\frac{\mathrm d\Gamma}{\mathrm d t}=\oint_L \frac{\mathrm d \vec{V}}{\mathrm dt}\cdot \delta l=
\oint \vec{F}\cdot \delta l-\oint_l\frac{1}{\rho}\nabla p\delta b-\nu\oint_l\nabla\times\xi\delta l
又：理想流体，且仅受有势力作用
\therefore\oint\vec{F}\cdot \delta l=0,\\
v\oint\nabla\times\xi\delta l=0\\
\therefore \frac{\mathrm d \Gamma}{\mathrm dt}=-\oint_l\frac{1}{\rho}\nabla p\delta l\\
又\because \alpha=\frac1\rho, \nabla\cdot\delta l=\mathrm d p\\
\therefore \frac{\mathrm d \Gamma}{\mathrm dt}=-\oint\alpha \mathrm d p\\
又由克拉伯龙方程，p=ρRT
\therefore \frac1\alpha=\frac{RT}{p},\\
\therefore \frac{\mathrm d \Gamma}{\mathrm dt}=-\oint \frac{R_dT}{p}\mathrm dp=R_d\delta \bar{T}\ln\frac{p}{p-\delta p}≈R_d\delta \bar{T}\ln\frac{\delta p}{p}
流体力学我cnm，，，
