Fluid Mechanics: 2 Connected Cylinders w/ Different Diameters

[Carolyn]

Hi, we are doing an experiment and encountered the following problem

We have two cylindrical tubes connected together and the two tubes have different diameters (laying horizonally on the table, for example). So if we put water into the tubes and apply the same pressure to the two water surfaces (each with the same diameter as the two tubes, ie. one is smaller than the other). Will the water start flowing in the tubes this case? If so, which direction will it flow?

 

[mgb_phys]

What is the definition of pressure?
Ignoring for the moment the weight of the fluid - in a closed system is the pressure the same everywhere?

 

[Carolyn]

What is the definition of pressure?
Ignoring for the moment the weight of the fluid - in a closed system is the pressure the same everywhere?

Basically what we are thinking is it that since one has a larger surface area than the other one and the pressures are the same for both water surfaces, and F = PA, so force is larger on the bigger surface area than the smaller one. So the water should flow in the direction of the smaller surface.

We did the experiment and the water didn't flow, so we thought it's probably because of friction?

But then according to Bernulli's Principle, as long as the pressure are the same and the height are the same, then the velocity should be the same. But since the surface areas are different, obviously the velocity shouldn't be the same if it indeed flows. So Bernulli's principle says the water shouldn't flow?

That's why we are really confused...

 

[Andy Resnick]

Flow only occurs if there is a pressure gradient, and you needed to apply different forces in order to apply identical pressures to the two surfaces.

I assume that when you say both ends of the compound tube are at the same pressure, you are taking into account gravity as well- otherwise there will be a pressure gradient due to the difference in hydrostatic pressure.