}{C_p(T_{sta})-R_g}}
\end{equation}
$\bullet$求解静压(已知总温、总压和静温)
\par由p等熵过程
\begin{equation}
ds = C_p(T)\frac{dT}{T} -R_g\frac{d p}{p}=0
\end{equation}
\par两边同时积分有
\begin{equation}
\int_{T_{tot}}^{T_{sta}}C_p(T)\frac{dT}{T} =\int_{p_{tot}}^{p_{sta}} R_g\frac{d p}{p}
\end{equation}
\par记
\begin{equation}
S(T_{x})=\int_{T_{0}}^{T_{x}}C_p(T)\frac{dT}{T}
\end{equation}
\par则
\begin{equation}
S(T_{sta}) - S(T_{tot}) = R_g\ln\frac{p_{sta}}{p_{tot}}
\end{equation}
\par那么
\begin{equation}\label{equNS_psta}
p_{sta}=p_{tot}e^{\left(\frac{S(T_{sta})-S(T_{tot})}{R_g}\right)}
\end{equation}
