대학원 공부노트

Delft university, Introduction to Aeronautical Engineering $$p_{total}-p_{static}+\frac{1}{2}\rho\vec{v}^{2}$$ 이때 \(p_{static}\)은 정압으로서 고도에 대한 정보도 알려준다. $$\frac{1}{2}\rho_{0}\vec{v}_{EAS}^{2}=\frac{1}{2}\rho\vec{v}_{TAS}^{2}$$ Here, EAS is equivalent air speed and TAS is true air speed. $$\vec{v}_{TAS}=\sqrt{\frac{\rho_{0}}{\rho}}\cdot\vec{v}_{EAS}$$

EPFL Class First, if velocity of exhaust gas is constant, \(\vec{v}_{e}=\rm{const}\) $$\vec{F}=\frac{d\vec{P}}{dt}=\frac{d(m\vec{v}_{e})}{dt}=m\frac{d\vec{v}_{e}}{dt}+\vec{v}_{e}\frac{dm}{dt}=\dot{m}\vec{v}_{e}$$ $$\vec{F}=\dot{m}\vec{v}_{e}$$ Second, for velocity of the spacecraft. $$\frac{d\vec{v}}{dt}=\frac{\vec{F}}{m}=\frac{\dot{m}\vec{v}_{e}}{m}=\vec{v}_{e}\frac{\dot{m}}{m}\cdots(1)$$ Third..

Speed of sound $$a^{2}=\frac{\partial P}{\partial \rho}\Bigg|_{x}^{y}$$ 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..

$$T_{0}=T+\frac{1}{2C_{P}}\vec{v}^{2}$$ $$\frac{T_{0}}{T}=1+\frac{\vec{v}^{2}}{2C_{P}T}$$ $$=1+\frac{1}{2}\frac{\vec{v}^{2}}{C_{P}}\frac{\gamma R}{\gamma R}$$ $$a^{2}=\gamma RT$$ $$=1+\frac{1}{2}\frac{\gamma R}{C_{P}}\frac{\vec{v}^{2}}{a^{2}}$$ $$M=\frac{\vec{v}}{\vec{a}}$$ $$=1+\frac{1}{2}\frac{\gamma R}{C_{P}} M^{2}$$ $$\frac{\gamma R}{C_{P}}$$ $$=\frac{\gamma (C_{P}-C_{v}}{C_{P}}$$ $$=\gamma\..