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handbook of modern sensors

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376 11 Flow Sensors<br />

11.8 Coriolis Mass Flow Sensors<br />

Coriolis flowmeters measure flow <strong>of</strong> mass directly, as opposed to those that measure<br />

velocity or volume [10]. Coriolis flowmeters are virtually unaffected by the fluid<br />

pressure, temperature, viscosity, and density. As a result, Coriolis meters can be used<br />

without recalibration and without compensating for parameters specific to a particular<br />

type <strong>of</strong> fluid. Although these meters were used mainly for liquids when they were<br />

first introduced, they have recently become adaptable for the gas applications.<br />

Coriolis flowmeters are named after Gaspard G. Coriolis (1792–1843), a French<br />

civil engineer and physicist.ACoriolis sensor typically consists <strong>of</strong> one or two vibrating<br />

tubes with an inlet and an outlet. A typical material for the tube is stainless steel. It is<br />

critical for meter accuracy to prevent any mechanical or chemical attack <strong>of</strong> the tube or<br />

its lining by the flowing fluid. Some tubes are U-shaped but a wide variety <strong>of</strong> shapes<br />

have been also employed. The thinner tubes are used for gas, whereas thicker tubes<br />

are more appropriate for liquids. The Coriolis tube is set to vibration by an auxiliary<br />

electromechanical drive system.<br />

Fluid enters the meter in the inlet. A mass flow is determined based on the action<br />

<strong>of</strong> the fluid on the vibrating tubes. As fluid moves from the inlet to outlet, it develops<br />

different forces depending on its acceleration that is the result <strong>of</strong> the tube vibration.<br />

The Coriolis force induced by the flow is described by<br />

F = 2mωv (11.27)<br />

where m is the mass, ω is the rotating circular frequency, and v is the vector <strong>of</strong> the<br />

average fluid velocity. As a result <strong>of</strong> these forces, the tube takes on a twisting motion<br />

as it passes though the vibrating cycle. The amount <strong>of</strong> twist is directly proportional<br />

to the mass flow through the tube. Figure 11.17A shows the Coriolis flow tube in a<br />

no-flow situation, and Fig. 11.17B shows Coriolis tube with the flow.<br />

(A)<br />

(B)<br />

(C)<br />

Fig. 11.17. Coriolis tube with no flow (A); twist <strong>of</strong> the tube with flow (B); vibrating phase shift<br />

resulting from Coriolis forces (C).

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