The claim about Bernoulli effect would be flat out wrong. Moving fluid that has been pumped into motion doesn’t normally have lower pressure than the ambient pressure (i.e. exit pressure). Wikipedia better explains it - they’re using a venturi pump - i.e. there is a construction in the tube that causes the fluid to have faster speed and lower pressure than the exit.
Now, whether this pressure drop causes underpressure is another matter and depends on whether the effect is stronger than possitive pressures in the system relative to your point of reference (for example, outside atmospheric pressure).
For example, there might be obstruction downstream which means there is already positive pressure in the pipe so the pressure drop from Bernoulli effect is lower than the positive pressure and you still get overpressure (Bernoulli effect is rather weak at slow speeds as it is proportional to square of the velocity of liquid in the pipe).
So, in general, when you have fast flow through a pipe, a hole in the pipe might cause the water to flow out but it could also be sucking air in. It all depends on whether positive pressure is stronger than the effect.
Yes, that is all true. More specifically though, in the particular system we're talking about, gasoline flowing through the main nozzle (which has the same diameter up to the exit) has essentially the same pressure as the ambient pressure. There is an obstruction downstream past the nozzle known as the "splash" which is responsible for bringing the liquid's velocity to zero.
The linked article invoked the Bernoulli effect to compare the pressure of the pumped gasoline in the pipe to the pressure of the ambient air; the Bernoulli effect is based on conservation of energy and does not apply here because the pumped fuel is not magically transforming into ambient air in an energy conserved way.
This is incorrect, moving fluid always has lower pressure, you don’t need the narrowing of the venturi to get suction, it just works better when you do.
An intuitive way to think about it is to set up a straight tube with a fan at one end, open on the other end, with a small hole drilled somewhere in the side.
With the fan off, clearly the pressure is the same everywhere.
With the fan on though, air moves out the open end. That moving air has to stop once it is out of the tube, that resistance to the moving air at the end of the tube is dynamic pressure. The hole in the side though has no moving air directed at it, not having to resist that moving air, the pressure is less at that interface than at exit.
If this wasn’t true, you would have to be compressing the air, that is increasing its density. Saying a fluid is incompressible is equivalent to saying the speed of sound in it is infinite; that is obviously never true, however the effects of compressibility are relative to the speed of sound so as long as you aren’t dealing with flow of hundreds of miles per hour in air, incompressability is a very accurate approximation.
In your particular example, the air in the tube would be at slightly higher pressure than ambient, and because it doesn't have much surface tension (unlike gasoline) would slightly leak out of the hole on the side as well.
In normal conditions fluid has lower pressure if:
(a) it was flowing and is now moving faster because of a geometric constriction
(b) it is being sucked (i.e. being pulled into a lower pressure region than ambient)
Moving fluid has higher pressure if:
(c) it was flowing but isn't flowing as fast due to a geometric expansion
(d) it was pushed (i.e. coming from a higher pressure area than ambient)
Note that in the case of a fan in a tube, the fluid has lower pressure than ambient behind the fan, and higher pressure than ambient after the fan.
