I am just starting on this subject and I am trying to get a feeling for the concepts. One thing that confuses me a lot is the idea of an advective acceleration. We have that the rate of change of the velocity in a fluid is given by the material time derivative: Dv/Dt = ∂v/∂t + (v⋅∇)v Now in undergraduate mechanics an expression like this did not exist. You had a body subjected to some forces and could then calculate acceleration, velocity and position from that using Newtons 2nd law. You can still use Newtons 2nd law for the above equation if you identify the material time derivative of v with the acceleration and equate this to a force density. But is this valid to assume and to what body exactly do you apply Newtons 2nd law? It is certainly not each particle in the fluid since this is subject to all kinds of fluctuations. Also which type of forces are included in the effective force density? For example if you have a fluid flowing through a pipe and the cross-section becomes smaller, then the fluid will accelerate, i.e. there is an effective force acting on it. Is this force contained in the above equation? For me this is all very confusing, since I am only used to undergraduate mechanics, where you have given that some force acts on a body and start from there. What do you know from the start in problems with fluid mechanics? I hope you understand my confusion.. It seems there is a big step to fluid mechanics from undergraduate mechanics.