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My question concerns a control volume with a changing area. The momentum equation: p

_{1}A

_{1}-p

_{2}A

_{2}= ṁ(V

_{2}-V

_{1}) is applied to the control volume.

The image shows the equation found when applying the above momentum equation to the control volume:

The bit I'm having difficulty with is the part in the red box, as I don't see how that part fits in with the original momentum equation. Apparently it accounts for the "average pressure on the side" but what does this actually mean? Any help in understanding this would be much appreciated.

Thanks x