Physics
How the Hell DO We Measure Fluid Flow?
Whether the fluid is water, lava, liquid helium, or Earth’s atmosphere, it can flow under various conditions. But, how exactly would you measure that flow, and why would you even want to measure it? It’s more important to you than you think…
For unknown reasons, I’ve always had a passion for measurement, or “metrology”, and so it would only make sense that I’ve spent my entire adult life surrounded by measurements of some kind.
From working in a machine shop and having to measure physical dimensions of various parts to selling process instrumentation, I’ve always been around measurement devices. Needless to say, I’ve learned a lot about measurement in general along the way.
More importantly, I’ve also learned why measurement in and of itself is very important to society. In fact, I am of the opinion that standardization in measurements is what truly brought us out of the dark ages.
But, how exactly would you measure something like the flow of water in a pipe? When you turn your faucet on, you can vary the amount of water which comes rushing out, but how would you physically measure that amount of water?
There are quite a few different technologies that can be deployed to measure flow, but we’ll only take a look at a few of the technologies, specifically the more modern instruments.
Working Well Under Pressure
The very first ways to measure fluid flow was done using what’s called a “Venturi Meter”. A venturi is something which is used quite a lot for all sorts of reasons other than measuring flow. The best known use would be your typical vacuum cleaner.
Without getting too bogged down in detail, a venturi is essentially a specific decrease in the width of a pipe through which a fluid is flowing. The sudden change in diameter creates a pocket of negative pressure which changes the pressure of the water before and after the venturi.
Using some math, the fluid flow is essentially calculated in proportion to the differential pressure across the ventrui tube.
Now, that is, of course, an over simplified explanation of the device and the calculations. But, for the purposes of this article, that’s as in depth as we’ll need to get!
However, one thing to keep in mind is that regardless of the technology being used, pressure, in one way or another, will be used to help us calculate the flow rate of a fluid!
That also means that we need to ensure we maintain a specific pressure in order to accurately calculate a flow rate. That’s where geometry comes into play!
A Known Geometry
The most important part of measuring a flow rate is having a known geometry through which our fluid can flow, while being measured.
This is probably most important when measuring the flow of a natural body of water, like a river. This type of flow is called, “open channel flow”. While a river does have measurable dimensions, they change significantly depending on the location of the measurement.
For example, if you were to measure the height of the river a few feet from the shore, you’ll get one measurement. But, if you were to make that same measurement from the middle of the river, you’ll get a much different measurement indeed!
While that is the extreme example, the measurement can even vary quite a bit between any two spots in the middle of the river.
That discrepancy in dimension is not going to make measuring the flow of the river simple, if at all possible — to any degree of certainty. That means we need to somehow make the fluid form a uniform and known geometry. Luckily for us, water seeks its own level…
To achieve this uniform geometry, we enlist the help of tools called “weirs” and “flumes”.
As you can see in the photo above, the water is flowing through a concrete structure. The height of the water throughout the the entire structure (where the flow is smooth) is the same, and the width and length of the flume are of known dimensions as well.
This would imply that the only variable, or changing dimension, would be the water level. The flow of the water would therefore be proportional to the height of the water flowing through the structure!
The crudest way to measure the flow would be to dip a ruler or gauge into the water, and convert the height to a flow rate using a very specific formula. Of course, all of these formulas are already figured out for weirs and flumes of various dimensions and can be referenced in the ISCO Handbook.
The more convenient, and modern, way to perform the measurement is with something called a “level transmitter”. A level transmitter, or sometimes called a “transducer”, is a device with an element that can measure the distance between the device and the surface toward which it is facing.
There are various types of level transmitters in existence, and they use various forms of technology from ultrasonic, radar, laser, and even nuclear! Of course, you wouldn’t use a nuclear device to measure a natural body of water, and they are very rarely used in normal processes anyhow.
The point is, a known geometry with the fewest dimensional variables is what we need to accurately measure fluid flow.
