Analyzing a simple piston-pump (energy balance? deforming control volume?)

May 2014
I'd like analyze the internals of the simple pump shown in the attachment. It replaces old engine oil with fresh oil simultaneously, pumping the old into a waste tank and pumping the new into the engine via a make-up tank.

I think I'd want to create two deformable control volumes, one for each side of the piston and there will be multiple states (ie solenoid being energized or de-energized, which side the piston is on, etc.)

I want to know how the various pressures and geometries might affect its operation (ie. inlet/outlet diameters, spring stiffness, inlet/outlet pressures, etc.)

I'm getting a little confused with all the different variables I will have to keep track of. I think this would be an energy balance, no use of Bernoulli's equation here.

Thanks for any tips you can give!


May 2014
And I apologize, the graphic is a bit confusing...

Red and Green are separate oil volumes. The spring forces the piston and the only side that should be at a very high pressure is the 'Oil supply' which is pressurized by the engine oil pump.

everything else could be at atmospheric pressure or close to it...


PHF Helper
Jun 2010
Morristown, NJ USA
Please clarify:

1. The purpose of this device is to move oil from the feed oil supply to the fuel system, and also move a separate supply of oil from the make-up tank to the oil pan, correct?

2. The solenoid opens and closes four separate valves, but does it also move the piston? Or are you expecting the pressure from the feed oil supply to cause the spring to compress, and when the pressure is cut off the spring relaxes, thus pumping oil from the make-up tank to the oil pan? In other words the oil pressure from the feed oil supply makes the pump run, correct?

It would be very dificult to optimize this design, as its operation will depend very much on the viscosity of the oil, pressure from the feed oil supply, and back pressure from the oil pan. Clearly the larger diameter the oil lines, the better it will flow. As for flow rate - that would be the volume displaced by the piston on each stroke times the strokes per minute. Not sure what else you're expecting in terms of analysis here.

EDIT - one thing that's apparent is that the pressure from the feed oil supply must be greater than the the sum of pressure in the oil pan plus the spring constant times its deflection when in the right position:

P_{feed oil) > P_{oil pan} + kx_{right}
where 'x_c' is the compressed deflection of the spring from rest. Otherwise the spring won't be compressed, forcing oil up to the oil pan

Secondly, the back pressure of the fuel system must be less than k times the deflection of the spring when at the left position (perhaps this deflection is zero?) plus presure from the make up tank:

P_{fuel system} < P_{make up tank}+kx_{left}
Last edited:
May 2014
thanks for the reply!

answering your questions:
1. yes, that's a correct description of the device.
2. the solenoid opens/closes the ports on the left of the piston. it appears as though the two ports to the right of the piston both have check valves, not controlled by the solenoid. so, when the piston is forced to the left, makeup oil is pulled into the cylinder and then as the piston moves to the right, pressure builds until it opens the check valve on the top connected to the oil pan.

i agree with the comment about oil viscosity and pressure levels in the ports. this thread is a little vague in terms of what I want to analyze, but I think it's a cool project to catalog the effects of each parameter of the system.

the main question I was running into was how to break up the system into two deformable control volumes... left side of piston and right side of piston (and how to account for the spring -- as an external load/work on only one control volume?). and I guess I would create multiple states of the system with each port open/close configuration and how pressures affect the operation, etc.

I guess I should start and then post questions when I run into them! :)


Apr 2008
Bedford, England
I have little to add to ChipB's analysis except that I suspect the spring is there purely to even out hydraulic pulses.
Otherwise, as the solenoid opens and closes the valves, hard (possibly damaging) shocks will hammer through the oil.
The spring will help to smooth these out.