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.
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.