My book says that divergence can be understood in the context of fluid flow as the rate at which density flows out of a given region. It says that if F(x,y,z) is the velocity of a fluid, then that is the interpretation of the divergence. I fail to understand where the density comes in when we are only dealing with velocities at first and we only take a spatial derivative. It seems like the interpretation should be the rate of change of velocity i.e. acceleration.