## People of Interest: Daniel Bernoulli

Whenever there is a discussion about fluid dynamics, Bernoulli’s equation generally comes up. This equation is unique as it relates flow energy with kinetic energy and potential energy. The formula was mainly linked to non-compressible fluids, but under certain conditions, it can be significant for gas flows as well. My colleague, Tyler Daniel, wrote a blog about the life of Daniel Bernoulli (you can read it HERE). I would like to discuss how he developed the Bernoulli’s equation and how EXAIR uses it to maximize efficiency within your compressed air system.

In 1723, at the age of 23, Daniel moved to Venice, Italy to learn medicine. But, in his heart, he was devoted to mathematics. He started to do some experiments with fluid mechanics where he would measure water flow out of a tank. In his trials, he noticed that when the height of the water in the tank was higher, the water would flow out faster. This relationship between pressure as compared to flow and velocity came to be known as Bernoulli’s principle. “In fluid dynamics, Bernoulli’s principle states that an increase in the speed of fluid occurs simultaneously with a decrease in static pressure or a decrease in the fluids potential energy”1. Thus, the beginning of Bernoulli’s equation.

Bernoulli realized that the sum of kinetic energy, potential energy, and flow energy is a constant during steady flow. He wrote the equation like this:

Equation 1:

Not to get too technical, but you can see the relationship between the velocity squared and the pressure from the equation above. Being that this relationship is a constant along the streamline; when the velocity increases; the pressure has to come down. An example of this is an airplane wing. When the air velocity increases over the top of the wing, the pressure becomes less. Thus, lift is created and the airplane flies.

With equations, there may be limitations. For Bernoulli’s equation, we have to keep in mind that it was initially developed for liquids. And in fluid dynamics, gas like air is also considered to be a fluid. So, if compressed air is within these guidelines, we can relate to the Bernoulli’s principle.

1. Steady Flow: Since the values are measured along a streamline, we have to make sure that the flow is steady. Reynold’s number is a value to decide laminar and turbulent flow. Laminar flows give smooth velocity lines to make measurements.
2. Negligible viscous effects: As fluid moves through tubes and pipes, the walls will have friction or a resistance to flow. The surface finish has to be smooth enough; so that, the viscous effects is very small.
3. No Shafts or blades: Things like fan blades, pumps, and turbines will add energy to the fluid. This will cause turbulent flows and disruptions along the velocity streamline. In order to measure energy points for Bernoulli’s equation, it has to be distant from the machine.
4. Compressible Flows: With non-compressible fluids, the density is constant. With compressed air, the density changes with pressure and temperature. But, as long as the velocity is below Mach 0.3, the density difference is relatively low and can be used.
5. Heat Transfer: The ideal gas law shows that temperature will affect the gas density. Since the temperature is measured in absolute conditions, a significant temperature change in heat or cold will be needed to affect the density.
6. Flow along a streamline: Things like rotational flows or vortices as seen inside Vortex Tubes create an issue in finding an area of measurement within a particle stream of fluid.

Since we know the criteria to apply Bernoulli’s equation with compressed air, let’s look at an EXAIR Super Air Knife. Blowing compressed air to cool, clean, and dry, EXAIR can do it very efficiently as we use the Bernoulli’s principle to entrain the surrounding air. Following the guidelines above, the Super Air Knife has laminar flow, no viscous effects, no blades or shafts, velocities below Mach 0.3, and linear flow streams. Remember from the equation above, as the velocity increases, the pressure has to decrease. Since high-velocity air exits the opening of a Super Air Knife, a low-pressure area will be created at the exit. We engineer the Super Air Knife to maximize this phenomenon to give an amplification ratio of 40:1. So, for every 1 part of compressed air, the Super Air Knife will bring into the air streamline 40 parts of ambient “free” air. This makes the Super Air Knife one of the most efficient blowing devices on the market. What does that mean for you? It will save you much money by using less compressed air in your pneumatic application.

We use this same principle for other products like the Air Amplifiers, Air Nozzles, and Gen4 Static Eliminators. Daniel Bernoulli was able to find a relationship between velocities and pressures, and EXAIR was able to utilize this to create efficient, safe, and effective compressed air products. To find out how you can use this advantage to save compressed air in your processes, you can contact an Application Engineer at EXAIR. We will be happy to help you.

John Ball
Application Engineer
Email: johnball@exair.com

## Laminar Flow and Digital Flowmeters: An Explanation On How To Achieve Laminar Flow

When I see turbulent flow vs. laminar flow I vaguely remember my fluid dynamics class at the University of Cincinnati.  A lot of times when one thinks about the flow of a liquid or compressed gas within a pipe they want to believe that it is always going to be laminar flow. This, however, is not true and there is quite a bit of science that goes into this.  Rather than me start with Reynolds number and go through flow within pipes I have found this amazing video from a Mechanical Engineering Professor in California. Luckily for us, they bookmarked some of the major sections. Watch from around the 12:00 mark until around the 20:00 mark. This is the good stuff.

