I am learning fluid dynamics, and I have questions about how to calculate pressure differences in pipes using a differential gauge.
In the following pipe there is water flowing from point A to point B.
I want to calculate the pressure difference between A and B.
The darker fluid has a specific gravity of 1,25, which means that its specific weight is 1,25 times the specific weight of water (4ºC and 1 atm).
The lighter fluid is water at 60 ºC, with a specific weight of $9.65 kN/m^3$.
As far as I learned, the pressure difference is given by the height of the fluid column multiplied by its specific weight.
So, in this case, I would do:
$$p_A + \gamma_{dark}(1.18 m) + \gamma_{water}(0.46 m) = p_B$$
I have two questions about this:
I am confused because there is a little extra space between the fluids that is not being considered and I also have no information about that remaining height.
Would the same be true if the pipes are not in a vertical position? Gravity would apply differently there. I see two cases: inclination between 0 and 90 degrees and completely horizontal. But I do not know how those affect the equation stated above.
UPDATE:
I ended up doing it as follows: