대학원 공부노트

Delft university, Introduction to Aeronautical Engineering $$p_{total}-p_{static}+\frac{1}{2}\rho {\overrightarrow{v}}^2$$ 이때 $p_{static}$은 정압으로서 고도에 대한 정보도 알려준다. $$\frac{1}{2}{\rho }_0{\overrightarrow{v}}_{EAS}^2=\frac{1}{2}\rho {\overrightarrow{v}}_{TAS}^2$$ Here, EAS is equivalent air speed and TAS is true air speed. $${\overrightarrow{v}}_{TAS}=\sqrt{\frac{{\rho }_0}{\rho }}\cdot {\overrightarrow{v}}_{EAS}$$

EPFL Class First, if velocity of exhaust gas is constant, ${\overrightarrow{v}}_e=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ $$\overrightarrow{F}=\frac{d\overrightarrow{P}}{dt}=\frac{d(m{\overrightarrow{v}}_e)}{dt}=m\frac{d{\overrightarrow{v}}_e}{dt}+{\overrightarrow{v}}_e\frac{dm}{dt}=\dot{m}{\overrightarrow{v}}_e$$ $$\overrightarrow{F}=\dot{m}{\overrightarrow{v}}_e$$ Second, for velocity of the spacecraft. $$\frac{d\overrightarrow{v}}{dt}=\frac{\overrightarrow{F}}{m}=\frac{\dot{m}{\overrightarrow{v}}_e}{m}={\overrightarrow{v}}_e\frac{\dot{m}}{m}\cdots (1)$$ Third..

Speed of sound $$a^2=\frac{\partial P}{\partial \rho }{|}_x^y$$ As our flow condition is all isentropic, $ds=0$ $$dP=a^{2}d\rho \cdots (b)$$ Substitute equation (a) with (b), Then $$\frac{dP}{\rho }+vdv=0$$ $$\frac{a^{2}d\rho }{\rho }+vdv=0$$ And $$\frac{a^{2}d\rho }{\rho }+vdv=0$$ $$\frac{d\rho }{\rho }+\frac{v}{a^2}dv=0$$ $$\frac{d\rho }{\rho }+\frac{v^2}{a^2}\frac{dv}{v}=0$$ $$\frac{d\rh..

$$T_0=T+\frac{1}{2C_P}{\overrightarrow{v}}^2$$ $$\frac{T_0}{T}=1+\frac{{\overrightarrow{v}}^2}{2C_{P}T}$$ $$=1+\frac{1}{2}\frac{{\overrightarrow{v}}^2}{C_P}\frac{\gamma R}{\gamma R}$$ $$a^2=\gamma RT$$ $$=1+\frac{1}{2}\frac{\gamma R}{C_P}\frac{{\overrightarrow{v}}^2}{a^2}$$ $$M=\frac{\overrightarrow{v}}{\overrightarrow{a}}$$ $$=1+\frac{1}{2}\frac{\gamma R}{C_P}{M}^2$$ $$\frac{\gamma R}{C_P}$$ $$=\frac{\gamma (C_P-C_v}{C_P}$$ $$=\gamma\..