목록전공/대학물리 (2)
공대생 공부노트
Given equation: $$\dot{m}=\rho A\vec{v}$$ $$\rho A\vec{v}=(\rho+\Delta\rho)A(c-\Delta\vec{v})$$ $$\rho c=(\rho+\Delta\rho)(c-\Delta\vec{v})$$ $$\rho c = \rho c - \rho\Delta\vec{v}+\Delta\rho c-\Delta\rho\Delta\vec{v}$$ We can neglect the last term of equation $$0=-\rho\Delta\vec{v}+\Delta\rho c$$ $$c\Delta\rho=\rho\Delta\vec{v}$$ $$c\frac{\Delta\rho}{\rho}=\Delta\vec{v}\cdots(1)$$ Given equation..
운동량(Momentum) $$p=m\vec{v}$$ 운동량의 시간에 대란 변화량 $$\frac{\partial p}{\partial t}=\frac{\partial m}{\partial t}\vec{v}+m\frac{\partial \vec{v}}{\partial t}$$ Let's assume \(\vec{v}=const\) $$\frac{\partial p}{\partial t}=\frac{dp}{dt}=\frac{dm}{dt}\vec{v}=\dot{m}\vec{v}\cdots(1)$$ Bring the concept 'mass flowrate' \(\dot{m}\) $$m=\rho V$$ $$\dot{m}=\frac{dm}{dt}=\frac{d\rho}{dt}V+\rho\frac{dV}{dt}$$ ..