## 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

## Factors in Selecting an Air Knife – Size, Materials, Stock Levels, Accessories

EXAIR has been manufacturing Intelligent Compressed Air® products since 1983.  In the beginning, the Standard Air Knives and Full Flow Air Knives were very effective at that time.  But as leaders in this market, EXAIR did not want to stop there.  We were able to engineer a more efficient, more powerful, and much safer air knife, the Super Air Knife.  In this blog, I will discuss the features and benefits that the Super Air Knives can offer.

Bernoulli’s principle explains how a high velocity fluid can generate a low pressure.  The EXAIR Super Air Knife creates a high velocity air stream to produce a low pressure to entrain ambient air.   What does this mean for you?  It will save you much money by using less compressed air.  The mass of the ambient air is added into the air stream to give a strong blowing force.  The Super Air Knife has an amplification ratio of 40:1. For every 1 part of compressed air, 40 parts of ambient air is drawn into the blowing air stream.  Ambient air is free, and compressed air is expensive.  EXAIR was able to engineer a design to use the Bernoulli’s principle to make one of the most efficient air knives in the market place.

What else makes EXAIR unchallenged?  We manufacture and stock the widest range in lengths and materials.  To start, EXAIR has Super Air Knives ranging from 3” to 108” (76mm to 2,743mm) in three different materials; aluminum, 303 stainless steel, and 316/316L stainless steel.  There is no-one else in this industry that can manufacture to those lengths.  EXAIR also offers Super Air Knives in PVDF material with Hastelloy hardware for chemical resistant applications from 3” to 54” (76mm to 1,372mm).  Depending on the temperature requirement, chemical resistance, OSHA and FDA regulations, or application details, we probably will have one on the shelf for you.  If EXAIR does not have it, we can make special air knives in different lengths and materials to best fit your application.

Some interesting features for the Super Air Knives are as follows.  They have a compact design that can fit into tight places for blowing and cooling.  The footprint is very small compared to blower-air knife system.  They do not have any moving parts to wear or maintenance to do.  They only need clean compressed air to work.  They blow a laminar air stream which reduces noise levels and create a consistent force along the entire length.  An even force will give you tighter control for blowing applications which will cut compressed air usage unlike the inconsistent and turbulent air flows caused by drilled pipes.

To adjust the force and air usage, this can be easily controlled with a regulator.  The advantage that EXAIR Super Air Knives have is the replaceable shims.  So, you can increase or decrease the gap to get a variety of force ratings.  The Aluminum version uses colored plastic shims for visual verification.  They come stock with a 0.002” (0.05mm) red shim installed.  We have other thicknesses in our Shim Sets which includes a 0.001” (0.03mm), 0.003” (0.08mm), and a 0.004” (0.10mm) colored as amber, green, and tan respectively.  The Stainless Steel Super Air Knives come with a stainless steel shim for higher temperatures and chemical resistance.  Stock units have the 0.002” (0.05mm) thickness as well.  The Shim Sets come with three additional 0.002” (0.05mm) shims to stack.  Similarly, the PVDF Super Air Knives use a PTFE shim for maximum chemical resistance.  It is also 0.002” (0.05mm) thick, and there are three more shims in the Shim Set.  This unique feature of using shims allows for the most flexibility in creating forces for different applications ranging from a blast to remove rocks from a conveyor to a breeze for light duty work.

We also offer the Super Air Knives in kits as a more complete system.  The kit includes a filter, regulator and the above-mentioned Shim Set.  The filter removes the debris and water from the compressed air line to optimize the performance of the air knife as well as keeping your product clean.  The regulator is used to make the “fine” adjustment to the blowing force while the shim set is used as the “coarse” adjustment.  EXAIR sells this kit as one model number for simple ordering, and the accessories are properly sized to not hinder the performance of the Super Air Knife.

