Rotameters buoyancy force

The buoyancy force was discovered by Archimedes in 212 BC in Syracuse. He found that an object that is partially or wholly immersed in a fluid is buoyed by a force equal to the weight of fluid displaced by the object (up to the point at which it is submerged). In the case of a bob in a rotameter, since it is entirely submerged, the buoyancy force is simply the product of the fluid density, pf, the bob volume, V, and the gravitational constant. 

Fig. 12.15. Flow measurement with float (rotameter), a Conical flow pipe b float F gravity force Fe buoyancy force Fo- drag force [1].

Rotameter A rotameter consists of a vertical tube with a tapered bore in which a float changes position with the flow rate through the tube. For a given flow rate the float remains stationary since the vertical forces of differential pressure, gravity, viscosity, and buoyancy are balanced. The float position is the output of the meter and can be made essentially linear with flow rate by makiug the tube areavaiy hn-early with the vertical distance. 

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