# Coriolis Mass Flowmeter

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## The Coriolis Principle

It was G.G. Coriolis, a French engineer, who first noted that all bodies moving on the surface of the Earth tend to drift sideways because of the eastward rotation of the planet. In the Northern Hemisphere, the deflection is to the right of the motion; in the Southern Hemisphere, the deflection is to the left. This drift plays a principal role in both the tidal activity of the oceans and the weather of the planet. Because a point on the equator traces out a larger circle per day than a point nearer the poles, a body traveling towards either pole will bear eastward because it retains its higher (eastward) rotational speed as it passes over the more slowly rotating surface of the Earth. This drift is defined as the Coriolis force.

When a fluid is flowing in a pipe and it is subjected to Coriolis acceleration through the mechanical introduction of apparent rotation into the pipe, the amount of deflecting force generated by the Coriolis inertial effect will be a function of the mass flow rate of the fluid. If a pipe is rotated around a point while liquid is flowing through it (toward or away from the center of rotation), that fluid will generate an inertial force (acting on the pipe) that will be at right angles to the direction of the flow. With reference to image above, a particle (dm) travels at a velocity (V) inside a tube (T). The tube is rotating about a fixed point (P), and the particle is at a distance of one radius (R) from the fixed point. The particle moves with angular velocity (w) under two components of acceleration, a centripetal acceleration directed toward P and a Coriolis acceleration acting at right angle to ar:

ar (centripetal) = w2r

at (Coriolis) = 2wv

In order to impart the Coriolis acceleration (at) to the fluid particle, a force of at (dm) has to be generated by the tube. The fluid particle reacts to this force with an equal and opposite Coriolis force:

Fc = at(dm) = 2wv(dm)

Then, if the process fluid has density (D) and is flowing at constant speed inside a rotating tube of cross-sectional area A, a segment of the tube of length X will experience a Coriolis force of magnitude:

Fc = 2wvDAx

Because the mass flowrate is dm = DvA, the Coriolis force Fc = 2w(dm)x and, finally:

Mass Flow = Fc / (2wx)

This is how measurement of the Coriolis force exerted by the flowing fluid on the rotating tube can provide an indication of mass flowrate. While rotating a tube is not necessarily practical standard operating procedure when building a commercial flow meter, oscillating or vibrating the tube – which is practical – can achieve the same effect.

## How Does a Coriolis Flow Meter Work?

Coriolis mass flow meters measure mass through inertia. A liquid or gas flows through a tube which is being vibrated by a small actuator. This artificially introduces a Coriolis acceleration into the flowing stream, which produces a measurable twisting force on the tube resulting in a phase shift. This twisting force is proportional to the mass – and the meter measures mass flow by detecting the resulting angular momentum. Coriolis flow meters are capable of measuring flow through the tube in either the forward or the reverse directions.

In most designs, the tube is anchored at two points and vibrated between these anchors. This configuration can be envisioned as vibrating a spring and mass assembly. Once placed in motion, a spring and mass assembly will vibrate at its resonant frequency, which is a function of the mass of that assembly. This resonant frequency is selected because the smallest driving force is needed to keep the filled tube in constant vibration.

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