A positive displacement flow meter is a cyclic mechanism built to pass a fixed volume of fluid through with every cycle. Every cycle of the meter’s mechanism displaces a precisely defined (“positive”) quantity of fluid, so that a count of the number of mechanism cycles yields a precise quantity for the total fluid volume passed through the flow meter.
Many positive displacement flow meters are rotary in nature, meaning each shaft revolution represents a certain volume of fluid has passed through the meter.
Some positive displacement flow meters use pistons, bellows, or expandable bags working on an alternating fill/dump cycle to measure discrete fluid quantities.
Positive displacement flow meters have been the traditional choice for residential and commercial natural gas flow and water flow measurement in the United States (a simple application of custody transfer flow measurement, where the fluid being measured is a commodity bought and sold).
The cyclic nature of a positive displacement meter lends itself well to total gas quantity measurement (and not just flow rate), as the mechanism may be coupled to a mechanical counter which is read by utility personnel on a monthly basis.
Positive Displacement Flow Meter
A rotary gas flow meter is shown in the following photograph. Note the odometer-style numerical display on the left-hand end of the meter, totalizing gas usage over time:

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