hey pf!
so i have a small question when deriving the navier-stokes equations from newton's 2nd law. specifically, newton states that $$\Sigma \vec{F} = m \vec{a} = m \frac{d \vec{v}}{dt}$$
when setting a control volume of fluid and dealing with the time rate-of-change of momentum we write $$m \frac{d \vec{v}}{dt} = \frac{\partial}{\partial t} \iiint_V \rho \vec{v} dV$$ but isnt it true that $$\frac{\partial}{\partial t} \iiint_V \rho \vec{v} dV = \frac{d (m \vec{v})}{dt}$$
can someone please help me out here?
thanks!
so i have a small question when deriving the navier-stokes equations from newton's 2nd law. specifically, newton states that $$\Sigma \vec{F} = m \vec{a} = m \frac{d \vec{v}}{dt}$$
when setting a control volume of fluid and dealing with the time rate-of-change of momentum we write $$m \frac{d \vec{v}}{dt} = \frac{\partial}{\partial t} \iiint_V \rho \vec{v} dV$$ but isnt it true that $$\frac{\partial}{\partial t} \iiint_V \rho \vec{v} dV = \frac{d (m \vec{v})}{dt}$$
can someone please help me out here?
thanks!
0 commentaires:
Enregistrer un commentaire