Here, I'll extend the discussion of the integral form of mass conservation to look at the integral form of momentum conservation. And I will anchor this discussion in the same channel flow example. Momentum is mass times velocity. And Newton's second law says that for momentum to change, the rate of change of momentum, is balanced by the forces on any particular body. So this is the form we apply to the infinite sum of fluid particle. In the integral form, we apply this in aggregate to the control volume. And this can be any particular control volume, as we talked about in the integral form of mass conservation. And when we talked about mass conservation, we saw that the net mass outflow rate through any controlled surface is given by that expression. Let's extend that to the net momentum outflow rate. So now I'm looking at the net momentum outflow rate through a controlled surface. And so let's consider first an elemental surface dS like that.
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- Summer '18