Variable area flowmeters consist of a tapered, vertically-oriented tube with the smallest diameter at the base and largest at the top. As a result, the cross-sectional area of the tube changes based on height. In this example, a ball indicator sits at the base due to the downward force due to gravity (Fgravity). As gas flow encounters the indicator, an upward, applied force (Fapplied) pushes the ball up a tube precalibrated for the specific gas being used. The pictured tube has been calibrated for oxygen, so a given flow rate will cause the ball indicator (which should be read at its center) to rise to a certain height.
But how?
The ball has a fixed diameter and mass. Since the tube’s diameter increases as the ball rises, more gas can flow around the indicator at a rate faster than below it. According to Bernoulli’s principle, this leads to decreased pressure above the ball allowing it to rise to a point of equilibrium where Fgravity = Fapplied.
At low flows when the ball is still near the tube’s base and there isn’t much flow around it, gas flow is laminar and related to the gas’ viscosity. At higher flows when the ball rises and there is much more flow around it, turbulence makes the gas’ density (affected by altitude) more important in determining flow. Calibration of the tube and maintaining vertical orientation are key!
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