The simplest example of a variable-area flowmeter is the rotameter, which uses a solid object (called a plummet or float) as a flow indicator, suspended in the midst of a tapered tube:

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As fluid flows upward through the tube, a pressure differential develops across the plummet. This
pressure differential, acting on the effective area of the plummet body, develops an upward force
(F = P/A). If this force exceeds the weight of the plummet, the plummet moves up. As the plummet
moves farther up in the tapered tube, the area between the plummet and the tube walls (through
which the fluid must travel) grows larger. This increased flowing area allows the fluid to make it past the plummet without having to accelerate as much, thereby developing less pressure drop across the plummet’s body. At some point, the flowing area reaches a point where the pressure-induced force on the plummet body exactly matches the weight of the plummet. This is the point in the tube where the plummet stops moving, indicating flow rate by it position relative to a scale mounted (or etched) on the outside of the tube.

The following rotameter uses a spherical plummet, suspended in a flow tube machined from a
solid block of clear plastic. An adjustable valve at the bottom of the rotameter provides a means
for adjusting gas flow:

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The same basic flow equation used for pressure-based flow elements holds true for rotameters as
well:

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However, the difference in this application is that the value inside the radicand is constant, since
the pressure difference will remain constant and the fluid density will likely remain constant as
well. Thus, k will change in proportion to Q. The only variable within k relevant to plummet
position is the flowing area between the plummet and the tube walls.

Most rotameters are indicating devices only. They may be equipped to transmit flow information
electronically by adding sensors to detect the plummet’s position in the tube, but this is not common practice. 
Rotameters are very commonly used as purge flow indicators for pressure and level measurement
systems requiring a constant flow of purge fluid. Such rotameters are usually equipped with hand-adjustable needle valves for manual regulation of purge fluid flow rate.

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