But, why would open channel flow even be important to you? Well, if you’re the type of person who cares about your drinking water and the chemicals being added to it in the correct proportions, flow rate should matter a great deal to you.
That said, open channel flow isn’t the only way we can measure fluid flow. But, regardless of how we want to measure it, we still need the all-important, known geometry.
Paddle Wheels and Magnets?
So, what do paddle wheels and magnets have in common? Well, for all other intents and purposes, they basically have nothing in common. But when you use them together, you get a very cost-effective and simple way to measure flow!
In almost every other fluid flow measurement, the fluid will be flowing through a pipe. And you guessed it, that pipe has a known geometry!
In most cases, you’ll need the pipe to be full, and under a certain minimum amount of pressure in order to accurately measure flow. All of those characteristics are calculated by automation engineers and other folks who are experts in flow measurement, but it’s an absolutely fascinating topic to explore if you’ve enjoyed this article so far!
Going back to the paddle wheels, a “paddle wheel flow meter” is one of the simplest ways to explain flow measurement, and it also happens to be an effective way to measure flow in certain conditions.
The basic principle is very simple. You have a fluid flowing through a pipe in a certain direction which enters the flow meter in only one direction. As the flow of water enters the center chamber there, the water current applies force to the paddle wheel and causes it to rotate about.
Now, imagine you have a magnet attached to one of the paddle legs. You also have another magnet attached to the top of the flow meter which has some wires and electronics wired up to it.
The two magnets meet once per revolution of the paddle wheel. Every time the magnetic fields of the two magnets interact, it induces a small pulse of current in the electronics on the flow meter. The speed at which this happens, or frequency, is proportional to the flow velocity of the fluid pushing on the paddle wheel.
The faster that paddle wheel spins, the more pulses per second will be generated. Those pulses are going to represent a certain amount of fluid flow across the paddle wheel.
In fact, most flow meters will come with a known “K-factor” that tells the user how much volume of liquid they can expect per generated pulse.
Now, the reason we know that each pulse represents a specific amount of fluid flow is because of… that’s right, the known geometry of the pipe and the flow element itself!
Now, of course, the fluid’s viscosity is going to completely change the behavior and frequency of the paddle wheel, and that is precisely why flow meters tend to be specifically manufactured for specific applications.
That is also part of the reason why there are so many different kinds of flow technologies. Of course, there are other more important reasons for having different technologies. Every flow technology has its limitations, and benefits.
For example, a paddle wheel flow meter is known to not be the most accurate for low flow measurements. There are obvious reasons for this, but we won’t go over them here for your sake!
The point is, there are other types of flow meters, and some of them are totally cool!
Flowing Through a Vortex
When you first hear the word, “vortex flow meter”, you may get an image of some sort of big whirlpool of water or something wild like that, right?
Well, that’s the first image that popped into my head, at least.
While the vortex meter has nothing to do with a giant whirlpool, it’s still pretty damn cool, in my opinion.
To understand the working principle behind the vortex flow meter, just imagine standing next to a calm stream with the slightest of current. The surface is calm and undisturbed, but the current is there.
If you were to place a stick perpendicular in the stream, sticking straight up out of the water, you may notice something interesting. You’ll start to notice little whirlpools, or vortices, coming off each side of the stick you placed in the stream.
It doesn’t have to be a stick. You could have just as easily placed a rock in the middle of the flowing stream, and it would most likely produce vortices. But, the “quality” of the vortices is dependent on the shape of the body obstructing the flow of water.
If you couldn’t guess, this is precisely how a vortex flow meter measures fluid flow! However, one of the cooler things about the technology is that it can be used to measure the flow of vapors and gasses — not just liquids!
The above photo is an illustration of what the inside of a vortex flow meter looks like. Just like the paddle wheel flow meter, the fluid only enters and flows through the device in one direction.
