Differential Pressure measurement problem

[vega7]

Here is a relatively simple problem. I'm wondering if someone can give me their opinion on it or actually know experimentally if it is true.

Here is the diagram:

A flow of liquid (say water) is pumped through a pipe that has a reduction in diameter. You place a pressure gauge before and after the reduction to measure the pressure.
In setup 1, you have 15psi before and 10psi after. The pressure differential is 5psi.

Now, here is the part I am not sure about. In setup 2, If you connected a thin tube (as not to disturb system) between both diameters and then placed one gauge. What would that gauge read? Would this setup work?
Would the pressure read the differential pressure of 5psi (as above)? Or, would it just be the average of the pressures 12.5psi? Or, would it read something else?

Has anyone tried this?

 

[AlephZero]

Think about the limiting case where there was no flow through the system and the pressure was the same everywhere (say 10psi). Why do you think the gauge in setup 2 would read zero?

If there is some flow through the large pipe, there will also be flow through the small pipe. The gauge will read the static pressure in the small pipe, which will be some value between 15psi and 10psi depending on the exact geometry of the system.

You could connect a single gauge to measure the pressure difference across the change in area, but you would need a gauge with NO flow through it, e.g. a U-tube manometer with the one arm of the U connected to the upstream side and the other to the downstream side.