Any sprinkler contractors? Fluid dynamics engineers? Help determine water pressure

Setup:

Pressurized irrigation system. 1 1/2" service line, gravity fed, ~20psi.

I added a 1/2 hp booster pump and reduced the line to 1 1/4". At the end of the 300' "main line" (which is 1 1/4") I measured the flow:

~15 gpm

I then turned on the 1/2 hp booster pump and measured the flow

~20 gpm

Question: What do you think the pressure is if I restrict the output to 13gpm (which is the size of the largest sprinkler zone I am planning to install). I would like to see a minimum of 45psi -- but since I am a mere mathematician and not too well versed in Bernoulli's Principle I figured I throw it out to the wise engineers.

If you have a six inch line at pressure A, and then reduce that line down to two inches, the pressure will still be A. The difference will be how much flow (gpm) comes out of the two inch line versus the six inch line. If you can get 20 gpm at the end of the line at your value of 45 psi, then one 13 gpm head will work fine and the pressure will still be 45 psi. If you put two 13 gpm heads on that line, then you will need to increase you delivery capacity to 26 gpm- either by increasing line pressure or supply line diameter. What will happen is that at the same 45 psi, with two heads requesting 26 gpm total you will only get about 10 gpm to each head, assuming that they are equidistant from the pump. In reality, most likely the closest one will get a little more pressure, and subsequently a slightly higher output.

Or, you could just put a pressure gauge on the line.

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As a sanity check,
HP ≈ GPMxHD/(40xEfficiency)
e.g., 100x120'/[40x50%] = 6.1 hp, depending on the efficiency of the pump you select.
Pump efficiencies range from 15% to over 90%.

That Bernie guy says that 14.7 psi ≈ 33' of head.

Would you post a diagram of your before and after setup, showing pipe lengths, pump location and relative heights, along with a link to your pump spec's and curve?