01 June 2003

Coriolis: Twist and Shout

Coriolis flow measurement is a comparatively new technology. The first commercial meters appeared in the 1970s. They measure mass flow directly with high accuracy and rangeability.

A French engineer and mathematician, Gustave-Gaspard Coriolis, first described the Coriolis force in the early 1800s. It's an effect of motion on a rotating body and is of paramount importance to meteorology, ballistics, and oceanography.

Whereas pressure differences tend to push winds in straight paths, winds follow curved paths across the Earth. In 1835, Coriolis first gave a mathematical description of the effect, giving his name to the Coriolis force.

While air begins flowing from high to low pressure, the Earth rotates under it, thus making the wind appear to follow a curved path.

In the Northern Hemisphere, the wind turns to the right of its direction of motion. In the Southern Hemisphere, it turns to the left. The Coriolis force is zero at the equator.

This force results from acceleration acting on a mass, and anyone who walks radially outward on a moving merry-go-round experiences the force. A person must lean toward or direct the mass of his or her moving body against the force that the Coriolis acceleration produces.

If we know the force (F) acting on the body, the velocity (V) of the body, and the angular velocity (ω) of the platform, we can calculate the person's mass (M).

By applying this phenomenon to mass-flow measurement, we create a Coriolis mass flowmeter. Indeed, there are several types of meters leveraging the Coriolis effect. One straight-up mass-flow device has rotors containing metal vanes that form several channels.

This gadget operates at a constant angular velocity per an external power source. Any particle of fluid traveling through the radial channel with velocity V will experience the Coriolis force, resulting in a torque acting in the plane of rotation.

With the torque acting in the plane of rotation, measurement of the torque happens by placing a sensing means, such as a strain gage, in the drive shaft. To measure the mass-flow rate, we hold the angular velocity-the motor rotational speed-constant, leaving the torque as a direct measure of mass flow.

Another type of mass flowmeter using the effect of Coriolis acceleration is the gyroscopic mass flowmeter. Gyroscopic precession occurs in a gyroscope when a torque is applied perpendicular to the axis of rotation.

The precession is a slow rotation of the spin axis about an imaginary line intersecting the spin axis, so as to describe a cone where the torque acts perpendicular to the cone surface.

The reaction force producing the torque in a gyroscopic mass flowmeter is, in reality, a Coriolis force.


A very advantageous means of eliminating the need for rotating seals and rotating parts is to generate a Coriolis force through vibration or oscillation of the flow tube.

Two identical tubes, A and B, are constructed so that both may be oscillated at constant frequency and amplitude about the axis of symmetry or primary flow axis.

Tube A is the measuring tube through which all the fluid passes, and tube B is the mass-flow compensation mechanism containing the stationary fluid.

Fluid flowing in the oscillating measuring tube A exerts a variable force on the tube walls, thereby creating an oscillating torque in the plane of the oscillation.

The torque produced is comprised of three components: the torque resulting from the Coriolis force, which is directly proportional to mass flow; the torque component arising due to the inertia of the tube; and the torque component arising from the inertia of the fluid in the tube, which is proportional to the fluid density.

For the Coriolis flowmeter operating with constant angular velocity, the inertia effects do not exist. However, in an oscillating system, the angular velocity varies in magnitude and sign, thereby causing the resulting torque measurement to be dependent not only on mass flow, but also the moment of inertia of the system.

To compensate for the torque produced by the inertial components of the system, a similar tube, B, filled with stationary fluid, is used such that the moment of inertia of tube B matches that of tube A. The resulting output is subtracted from the total output of tube A, leaving then only the torque sensitive to mass flow.

The gyroscopic principle may also play in the oscillatory mode. In geometric form, the oscillating gyroscopic flowmeter is similar to the one employing constant angular rotation.

The circular tube has two degrees of freedom, one about axis A-A and the other about axis B-B, which drives the vibratory mode, usually at the resonant frequency of the system. Once in oscillation, the circular tube, due to gyroscopic effect, goes into a vibration precession or a motion similar to a nutating-wobbling-disk, about the axis C-C.

The amplitude of these precessional oscillations is not only proportional to the mass flow of the fluid, but is also dependent on the moment of inertia of the circular tube and the inertia of the fluid.

Another form of device employing the gyroscopic principle of operation in the oscillatory mode is a tube shaped in the form of the letter "U" that forms one-half of the classical gyroscopic mass flowmeter.

An electromagnetic oscillator drives the U-shaped tuning-fork-like structure at the resonant frequency of the system, thereby producing a Coriolis acceleration and resultant force.

The force acts alternately-perpendicular to the flow path-in opposite directions, causing an oscillating moment about axis O-O of the flowmeter.

The resulting moment (m), acting about the central axis and in a plane perpendicular to the driving moment (w), produces a twist-type motion, where the deflection angle between FC1 and FC2 is directly proportional to the mass-flow rate. IT

Nicholas Sheble (nsheble@isa.org) writes and edits the Control Fundamentals department. The source for this article is Fundamentals of Flow Measurement, by Joseph DeCarlo and ISA Press.

Coriolis mass flowmeter


Coriolis force


Oscillating Coriolis mass flowmeter
Oscillating gyroscopic mass flowmeter

U-shaped gyroscopic mass flowmeter