Coriolis effect: the physics behind Coriolis flow meters

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Coriolis effect: the physics behind Coriolis flow meters

Pull up your favorite note-taking app, because we’re learning about the principles behind the instruments again! Today we’ll tackle the Coriolis effect, the principle Coriolis flow meters use to measure flow and density.

If you work with automation, you’ve at least heard of Coriolis meters. But do you know how they work? The physics behind them? Don’t worry, we got you covered. We’ll explain it step by step so you can be a Coriolis expert by the end of the article.

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All right. Now that you’re in, we can move on to the basics of the Coriolis principle.

The Coriolis effect

You might have heard about it in high school, since teachers use it to explain wind currents deflection. It’s okay if you forgot. I did too.

As you may have guessed, the Coriolis force is named after a French scientist, Gaspard-Gustave de Coriolis. Other scientists had already discovered this concept, but Coriolis wrote the mathematical expression for it first in a paper on water wheels published in 1835.

Coriolis effect
Courtesy of Math.info

Okay, maybe you forgot about Coriolis, but do you remember Newton’s laws of motion? For those of us too embarrassed to admit it, I’ll do a  refresher on the relevant bits. The first law of motion, called the inertial law, states that if no external forces affect an object, it will stay in the same state, either resting or moving uniformly in a straight line. Remember this last bit – in a straight line.

However, this law only applies to an inertial frame of reference. So what happens in a rotating frame? That’s where Coriolis force comes in. Let me give you an example.

The merry-go-round

Imagine you’re playing catch with a friend on a merry-go-round, your friend in the middle and you on the outer edge. For the purpose of this example, let’s say there’s no wind at the moment, so no external forces interfere with the ball’s trajectory. When the merry-go-round is still, your friend throws the ball to you. Since there’s no wind, Newton’s first law of motion has the ball going from the center out to you in a straight line.

Now let’s say you have another friend who like to disrupt people’s games. We all had that friend in our childhoods, didn’t we? Anyway, the annoying friend spins the merry-go-round. This time, when your friend in the center throws the ball at you, it still goes in a straight line in an inertial reference frame. But in your perspective, a rotating perspective, the ball makes a curve. And guess what creates that curve? You got it. The Coriolis force.

Merry go round Coriolis effect
Courtesy of University of North Georgia

If we analyze the example, then we see that the Coriolis force describes a matter of perception. The ball goes straight, but you see it making a curve because you’re moving. Many people now call it the Coriolis effect rather than Coriolis force, because no actual external force affects the ball. But for the math, we still say Coriolis force for this inertial or fictitious force.

The math

As I said earlier, even though no force affects the ball in the merry-go-round example, the two people in the rotating plane see it making a curve. We can calculate the acceleration these people see because the ball’s inertia is proportional to (a) the velocity of the ball in the straight line and (b) the velocity of the merry-go-round’s rotation.

We call this the Coriolis acceleration and use the following formula to reveal it:

ac = 2*ω*v

  • ac = Coriolis acceleration
  • ω = rotational speed (merry-go-round)
  • v = velocity perpendicular to the axis of rotation (ball in a straight line)

If we go back one more time to Newton’s laws of motion, to the second one specifically, we can find a relation between force and acceleration:

F = m*a

  • F = force
  • m = mass
  • a = acceleration

So when we multiply both sides by the mass of the object, in our example the ball, and replace the acceleration with the Coriolis formula, we can find the Coriolis force with the resulting formula:

Fc = m*2*ω*v

So to sum up, the Coriolis force is proportional to the angular velocity, rotational velocity, and mass. That also explains why you can use a Coriolis flow meter as a mass flow meter. Look, we finally got to talk about flow meters!

The application

So yes, you know you can use Coriolis meters to measure flow as one application. We’ll have another article later to explain how this principle applies to the flow meter itself. Patience, young grasshopper. However, another field also commonly studies the Coriolis effect.

To explain the Coriolis effect in our example, we used a merry-go-round. But can you name another object that also creates a rotating reference frame by spinning around an axis? Yeah, you know this one. The very planet you stand on. Or sit or whatever.

Meteorologists also use the Coriolis effect in a similar way. Winds blow across the Earth from high-pressure systems (the poles) to low-pressure systems (the equator). The Earth keeps rotating as the winds blow. However, it rotates faster at the equator than at the poles, because a point at the equator has to travel farther in 24 hours than a point near one of the poles.

Earth Coriolis effect
Courtesy of CIMI

If you throw a ball from the North Pole to your friend at the equator, then the ball trajectory will look like it curves to the right. And if your friend throws the ball back to you, it will seem to him that the ball curves right again because you’re slower than him. So all the winds in the northern hemisphere deflect to the right and in the southern hemisphere to the left because of the Coriolis effect.

In the past, navigators used the Coriolis effect to forecast the so-called “trade winds” which influenced their travel between Europe and South America. Airplanes and rockets also experience the Coriolis effect, so pilots must take the Earth’s rotation into account when flying long distances.

Stay tuned! This is just the beginning of Coriolis topics on Visaya!

Related tags: Coriolis flow meters Coriolis force Flow flow measurement
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