Splitting the GPM output of a circulation pump?

The pressure will not be any different in theory, if its a closed system. You probably meant flow is my guess. The back of the envelope answer is that the 2" pipe will carry 78% more flow than the 1.5" pipe. So if your total flow is 60 gpm, the 2" pipe will carry around 38.4 gpm and the smaller on will be around 21.6 gpm.

The pipe layout of geometry will also enter into the equation if there is no method to adjust the flow.

As an example, even with two branches of the same diameter, if you use a tee and do not have perfectly symmetrical piping, one line is get more flow that the other. Likewise, it you use a non symmetrical wye the same thing will occur.

This why it is best to have valves, orifices or other methods to adjust the pressure drops to assume correct distribution of flow.

Oil will travel the path of least resistance. If both pipes are the same length and inside diameter the flow may be close to the 30 gpm down each pipe. If the pipes have different inside diameters the bulk of the oil will travel down the larger pipe unless the larger pipe is longer.

The pressure drop and flow rates if you split the flow will depend upon the total system characteristics downstream. The diameter of the pipes is only one factor.

You will alter the velocity, but the pressure in both lines will have the potential to be the same. You would have to add a regulator in the branch you want at a lower pressure.

The pressure will be the same, but your flow rate through them will be as follows.

With the same resistance at the ends (and ignoring the slightly different coefficient of friction due to sizes).........

If you are using regular schedule 40 pipe, then the areas for the 1.5" and 2" would be: 2.03 in^2, and 3.36 in^2.

Flow through the 1.5" would be (2.03/(2.03+3.36))=37.66%

With that balance left through the 2" pipe............

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