As the water passes by the “bluff body” (various and interchangeable nomenclature is often used in this industry — as seen in the illustration) which is of a known and specific geometry, vortices are produced on each side of the bluff body.
You’ll also notice how the vortices alternate which is useful for measuring the flow.
As those vortices make their way through the flow tube, there is a sensor element which can detect the frequency of the vortices. Needless to say, the frequency of the vortices is proportional to the flow velocity of the fluid across the bluff body. Faster flow means a higher frequency.
Wait… Didn’t I say that a vortex flow meter can be used on vapor and gasses?
How is that supposed to work? Wouldn’t the amount of vapor or gas flowing through the flow meter depend on the temperature of said fluid? Meaning, if the temperature of the fluid were to change mid-flow, how could the flow meter make an accurate measurement?
Some vortex flow meters, like some of the OPTISWIRL models manufactured by KROHNE, feature a temperature sensor in the flow tube.
More specifically, they typically use what’s called an “RTD” (Resistance Temperature Detector) to measure the temperature of the fluid as it flows through. This is what’s called, “temperature compensation”.
The flow meter uses the flow velocity, temperature, and other factors to produce a temperature corrected measurement of the mass (or, weight, usually in ‘pounds per minute’) flow of the vapor or gas. Keep in mind, the vortices are still being counted as well!
But… the vortex flow meter isn’t the only instrument used to measure the mass flow of a fluid. In fact, it doesn’t even compare to the next technology on our list…
“Coriolis”? The Prospector from Rudolf?
No, no, Yukon Cornelius isn’t too involved in the measurement of flow rates these days, but you have to admit it was a decent attempt at a joke…
Rather, a “Coriolis Meter”, or “mass flow meter”, is a very advanced and interesting instrument used to measure the flow all sorts of substances to painstaking accuracy.
To understand how this impressive technology works, you first have to take a look at the “Coriolis Effect”.
I have explained it in more detail in a previous article, but the Coriolis Effect is essentially the effect, or force, put on an object moving in a straight line across a rotating surface. The actual explanation isn’t completely important to understand the basics of how the flow meter works, but it’s still an interesting topic to check out!
The biggest thing to take away from that video is that the concept of the Coriolis Effect was actually used to develop a technology to measure the mass flow of a fluid — liquid or gas.
To this day, I’m still blown away that someone actually sat down and figured this out. It’s an incredibly accurate, intricate, and expensive piece of equipment that is used in all sorts of applications!
While a lot of different companies manufacture them, the most well known are Micro-Motion (an Emerson Electric company), Endress+Hauser, and KROHNE.
There are different styles and forms, but they all follow the same basic principles, and they all pretty much look the same — inside and out.
The image above is a model OPTIMAS 6400 manufactured by German company, KROHNE. Fun fact, one of the first mass produced flow meters, the variable area flow meter, was invented by Ludwig Krohne in 1912 and is still the most widely used flow meter technology in the world!
Anyway, the first thing you’ll notice about the Coriolis meter is the really exaggerated curved body on the bottom. Sometimes, folks refer to that as “the bell”.
Inside of that “bell” is typically a pair of tubes (some have one tube, and some have more than two) that follow the slope of the flow meter’s body. Those are often referred to as the “flow tubes”. Needless to say, the flow tubes are made to very exact dimensional specification with very careful machining.
When the flow meter is powered on (typically with 24 VDC) the tubes are made to oscillate at a specific fundamental frequency.
Imagine there are sensors attached to the flow tubes which can sense when they are close to one another. Let’s also say that each time the tubes come together, it generates a pulse of current — just like the paddle wheel flow meter.
When there is no flow present, the pulses will be of a certain frequency and both tubes will swing evenly, or better put, “in phase”.
However, when a fluid begins to flow through the flow tubes, something happens to the oscillation of the flow tubes. They no longer swing in phase with one another.
