I'm no fluids whiz. But as a first GUESS. The pump will deliver flow-rate equivalent to nameplate on a volume-flow-rate basis, (assuming the output is not restricted beyond reason). The DP can be determined from the system headloss characteristic curve.
Forgive me if this is totally obvious or totally incorrect.
I think electricpete's answer is what you are implying but if not. PD pumps (neglecting the design pressure of the pump and piping system) have a theoretical maximum discharge pressure set by the motor driver, is this what you are asking? If you can explain your question in some more detail, it would help.
Take motor's output (and that's an open question if you want to use the nameplate, with any additional design allowances or a short-term start-up value), the flow rate and the pump's (and gearing if applicable) efficiency. That will allow to you calculate the maximum discharge pressure.
Essentially the formula is the same as for sizing the pump in the first place:
Tri-lobe pumps will experience internal leakage known as "slip" that keeps the actual discharge lower than the theoretical discharge. Slip is dependant upon the differential pressure and the product viscosity.
For modeling purposes, assume a pump that truly moves a fixed flow rate. A recirculation line from discharge to suction with a flow restricing orifice in it is added. The flow orifice size is "tweaked" to produce the same amount of slip as at a given differential pressure and viscosity as the pump manufacturer's literature suggests. The pump-orifice combination fairly accurately models the performance of an actual lobe pump. By the way, the same applies to a roots blower moving gases.
