Why pumps in a hydraulic system must be positive displacement?
Questions & Answers - Hydraulic Pumps
In a hydraulic system for power transmission taking advantage of the incompressibility of the
fluid, all
the
volume that is suctioned from the tank by the pump should be discharged out of the outlet unabated regardless of the
pressure needed.

For this reason, the
pump is constructed in a way that it has inside hermetic chambers that are connected to the drive shaft for pumping. When the shaft rotates, the chambers do the same in such so that when each is connected to the suction its volume of fluid is collected and moved towards the outlet where it is discharged.
There is no connection among chambers and therefore no connection or possibility of
passage from the inlet and outlet.
The most important fact about
positive displacement pumps is that if the shaft rotation speed is constant, the volume per unit of time or
flow rate is constant too.

In graphic 1 we can see an analogy of a positive
displacement pump. The turntable and 12 persons on top represent the pump and 12 chambers respectively, the yellow and red balls represent the fluid under no pressure and pressure respectively. As the table(shaft and chambers) rotates CW, the guy in the left pipe gives fluid to the one in the turntable. Once the table rotates 1/12 of a turn, the following guy in the table gets a ball(fluid) and the guy next to the right pipe gives a red ball(fluid under pressure).
Let's end this analogy saying that for a complete turn of the shaft there are 12 yellow balls picked up and 12 red balls delivered.
In graphic 2 we can see what happens with a gear pump. The # of chambers is the volume contained between teeth (12 per gear) and inside the wall. The chambers are separated by the teeth and the wall also.
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