Bernoullis versus Continuity

[CrazyCarl461]

What billbo911 is hinting at, is that incompressible fluid does not mean constant pressure. It only means that you are allowed to use Bernoulli's equation. Bernoulli's has three parts and they are all pressure terms:

static pressure + dynamic pressure + head pressure = constant along a streamline

p + .5*density*velocity^2 + density*g*height = C

You can use this equation to relate two different points on a streamline (for example, the ends of a pipe). Because this is a fixed relation, you cannot just "decide" the values for them. In Corey's problem all three terms are being predetermined, which wont give you an answer. Alan gave a very visual description of how you can't say the velocity gradient is zero AND the pressure gradient is zero AND there is a height change. If you say there is constant velocity and pressure, solving makes height zero (horizontal).

It would really be helpful if you drew a picture, which is where all good solutions begin.