Variable area meter
A variable area meter is a meter that measures fluid flow by allowing the cross sectional area of the device to vary in response to the flow, causing some measurable effect that indicates the rate.
A rotameter is an example of a variable area meter, where a weighted "float" rises in a tapered tube as the flow rate increases; the float stops rising when area between float and tube is large enough that the weight of the float is balanced by the drag of fluid flow.
Another type is a variable area orifice, where a spring-loaded tapered plunger is deflected by flow through an orifice. The displacement can be related to the flow rate.
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