It is that phase shift that allows the flow meter to detect the amount of fluid flowing through the tubes. The flow meter uses very sophisticated electronics and mathematical calculations to turn the phase shift of the flow tubes into an extremely accurate mass flow reading.
For a really great analogy, check out this quick video!
So, how accurate are they? Some Coriolis flow meter models boast a .00025% accuracy specification. That’s insanely accurate, if you couldn’t tell! And not only is the measurement accurate, it is also extremely precise which is even more important in sensitive flow measurements.
So, why would measuring the mass flow of a fluid be important to you? Well, if you like Entenmann’s cookies, or Wonder Bread, or any other mass produced baked good, you may really care about it — and its accuracy.
Most of those types of products use flour as a main ingredient in their process. If you were to look at some of the recipes, they may call for “pounds” or “kg” of flour at a time. Similarly, you’ll also need a certain mass of water to be flowing into the batch to ensure it all mixes properly.
I have personally done work in food processing plants and they use a lot of Coriolis meters for practically all their ingredients due to its accuracy and ability to measure mass flow.
If they need just 10 pounds of water for a specific recipe, the flow meter can measure out exactly 10 pounds of water for them.
Not only do they want the recipe to come out correctly, but they also want to make sure they aren’t using too much of any one ingredient to keep costs down and profit margins up.
More importantly, Coriolis meters are actually used in measuring the flow of gasoline, diesel, and other fuels as they are bought and sold between two companies. That type of application is called “custody transfer”, and it requires all measurements to be as accurate as possible to reduce the likelihood of getting “ripped off”. That obviously helps with keeping fuel prices as low as possible — at least theoretically…
In fact, if you’ve ever wondered about the price accuracy on the display at the gas pump, check out this article I wrote about how that all works!
While we only took a look at a few different technologies, there are a ton more out there which can be just as impressive!
In fact, all the technologies we’ve seen thus far have an element of the flow meter which comes in contact with the fluid in order to measure the flow velocity. That can be helpful for flow measurement in some cases, but it can also be undesirable in others.
For example, anything that obstructs the flow of a fluid will cause a pressure build up, or pressure loss. In some cases, it will cause turbulence, and none of those are good for flow measurement in most cases.
NO TOUCHING!!
The other type of flow meters we will quickly discuss here are in the “non-contact” category. Meaning, at no point in the flow measurement process is there any type of obstruction — solid or rotating.
That’s not to say there aren’t valves and pumps elsewhere on the line, but while the flow is being measured, there is nothing obstructing the flow.
The two most common forms of non-contact flow meters are ultrasonic and electromagnetic flow meters (often shortened to “mag meters”). Also, an ultrasonic flow meter can come in two varieties as well. They can either be “in-line” or “clamp-on”. Both have their advantages and disadvantages — and specific use cases which will not be discussed in detail here.
A typical ultrasonic flow meter, as shown above, uses ultrasonic pulses and difference in time to measure the flow velocity of some liquid. Usually it is water that is being measured with them, but that’s not always the case.
Thing of it this way: when there is no flow and the ultrasonic sensors measure the difference between transmit time and receipt time, it will always be the same. That’s the flow meter’s reference point. That is because sound waves, in the air, have a specific and constant rate of propagation.
Now, imagine if you filled that flow tube with water. For the time being, there is no flow, the water is just sitting in the flow tube. The time difference the flow meter measures is now going to be shorter since sound waves move more quickly, and efficiently, in water.
If you were to then start flowing the water through the meter, in a specific direction, then the difference in time will be yet quicker, or slower depending on the direction and velocity of flow. That difference in transmit time is proportional to the flow velocity of the water, and that is how the most common of ultrasonic flow meters work.
Other types will use the doppler effect to measure flow velocity, and it works slightly differently — but relatively similar.
As you could imagine, as long as sound waves can propagate through the medium, an ultrasonic flow meter can be used for a lot of different liquids!
