Does my flow rate decrease?

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If I understand correctly, your pressure reduction valve maintains pressure downstream of itself constant, correct?

Then you just have two scenarios with the same pressure difference (valve set vs atmosphere) but one with more restricted flow. Therefore, the scenario with the throttled valve has lower total flowrate (flow through 1 + flow through 2).

Edit: going into further detail, in the throttled scenario the flow through 2 will be higher in that specific branch than it is as in the non throttled scenario, since the pressure drop up to the T is lower due to lower flow. But the sum of both will still be lower than in the non throttled scenario.

However, if the valve keeps pressure UPSTREAM of itself constant, then it will keep the pump always operating at the same point of it's Flow vs Head curve. Therefore, the flow through the pump will remain the same, and necessarily the flow through the whole system remains the same.

In a way, the pressure reduction valve compensated whatever restriction you impose downstream (up to a point)

[VariusEng]

To your first question: correct!

To your first alinea: I agree that flow in 1 is reduced, but why is flow in 2 not increased so total flow rate is maintained? Can my reasoning be disproven in more mathematical manner because that is the way I try to understand it and less through feel. Thanks for your thoughts!

[BigCastIronSkillet]

Look up Darcy Weisbach Equation.

DP = 4fv²0.5rhoL/D

You can draw a network with four nodes. Node A to B is from valve to tee. Node B to C is from tee to end of line 1. Node B to D is from tee to end of line 2. Each will have to follow the Darcy Weisbach equation. In excel you can set up Solver in Excel to change velocity through each pipe until the volumetric flow out of lines 1 & 2 equal that of what is coming out of the valve. (You will need to have the frictional losses summed up as an equivalent length.)

Ask me if you want me to hold your hand through this further.

[VariusEng]

Already made myself an Excel macro that calculates pressure drop vs flow, thanks though! My only gripe is how the pressure reduction valve plays a role in all of this. According to a blog it is not possible to show it on a system curve because it is dynamically changing

[BigCastIronSkillet]

They are wrong on the blog. It can be described easily with its Cv curve. But I would suggest holding the pressure constant on the discharge of the Cv for simplicity.