- #1
member 428835
Hi PF!
I was reading my book and I understand the following $$\sum \vec{F} = \frac{\partial}{\partial t} \iiint_{CV} \rho \vec{u} dV +\iint_{CS} \rho \vec{u} ( \vec{u_{rel}} \cdot \hat{n}) dS$$ ##CV## is a control volume, ##CS## is control surface, ##u## is velocity, ##u_{rel}## is velocity relative to control volume, and the rest is self-spoken for. However, then the book states the following $$m_{CV} \frac{d}{dt} \vec{u_{CV}} = \frac{\partial}{\partial t} \iiint_{CV} \rho \vec{u_{CV}} dV +\iint_{CS} \rho \vec{u_{CV}} ( \vec{u_{rel}} \cdot \hat{n}) dS$$ where ##u_{CV}## is the velocity of the control volume. Any help in understanding why this is?
I was reading my book and I understand the following $$\sum \vec{F} = \frac{\partial}{\partial t} \iiint_{CV} \rho \vec{u} dV +\iint_{CS} \rho \vec{u} ( \vec{u_{rel}} \cdot \hat{n}) dS$$ ##CV## is a control volume, ##CS## is control surface, ##u## is velocity, ##u_{rel}## is velocity relative to control volume, and the rest is self-spoken for. However, then the book states the following $$m_{CV} \frac{d}{dt} \vec{u_{CV}} = \frac{\partial}{\partial t} \iiint_{CV} \rho \vec{u_{CV}} dV +\iint_{CS} \rho \vec{u_{CV}} ( \vec{u_{rel}} \cdot \hat{n}) dS$$ where ##u_{CV}## is the velocity of the control volume. Any help in understanding why this is?