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potential theory for water waves

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hi :)

http://ocw.mit.edu/courses/mechanica...7JF09_ch06.pdf

In page 37 they use newton's 2nd law for a fluid element (while ignoring viscous forces) to derive the bernoulli equation for unsteady flow.

Well, what I am confused about is the last step: They integrate through the x direction, y direction and then z direction to get 3 separate bernoulli equations,,, but then they just add it all up to one??? I don't understand the mathematics behind this as I'm completely new to potential theory.

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