Bernoullis versus Continuity

[CrazyCarl461]

I agree, this seems like a pretty special problem. Generally, what Bernoulli's is trying to tell you is that if you have a tube with equal pressures at each end, you cannot have flow in the pipe (kind of makes sense, right?). So your constant velocity is zero. Remember, Bernoulli's relates the substantial derivative of the velocity (DV/Dt) with the pressure gradient, so with both equaling zero you can't say much.