The difference between entrance flow, turbulent flow and laminar flow is shown ideally at around the 20:00 mark.  This length of piping that is required in order to achieve laminar flow is one of the main reasons our Digital Flowmeters are required to be installed within a rigid straight section of pipe that has no fittings or bends for 30 diameters in length of the pipe upstream with 5 diameters of pipe in length downstream.

This is so the meter is able to measure the flow of compressed air at the most accurate location due to the fully developed laminar flow. As long as the pipe is straight and does not change diameter, temperature, or have fittings within it then the mass, velocity, Q value all stay the same.  The only variable that will change is the pressure over the length of the pipe when it is given a considerable length.

Another great visualization of laminar vs. turbulent flow, check out this great video.

If you would like to discuss the laminar and turbulent flow please contact an Application Engineer.

Brian Farno
Application Engineer
BrianFarno@EXAIR.com
@EXAIR_BF

1 -Fluid Mechanics: Viscous Flow in Pipes, Laminar Pipe Flow Characteristics (16 of 34) – CPPMechEngTutorials – https://www.youtube.com/watch?v=rQcZIcEa960

2 – Why Laminar Flow is AWESOME – Smarter Every Day 208 – SmarterEveryDay – https://www.youtube.com/watch?v=y7Hyc3MRKno

## Laminar vs. Turbulent Flow

Laminar flow is an fundamental component of compressed air efficiency. Believe it or not, laminar flow is controlled exclusively by the airline used in a compressed air system. To fully understand the effects of laminar flow in a compressed air system, we need to explain exactly what it is.

Fluids & gases are unique in their ability to travel. Unlike solid molecules that remain stationary whose molecules tend to join others of the same kind; fluid molecules aren’t so picky. Fluid molecules, such as gases and liquids, partner with different molecules and are difficult to stop.

Laminar flow describes the ease with which these fluids travel; good laminar flow describes fluid travelling as straight as possible. On the contrary, when fluid is not travelling straight, the result is turbulent flow.

Turbulent air flow results in an inefficient compressed air system. This may not seem like a major concern; yet, it has huge impacts on compressor efficiency. Fluid molecules bounce and circle within their path, causing huge energy wastage. In compressed air systems, this turbulent airflow results in a pressure drop. How do you avoid this from happening? It all comes down to compressed air system design.

The design and material of the air pipe, as well as the positioning of elbows and joints, has a direct connection to laminar flow and pressure drop. To avoid high energy consumption of your compressed air system, reducing pressure drop is key.

If your system is experiencing high pressure drop, your compressor has to work overtime to provide the needed air pressure. When your compressor works overtime, it not only increases your maintenance costs, but also your energy bills.

To discuss your application and how an EXAIR Intelligent Compressed Air Product can help your process, feel free to contact EXAIR and myself or one of our Application Engineers can help you determine the best solution.

Jordan Shouse
Application Engineer
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## EXAIR’s Super Air Knife: The Benefits of Laminar Airflow

When a wide, even, laminar flow is necessary there isn’t a better option available on the market than EXAIR’s Super Air Knife. We’ve been manufacturing Air Knives for over 35 years, with the Super Air Knife making its first appearance back in 1997. Since then, the Super Air Knife has undergone a few enhancements over the years as we’re constantly trying to not only introduce new products but also improve on the ones we have. We’ve added new materials, longer single piece knives, as well as additional accessories. But, by and large, the basic design has remained the same. As the saying goes: “If it ain’t broke, don’t fix it!”.

What really sets EXAIR’s Super Air Knife above the competition is the ability to maintain a consistent laminar flow across the full length of the knife compared to similar compressed air operated knives. This is even more evident when compared against blower operated knives or fans. A fan “slaps” the air, resulting in a turbulent airflow where the airflow particles are irregular and will interfere with each other. A laminar airflow, by contrast, will maintain smooth paths that will never interfere with one another.

The effectiveness of a laminar airflow vs turbulent airflow is particularly evident in the case of a cooling application. The chart below shows the time to cool computers to ambient temperatures for an automotive electronics manufacturer. They used a total of (32) 6” axial fans, (16) across the top and (16) across the bottom as the computers traveled along a conveyor. The computers needed to be cooled down before they could begin the testing process. By replacing the fans with just (3) Model 110012 Super Air Knives at a pressure of just 40 psig, the fans were cooled from 194°F down to 81° in just 90 seconds. The fans, even after 300 seconds still couldn’t remove enough heat to allow them to test.

