The information you seek should come from the pump manufacturer. If you are dealing with two external gears of equal size you can approximate the displacement in cubic inches per revolution by using the formula
(OD-CD)*L*CD*pi
where OD = Outside Diameter
      CD = Center Distance
      L  = Face Width of Gear
But this will only get you in the ball park and at a theoritical "0 psi" differential pressure.
The manufacturer can estimate net flow under pressure for a given pump when given the fluid viscosity, pressure, and rpm.

Hello,

If frequency of rotation of the gears is N, and if v represents the total volume of liquid displaced from each gear wheel during one revolution, then capacity is given by:

                         Q = 2vN         (1)

From geometric considerations, it is seen that the displaced volume, v, is given approximately by:

v = Pi/4[DSq.- DoSq.]x W = Pi x DSq. x W [1-(Do/D)Sq.]  (2)
                              -------------
                                    4

where: DSq. = Outside gear diameter in. (squared)
       DoSq. = Pitch Dia. of gear in. (squared)
       W = Width of gear in.

Equations (1) and (2) yield:

                     Q = a N                      (3)

where:     a = Pi x DSq. x W  [1-(Do/D)Sq.]       (4)
                   --------------
                          2

where:  Q = Volumetric flowrate in cubic inches/second
        a = Capacity of gear pump, cubic inches/revolution

I hope I have this right, please let me know how this works.

PS, v = Volume in cubic inches, N = rpm
In equation (2) Pi, DSQ. and W are all divided by 4, also, in equation (4) the three are divided by 2.

Hello,

Re: submittal by 186000,

Equation (3)     Q = a N shows that pump capacity is theoretically independent of factors such as viscosity, pressure, and pump speed.

Hello fredb,
You're right, of course.
Ergo "and at a theoritical "0 psi" differential pressure."

If, however, I wished to estimate flow under pressure I would calculate the total slip in gpm/psi based on the viscosity of the fluid. This brings up another point:
Automatic2 desires "constant repeatability". Unless the viscosity of the fluid is being held constant the flow will vary. This is where the viscosity and pressure become really important. Generally, the lower the viscosity and the higher the pressure, the greater will be the variations in flow as observed at the work as a result of variations in viscosity.

Also, as the pump wears the flow (at the work) will decrease. This too, (depending on pump design), is of greater concern as the pressure increases.     

I thank you for the excellent responses. My fluid is constant in viscosity/temperature (water base). My pressure is derived largely from overcoming a checkvalve at approx 8psi. This gives me a starting point. My requirements are for three identical flows. I've searched numerous suppliers looking for a pump head that could be stacked as a triple and driven off a common shaft, to no avail. I'm now pricing a custom assembly which will group 3 gears around a common driven gear, with appropriate housing profile to proved the pumping action. The idea is a compact pump head that will drop into a 45 gal barrel and provide the 3 equally metered streams. Any ideas as to possible suppliers?.