Consider a fluid in which [tex]\rho[/tex] = [tex]\rho[/tex](x,y,z,t); that is the density varies from point to point and with time. The velocity of this fluid at a point is
v= (dx/dt, dy/dt, dz/ dt)
dp/dt = [tex]\partial[/tex]t[tex]\rho[/tex] + v [tex]\cdot[/tex] [tex]\nabla\rho[/tex]
Combine the above equation with the equation of continuity and prove that
[tex]\rho\nabla[/tex][tex]\cdot[/tex] v + d[tex]\rho[/tex] /dt = 0
I have been attempting this problem for over a week. If anyone can solve this problem or help me out I would really appreciate it!
(Between the [tex]\nabla[/tex] and v is a dot but I am not sure if it is showing up!)