## gear pump volume

## gear pump volume

(OP)

I am investigating the use of a gear pump to use as a metering pump. By sensing the drive motor revolutions, I'm hoping to deliver a preset quantity of fluid with constant repeatability. My question for anyone that knows is, what formula can I use to calculate the volume per pump rotation. I'm starting off with a 20DP/10tooth/.500" face spur gear pair.

## RE: gear pump volume

(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.

## RE: gear pump volume

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.

## RE: gear pump volume

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.

## RE: gear pump volume

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.

## RE: gear pump volume