Help with Bernoulli Equation?

[LoveBeingHuman:)]

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I have attached a drawing I made. Suppose the width of the pipe is the same throughout the pipe and the fluid direction is from A to B. At point A, the fluid has more potential energy. But where does that potential energy go when it reaches point B? Does the velocity increase to make up for it? But if the velocity increases, doesn't that mean that the pressure decreases?

 

[Neuroplasticity]

The velocity at A and B have to be the same if the pipe diameter is the same and the fluid is incompressible. If the velocity was faster at B, the fluid would have to be 'stretching' and if it was slower at B, it would be getting compressed. This only leaves the pressure term, so the pressure increases from A to B.