The Coriolis flow meter is one of the most versatile flow meters available. One of the most important features of Coriolis effect flow meters is that they can measure mass flow, density, and temperature in the same device.

## The Coriolis effect, the Coriolis flow meter’s working principle

The Coriolis effect, the physical principle behind Coriolis flow meters, 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.

As per Newton´s law, 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. However, this law only applies to an inertial frame of reference.

So what happens in a rotating frame? That’s where the Coriolis effect comes in.

### The Coriolis effect on a merry-go-round

Let’s imagine we are playing catch with a friend on a merry-go-round, where the friend in the middle and we 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, the friend throws the ball to us. Since there’s no wind, Newton’s first law of motion has the ball going from the centre out to you in a straight line.

Now let’s say there is another friend. This time, when the friend in the centre throws the ball, it still goes in a straight line in an inertial reference frame. But as per the rotating perspective, the ball makes a curve, and this is the Coriolis effect.

If we analyze the example, then we see that the Coriolis effect describes a matter of perception. The ball goes straight, but we see it making a curve because we are 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.

To know about the types of flow meters in the industry, take a look at our article on flow meter types

The math describing the Coriolis force

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:

a_{c} = 2*ω*v

- a
_{c}= 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:

*F _{c} = m*2*ω*v*

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. If you would like to know more about the Coriolis force, we have an article about it.

## Mass flow measurement using the Coriolis effect

Now that we know all about the Coriolis effect or force, let’s see how to use it to measure flow. In the flow tube of a Coriolis flow meter, there is a drive coil that vibrates the tube at its natural frequency. The tube has inlet and outlet pickoffs at either end. These pickoffs measure the tube’s movement, the frequency at which the tube vibrates. To understand how to measure the flow from these pickoff signals, we’ll consider two situations: no flow and flow.

### Signals in sync mean that there is no flow

Imagine that we had to stop a process and had no flow through the measurement tube. Even without flow, the drive coil of the meter continues to vibrate the tube. So the pickoffs will still create the signal waves from the tube’s vibration. The signal waves create the movement of one tube relative to the other.

### Calculating mass flow from the phase shift of the signals

Now we can restart the process and once again have flow through the tube. The flow, in this case, creates the Coriolis effect, causing a little twist of a time difference between the inlet and outlet pickoffs.

If we analyze the signals we can see that the waves have phase-shifted from each other and are not synchronized anymore. With this tiny delay between the two waves, we can calculate the mass flow rate. The rate is directly proportional to the time delay. We’ll also need a temperature measurement to calculate the compensation factor.

As a side note, the pipe frequency can directly influence the measurement. We dug up an Endress+Hauser handbook and found that we’ll find the range of vibration in a pipe around 50 to 150 Hertz. If the Coriolis flow meter works in the same range, we’ll need some sort of vibration inhibitor to avoid problems. However, some measurement tubes work at high frequencies like 600 to 1000 Hertz.

### Why do we need different tubes?

As mentioned before, we’ll find variations on twin-tube Coriolis flow meter in the market – straight, looped, or bowed tubes. For each option, we’ll get pitches from the vendors on how this style can improve the application. Depending on the shape of our choice, we might need extra space to install the meter. But sometimes compact designs will bring higher pressure losses compared to bigger formats. That means that we’ll need to scale out to find the right option for a process

We also find single-tube measurement systems on the market. This style is easier to clean, has lower pressure loss, and won’t split the fluid inside. However, it usually has lower accuracy and repeatability than twin tubes.

To know more about ultrasonic flow meters, you can read our article on the basics of ultrasonic flow meters

### Pros and cons of a Coriolis mass flow meter

**Advantages**

- Easy to implement in gas and fluid flow measurement
- Doesn’t require inlet and outlet runs
- Can measure mass flow, volume flow, density, and temperature
- Supports measurement independent of fluid viscosity and density
- Measures mass flow directly

**Disadvantages**

- Costs more than most other options
- Has a limited temperature range
- Has limited applications in multi-phase fluids

## Density and viscosity measurement using the Coriolis effect

A Coriolis flow meter can measure not only flow but also density. Some of them even measure viscosity! Just as we use the time delay to measure mass flow, we can use another aspect of a signal to calculate the density of a fluid flowing through a pipe. Can you guess which one?

### Density measurement

We’ll use an analogy here to make it easier to visualize. Imagine there are two identical buckets, one filled with water and the other with an equal amount of mercury. Now if we hang each from a steel spring, and we can tell – just by watching the movement of the springs – which bucket has water and which has mercury.

The drive coil in the Coriolis flow meter makes the measurement tube move at its own frequency, right? So when you change the density of the fluid, the resonance frequency of the tube also changes. A higher density will reduce it, and a lower density increases it.

During the calibration process of a Coriolis flow meter, developers use different fluids to increase the accuracy of their devices. For example, the PROMASS F 300/500 from Endress+Hauser a has an accuracy of +-0.0005 grams per cubic meter.

A Coriolis flow meter can measure temperature too, and this also has to do with density. If we change a liquid’s temperature, then its density changes too. So a Coriolis flow meter can measure the temperature of the fluid and compensate for it. They can also calculate specific density values such as Brix, Plato, Baumé, and API.

### Viscosity measurement

Some brands can measure viscosity. Endress+Hauser, for example, has patented technology to do so in the PROMASS I. They call this tech the Torsion Mode Balanced (TMB) system. The magic happens using torsional action. The middle of the tube has a counter-oscillating mass. This motion exerts a shear force on the fluid flowing through the tube. The fluid’s viscosity changes the oscillation, and the meter reads this change, calculates it, and converts it into numbers we can read.

Just remember that other technologies on the market can measure viscosity too. But here we have a device to measure that along with flow, density, and temperature. Everybody likes a multi-purpose device, right? Again, whether we’ll get good value for all those functions in *your *process, only you can determine.

### Coriolis flow meter density measurement applications

A Coriolis flow meter can measure the density of liquids, but not gases. If we need gas density, then you can use a technology called MEMS (micro-electro-mechanical system). And if we use a Coriolis flow meter to measure just density, then we would not need to install it directly on the production line. We can save some money by installing a small Coriolis meter in a bypass.

Like density, viscosity measurement can indicate process quality and help improve process performance. If we install your Coriolis flow meter directly in the line, then you can measure flow, density, temperature, and maybe viscosity all at once. If we want to measure just viscosity, then you can use the bypass trick. We just need to decide which technology will benefit usthe most.

To get to know about electromagnetic flow meters, you can read our article on electromagnetic flow meters

## The best Coriolis flow meters on the market and some beer measurement

Trying to find the right instrument for your application can sometimes be tricky, as you have many options and brands to choose from. Luckily, we have another article where we compiled a list of the best Coriolis flow meters on the market. They come with advanced functions like digital protocols or meter verification, which can be very helpful in your daily field activities. Check them out here.

Let’s take a look at this video talking about these devices and how you can use them to brew beer:

If you need help choosing the right flow meter for your application, take a look at our new flow meter smart assistant.

To know more about Corolios flow meters, you can **get in touch with our engineers **and we will be happy to help.