On the other hand, “mag meters” are used for the measurement of conductive fluids with dielectric properties.
As the name suggests, the technology uses magnets and electrodes. Makes sense, right?
As you can see in the diagram above, the flow meter has two electrodes 180 degrees from one another along the flow tube. Those electrodes, when powered, will produce a magnetic field of a certain size between the two.
Now, one important thing to know is that a changing magnetic field induces an electric current. In this particular case, the flow of a conductive liquid through the flow tube can change the magnetic field produced by the electrodes.
Since that magnetic field is changing, electric current must be produced! As you can see in the diagram above, the “induced voltage” is proportional to the flow velocity of the liquid, and other known variables provided by the flow meter itself.
As the flow velocity increases, the induced voltage will increase proportionally. That voltage is precisely what is used to calculate, and communicate the flow readings.
As you can see, the mag meter requires no moving parts or consumable bluff bodies to measure the flow of a conductive fluid. That means there is no pressure drop across the flow meter which is very desirable in water and wastewater applications.
Of course, mag meters have their disadvantages, just like any technology. For example, a full pipe is essential for accurate measurement with a mag meter. That’s not always possible in certain situations.
KROHNE does make what they call the TIDALFLUX and it’s a mag meter with a capacitive probe that also measures the level inside the flow tube. This allows the flow meter to ensure accurate flow readings even when there isn’t a full pipe by compensating with a level measurement — to maintain the known geometry.
It’s actually a really unique and clever instrument!
So… How the Hell Do We Measure Fluid Flow?
To be honest, we didn’t even cover half of the ways that fluid flow can be measured. For example, there is a really clever type of flow meter called, a “thermal dispersion flow meter” which can measure the mass flow of natural gas using heating elements and temperature differentials!
However, the meters discussed here are the most commonly used flow meters, at least in my experience!
While we looked at the technical ways to measure flow, we didn’t discuss the actual flow measurements themselves.
In every instance here, we saw that the flow meters measure “flow velocity”. This could be expressed as “meters per second”, for example. But that’s not really a helpful unit of measure for us in our every day lives.
Rather, we want to convert that velocity into a flow rate in volume over time. This is typically expressed as, “gallons/liters per minute”. Your average size run of the mill flow meter will more than likely be calibrated in gallons per minute, but that’s not always the case.
In order to convert the flow velocity into a flow rate in volume over time, there needs to be some sort of calculation performed. That is typically done in the transmitter head of the the flow meter, but it can also be done in specialized equipment like a “flow computer”.
Of course, that calculation can only be done with a known geometry!
Another important calculation to be made is the total flow in a certain period of time. A flow rate is just an instantaneous rate at which a fluid is moving. The total flow is the accumulative volume of fluid that has flown through the flow meter during a specific period of time.
For example, if you wanted to measure how much water your household uses in a week, you would use a “totalizer” to see the accumulated volume of water that the family used in a given week. That also requires calculations that can either be done on the transmitter, but is typically performed on an external device like a remote flow totalizer.
An easy way to think of it is by imagining the instruments in your car!
You have a speedometer that indicates your current speed, and that is expressed in “miles per hour”. That is considered your “rate of speed” which is analogous to a flow RATE.
However, that dial is never going to tell you how many miles you drove during a road trip. That is what the odometer is for. The odometer keeps track of how many miles you have driven in a given period of time.
In other words, the odometer is like the totalizer for your car!
Speaking of your car, measuring fluid flow is also important to your every day life because of gas prices! Without an accurate measurement of fluid flow, you may not get all the fuel that you pay for!
But, you can rest assured, the flow meters are extremely accurate, and they must conform to strict accuracy standards for custody transfer purposes.
The point is, measuring fluid flow is extremely interesting and equally as important to us, and hopefully I succeeded in sharing my passion for measurement with you!
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What do YOU think?
Do you think fluid flow measurement is interesting? Had you ever considered any of this before?!