Utilizing a laminar airflow is also critical when the airflow is being used to carry static eliminating ions further to the surface. Static charges can be both positive or negative. In order to eliminate them, we need to deliver an ion of the opposite charge to neutralize it. Since opposite charges attract, having a product that produces a laminar airflow to carry the ions makes the net effect much more effective. As you can see from the graphic above showing a turbulent airflow pattern vs a laminar one, a turbulent airflow is going to cause these ions to come into contact with one another. This neutralizes them before they’re even delivered to the surface needing to be treated. With a product such as the Super Ion Air Knife, we’re using a laminar airflow pattern to deliver the positive and negative ions. Since the flow is laminar, the total quantity of ions that we’re able to deliver to the surface of the material is greater. This allows the charge to be neutralized quickly, rather than having to sit and “dwell” under the ionized airflow.

With lengths from 3”-108” and (4) four different materials all available from stock, EXAIR has the right Super Air Knife for your application. In addition to shipping from stock, it’ll also come backed up by our unconditional 30-day guarantee. Test one out for yourself to see just how effective the Super Air Knife is on a wide variety of cooling, cleaning, or drying applications.

Tyler Daniel
Application Engineer
E-mail: TylerDaniel@exair.com

## Fluidics, Boundary Layers, And Engineered Compressed Air Products

Fluidics is an interesting discipline of physics.  Air, in particular, can be made to behave quite peculiarly by flowing it across a solid surface.  Consider the EXAIR Standard and Full Flow Air Knives:

If you’ve ever used a leaf blower, or rolled down the car window while traveling at highway speed, you’re familiar with the power of a high velocity air flow.  Now consider that the Coanda effect can cause such a drastic redirection of this kind of air flow, and that’s a prime example of just how interesting the science of fluidics can be.

EXAIR Air Amplifiers, Air Wipes, and Super Air Nozzles also employ the Coanda effect to entrain air, and the Super Air Knife employs similar precision engineered surfaces to optimize entrainment, resulting in a 40:1 amplification ratio:

As fascinating as all that is, the entrainment of air that these products employ contributes to another principle of fluidics: the creation of a boundary layer.  In addition to the Coanda effect causing the fluid to follow the path of the surface it’s flowing past, the flow is also affected in direct proportion to its velocity, and inversely by its viscosity, in the formation of a boundary layer.

This laminar, lower velocity boundary layer travels with the primary air stream as it discharges from the EXAIR products shown above.  In addition to amplifying the total developed flow, it also serves to attenuate the sound level of the higher velocity primary air stream.  This makes EXAIR Intelligent Compressed Air Products not only as efficient as possible in regard to their use of compressed air, but as quiet as possible as well.

If you’d like to find out more about how the science behind our products can improve your air consumption, give me a call.

## What is Laminar Flow and Turbulent Flow?

Fluid mechanics is the field that studies the properties of fluids in various states.  There are two areas, fluid statics and fluid dynamics.  Fluid dynamics studies the forces in a fluid, either as a liquid or a gas, during motion.  Osborne Reynolds, an Irish innovator, popularized this dynamic with a dimensionless number, Reyonlds number. This number can indicate the different states that the fluid is moving; either in laminar flow or turbulent flow.  The equation below shows the relationship between the inertial forces of the fluid as compared to the viscous forces.  Reynolds number, Re, can be calculated by Equation 1:

Equation 1:  Re = V * Dh/u

Re – Reynolds Number (no dimensions)

V – Velocity (feet/sec or meters/sec)

Dh – hydraulic diameter (feet or meters)

u – Kinematic Viscosity (feet^2/sec or meter^2/sec)

The value of Re will mark the region in which the fluid (liquid or gas) is moving.  If the Reynolds number, Re, is below 2300, then it is considered to be laminar (streamline and predictable).  If Re is greater than 4000, then the fluid is considered to be turbulent (chaotic and violent).  The area between these two numbers is called the transitional area where you can have small eddy currents and some non-linear velocities.  To better show the differences between each state, I have a picture below that shows water flowing from a drain pipe into a channel.  The water in the channel is loud and disorderly; traveling in different directions, even upstream.  With the high speed coming from the drain pipe, the inertial forces are greater than the viscous forces of the water.  The Reynolds number is larger than 4000 which indicates turbulent flow.  As the water travels into the mouth of the river after the channel, the waves transform from a disorderly mess into a more uniform stream.  This is the transitional region.  A bit further downstream, the stream becomes calm and quiet, flowing in the same direction.  This is the laminar flow region where Re is less than 2300.  Air, like the water in the picture, is also a fluid, and it will behave exactly in the same way depending on the Reynolds number.

Why is this important to know?  In certain applications, one state may be better suited than the other.  For mixing, particle suspension and heat transfer; turbulent flows are needed.  But, when it comes to effective blowing, lower pressure drops and lower noise levels; laminar flows are required.  In many compressed air applications, the laminar flow region is the best area to use compressed air.  EXAIR offers a large line of products, including the Super Air Knives and Super Air Nozzles that uses that laminar flow to generate a strong force efficiently and quietly.  If you would like to discuss further how laminar flows could benefit your process, an EXAIR Application Engineer will be happy to assist you.

