Positive displacement  flowmeters are very accurate and have high turndown.  They can be used in very viscous, dirty and corrosive fluids and essentially require no straight runs of pipe for fluid flow stream conditioning though pressure drop can be an issue. They are widely used in the custody transfer of oils and liquid fluids (gasoline) and are applied on residential home natural gas and water metering.  A diaphragm meter, with which most homes are equipped, is an example of a positive displacement meter.  This type of meter is appealing in certain custody transfer flow applications where it is critical that the metering be functional in order for any flow to take place.
Positive displacement flowmeters, with internal wiping seals, produce the highest differential pressure (and subsequently greatest pressure drop head loss) of all the flowmeter types. Meters that rely on a liquid seal create a relatively low pressure drop.
Positive-displacement (PD) meters can measure both liquids and gases. Like turbine meters, PD flow meters work best with clean, non-corrosive, and non-erosive liquids and gases, although some models will tolerate some impurities. Because of their high accuracy, PD meters are widely used at residences to measure the amount of gas or water used. Other applications include:  chemical injection, fuel measurement, precision test stands, high pressure, hydraulic testing, and similar precision applications.
Some designs require that only lubricating fluid be measured, because the rotors are exposed to the fluid. PD meters differ from turbine meters in that they handle medium and high-viscosity liquids well. For this reason, they are often used to measure the flow of hydraulic fluids. Compared with orifice-type meters, PD meters require very little straight upstream piping since they are not sensitive to uneven flow distribution across the area of the pipe. Positive displacement flow meters can provide better relative accuracy at low flows than orifice-type flow meters. However, a positive displacement meter can be considerably heavier and more costly than non-positive-displacement types such as orifice plates, magnetic or vortex flow meters.