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I would like to ask about the Bernoulli's principle: as the principle states, increasing the velocity causes a decrease in the pressure. I made an experiment using a duct and 6 manometers and what I got is that decreasing the diameter the static head decreases and increasing the flow rate (increasing the velocity) the static head increases also by some values!

Can anybody explain why does that occur?

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I think it will be clear if you understand where Bernoulli's principle comes from.

If you have a duct, and you decrease its diameter, the same amount of water you put in has to come out the other side. If furthermore, the fluid is incompressible you have that:

$A_1V_1=A_2V_2$

where $V_{1,2}$ is the velocity of the fluid where the duct cross section area is $A_{1,2}$.

That means the water has to increase it's velocity, gaining kinetic energy upon reduction of the cross section area. Since energy is conserved, the energy will come from a drop of pressure. I hope that will answer you question.

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I have to disagree a little bit with @NoMorePen. In an incompressible fluid (the assumption usually made at low Mach numbers) there is no energy associated with a pressure change.

The principle at work is conservation of momentum.

You understand that the velocity of the flow changes.

Well, the only way a parcel of fluid can change velocity is by falling through a pressure difference. That's Bernoulli in a nutshell.

That is also a conversion between potential and kinetic energy, but the energy change does not explain the pressure change.

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