Let me re-phrase that..i meant "by changing flow VELOCITY", not flow rate...

When using the Bernoulli equation on incompressible fluids one must consider mechanical energy, not just static pressures, velocities or elevations and, of course, the friction losses along the fluid path. By using the search engine on Bernoulli you'll probably find hundreds of useful posts.

FBW- Bernouilli is a simple energy balance- forget for the moment about momentum which just confuses matters in my opinion. As you accelerate the fluid by increasing its velocity (reducing diameter), the extra kinetic energy of the fluid you accelerated (1/2 m v^2) has to come from somewhere. It comes from a reduction in potential energy, or more properly the fraction of the mechanical work done by the thing that pushed the fluid into the tube that is available as static pressure. Ignoring elevation head for the moment, that work is proportional to P*V where V is volume rather than velocity, which shows up as P/rho (density) in the Bernoulli equation, i.e. P/m*V, since the kinetic energy term in Bernouilli has similarly been divided by m). When you decelerate again, you get some of that kinetic energy back as increased P*V. In reality, you lose energy all along the way as a result of friction with the walls and within the fluid itself.

So: sure, assuming some perfect incompressible and inviscid fluid, if you had done some incredible amount of external work on the fluid to force it to flow in a pipe at some extraordinarily high velocity and only 1 psi of static pressure, you could, by decelerating it in increasing diameters, trade that enormous velocity for a high static pressure. But in reality there are limits due to friction, and with gases due to sonic flow, so perhaps that's why it offends your commonsense. Yes, I know it's peculiar to think of a fluid flowing from an area of low static pressure to one of higher static pressure, but that's because that notion is a simplified model of how fluids flow- easy to understand, and predictive in many circumstances, but inaccurate when velocity is changing (i.e. when flowing through an orifice, venturi etc.)

In addition to moltenmetal's excellent explanation, I'd only add that the Bernoulli's energy ebalance quation for frictionless incompressible, irrotational, flow per unit mass, between points 1 and 2, is:

where:

p, is static pressure, d is density, v is speed, z is elevation, g is acceleration of gravity and:

p/d is the flow work when the fluid is displaced through a volumetric space 1/d against the restraint of pressure
v²/2 is the kinetic energy per unit mass
zg is the potential energy per unit mass with the horizontal reference level 0-0.

Dividing all members of the equation by g, one gets the dimensions of length or height, in which the first term is called pressure head, and the second velocity head.

You start with a total head, T_H, = datum + pressure head + velocity head.
Then, mathematically, you can decrease V_H, say by some given amount, then you are mathematically permitted to increase pressure until you run out of T_H, or vice versa. You can't increase pressure indefinitely, because you soon run out of TH.

you must get smarter than the software you're using.

Thanks guys for the great replies, it helps a lot. I love this site.