대학원 공부노트
Stagnation temperature 본문
$$T_{0}=T+\frac{1}{2C_{P}}\vec{v}^{2}$$
$$\frac{T_{0}}{T}=1+\frac{\vec{v}^{2}}{2C_{P}T}$$
$$=1+\frac{1}{2}\frac{\vec{v}^{2}}{C_{P}}\frac{\gamma R}{\gamma R}$$
$$a^{2}=\gamma RT$$
$$=1+\frac{1}{2}\frac{\gamma R}{C_{P}}\frac{\vec{v}^{2}}{a^{2}}$$
$$M=\frac{\vec{v}}{\vec{a}}$$
$$=1+\frac{1}{2}\frac{\gamma R}{C_{P}} M^{2}$$
$$\frac{\gamma R}{C_{P}}$$
$$=\frac{\gamma (C_{P}-C_{v}}{C_{P}}$$
$$=\gamma\left(1-\frac{C_{v}}{C_{P}}\right)$$
$$=\gamma\left(1-\frac{1}{\gamma}\right)$$
$$=\gamma-1$$
$$\frac{T_{0}}{T}=1+\frac{1}{2}(\gamma-1)M^{2}$$
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