JBA said:
Stated another way, it appears you are simply saying you want an equal flow velocity through both inlets, that is the only way to achieve an equal static pressure at those two points. The flow rates will still be different if the two inlets are of different sizes or flowing backpressures.
I agree that if the total pressure is the same at the two inlets, then in order to have the same static pressure at the two inlets as well, the flow velocity would also need to be the same. Flow rate could be different.
I'll go into more detail about what I am considering, to make sure I understand regulator valves correctly.
Suppose I am analyzing a pipe network, same as above, two inlets and one (or more) outlets into atmosphere. And I disregard minor losses at the junctions of pipes in the network. Also, I assume fully developed laminar flow at the inlets. And I treat the network like a circuit by writing down the Poiseuille flow equation (
https://en.wikipedia.org/wiki/Hagen–Poiseuille_equation) for each pipe segment, which describes the static pressure loss over a straight pipe for a given flow rate. Now I set the static pressure at both inlets to be the same, and I write down conservation of flow rate equations for the junctions. Now I have a system of equations that I can solve, which will tell me the flow rate through each segment of the network. I then can use the calculated flow rate at the inlets along with the static pressure I chose for the inlets and calculate the total pressure at the inlets. I will likely find different total pressures at the inlets, particularly if the network is asymmetric.
Now I want to test my calculations. Hooking up my network to a reservoir is a different boundary condition than what I used in my calculations (it sets total pressure the same at the inlets, not static pressure). So what if I take a reservoir that is pressurized to a very high pressure. Now I attach a pressure regulator (like the single-stage one on this page,
https://en.wikipedia.org/wiki/Pressure_regulator) to each inlet of my network and then attach the regulators to the reservoir, will this achieve the boundary conditions I assumed in my calculations? That is, can I use the valves to set the static pressure at each inlet the same, while allowing the total pressure at the inlets to be different from each other, assuming neither total pressure exceeds the very high pressure that the reservoir is at?
Thanks again for the discussion everyone.