John Ball
Application Engineer
Email: johnball@exair.com

## Laminar Flow vs. Turbulent Flow – Calculations and Examples

What is laminar flow and turbulent flow?  Osborne Reynolds popularized this phenomenon with a dimensionless number, Re. This number is the ratio of the inertial forces to the viscous forces.  If the inertial forces are dominant over the viscous forces, the fluid will act in a violent and chaotic manner.  The formula to determine the Reynolds number is as follows:

Equation 1:  Re = V * Dh/u

Re – Reynolds Number (no dimensions)

V – Velocity (Feet/sec or Meters/sec)

Dh – hydraulic diameter (Feet or Meters)

u – Kinematic Viscosity (Feet^2/sec or Meter^2/sec)

The value of Re will determine the state in which the fluid (liquid or gas) will move.  If the Reynolds number, Re, is below 2300, then it is considered laminar (streamline and predictable).  If Re is greater than 4000, then it is considered turbulent (chaotic and disarrayed).  The area between these two numbers is the transitional area where you start to get small eddy currents and velocities in a non-linear direction.  When it comes to effective blowing, cleaning and lower noise levels, laminar flow is optimal.

Let’s do a comparison of Reynolds numbers between the EXAIR Super Air Knife and a blower-type air knife.  Both products are designed to clean and blow off wide areas like conveyor belts.  The EXAIR Super Air Knife is powered by compressed air, and the blower-type air knife is powered by an air blower.  The main difference between the two products is the dimension of the slot opening.  The Super Air Knife has a gap opening of 0.002″ (0.05mm).  It uses the force of the compressed air to “push” it through the small opening to create a strong velocity.  A blower does not generate a high force, so the opening of the blower-type air knife has to be larger to overcome any back pressure the opening creates.  The gap opening is typically 0.5″ (13mm).  From Equation 1 above, the gap opening helps determine the hydraulic diameter, Dh.  The hydraulic diameter is an equivalent tube diameter from a non-circular flow area.  Since both the Super Air Knives and blower-type air knives have rectangular cross sections, the Dh can be calculated as follows:

Equation 2: Dh = 2 * a * b/ (a + b)

Dh – Hydraulic Diameter (feet or meter)

a – Gap Opening (feet or meter)

b – Gap Width (feet or meter)

If we compare for example a standard 12″ wide air knife, we can calculate the hydraulic diameter, Dh, by using Equation 2:

The exit velocity of the Super Air Knives can be changed by regulating the air pressure.  The higher the air pressure, the higher the velocity.  The blower type air knives can use a blower with a variable frequency drive (VFD) to change the exit velocity .  A reasonable air pressure for the Super Air Knife is 80 PSIG, and the exit velocity is near 540 ft/sec (164 m/s).  To equate this to a blower system, the size of the blower will determine the maximum velocity.  To do this comparison, I will use the same velocity as the Super Air Knife.  With the kinematic viscosity of air, it has a value of 0.000164 ft^2/sec (0.000015 m^2/sec) at 70 deg. F (21 deg C).  Now we have all the information for the comparison, and we can now find the Reynolds number from Equation 1:

As you can see from the above calculations, the Super Air Knife has a Reynolds number, Re, below 2300.  The flow characteristic is in the region of laminar (predictable and streamline).  The blower air knife has a Reynolds number, Re, above 4000.  The flow dynamic coming out of the blower-type air knife is turbulent (chaotic and disoriented).  To better show the difference in laminar flow and turbulent flow, I have a picture below that shows both states with water as a fluid (being that air is an invisible fluid).   Here is an example of water  coming out of a drain pipe at Cave Run Lake (first picture below).  With the inertial forces much higher than the viscosity of the water, it is in a turbulent state;  loud and disorderly.  Reynolds number is greater than 4000.  The water is traveling in different directions, even upstream.  As the water flows into the mouth of the river after the channel (second picture below), the waves transform from a violent mess into a quiet, calm stream flowing in the same direction.  This is laminar flow (Re is less than 2300).

With the engineered design of the Super Air Knife, the thin slot helps to create that laminar flow.  All the air is moving in the same direction, working together to give a higher force to remove debris.  If you have turbulent flow like that of a blower air knife, the noise level is much higher, and the disoriented forces are less effective in blowing.  Turbulence is useful for mixing, but horrible for trying to clean or wipe a conveyor belt.  If you have any open pipes, drilled pipes or blower-type air knives in your application, you should try an EXAIR product to see the difference.  An Application Engineers can help you take advantage of laminar airflow.

John Ball
Application Engineer
Email: johnball@exair.com