To optimize the system even more, EXAIR offers a Deluxe Kit for the Aluminum and Stainless Steel models.  This includes the accessories in the kit above, plus an Electronic Flow Control, or EFC.  This exclusive instrument uses a photoelectric eye to start a timing sequence to control a solenoid valve.  So, when a part is not in front of the Super Air Knife for cleaning or cooling, the compressed air is turned off.  This will save you even more money and maximize your efficiency to only blow air when needed.

For the longer Super Air Knives, EXAIR can install a Plumbing Kit, or PKI, to help attach your compressed air to the Air Knife.  They are designed to help lessen the time for install as well as to properly supply compressed air equally along the entire length, specifically for 24” (610mm) and longer.  We can offer the Plumbing Kit separately if you find that it could benefit your fabricators during installation.  EXAIR also offers a Coupling Kit for the Aluminum and Stainless Steel versions.  If you need to extend past the 108” (2,743 mm) width, the Coupling Kit is designed to mount Super Air Knives together at the ends.  You will still get that consistent blowing force along the multiple of Air Knives.  Another helpful accessory is the Universal Air Knife Mounting System.  It has a bracket and an articulated arm that can reach up to 30” (762mm).  With this system, you can position your air knife securely and precisely in any orientation.  It attaches easily to your Super Air Knife and gives you the flexibility to maximize the blowing effect at your target.

With the today’s cost in making compressed air, it is important to use it as efficiently as possible.  The Standard and Full Flow Air Knives would be good options to use.  But the best way to conserve is with the Super Air Knife.  If you have any questions about the Super Air Knife or if you would like to discuss an application, you can contact an Application Engineer at EXAIR.   We will be glad to help you.

John Ball
Application Engineer

Email: johnball@exair.com

## The Bernoulli Principle

What do baseball, airplanes, and your favorite singer have in common? If you guessed that it has something to do with the title of this blog, dear reader, you are correct.  We’ll unpack all that, but first, let’s talk about this Bernoulli guy:

Jacob Bernoulli was a prominent mathematician in the late 17th century.  We can blame calculus on him to some degree; he worked closely with Gottfried Wilhelm Leibniz who (despite vicious accusations of plagiarism from Isaac Newton) appears to have developed the same mathematical methods independently from the more famous Newton.  He also developed the mathematical constant e (base of the natural logarithm) and a law of large numbers which was foundational to the field of statistics, especially probability theory.  But he’s not the Bernoulli we’re talking about.

Johann Bernoulli was Jacob’s younger brother.  He shared his brother’s passion for the advancement of calculus, and was among the first to demonstrate practical applications in various fields.  So for engineers especially, he can share the blame for calculus with his brother.  But he’s not the Bernoulli we’re talking about either.

Johann’s son, Daniel, clearly got his father’s math smarts as well as his enthusiasm for practical applications, especially in the field of fluid mechanics.  His kinetic theory of gases is widely known as the textbook (literally) explanation of Boyle’s law.  And the principle that bears his name (yes, THIS is the Bernoulli we’re talking about) is central to our understanding of curveballs, airplane wings, and vocal range.

Bernoulli’s Principle states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure (e.g., the fluid’s potential energy.)

• In baseball, pitchers love it, and batters hate it.  When the ball is thrown, friction (mainly from the particular stitched pattern of a baseball) causes a thin layer of air to surround the ball, and the spin that a skilled pitcher puts on it creates higher air pressure on one side and lower air pressure on the other.  According to Bernoulli, that increases the air speed on the lower pressure side, and the baseball moves in that direction.  Since a well-thrown curveball’s axis of rotation is parallel to the ground, that means the ball drops as it approaches the plate, leaving the batter swinging above it, or awkwardly trying to “dig it out” of the plate.
• The particular shape of an airplane wing (flat on the bottom, curved on the top) means that when the wing (along with the rest of the plane) is in motion, the air travelling over the curved top has to move faster than the air moving under the flat bottom.  This means the air pressure is lower on top, allowing the wing (again, along with the rest of the plane) to rise.
• The anatomy inside your neck that facilitates speech is often called a voice box or vocal chords.  It’s actually a set of folds of tissue that vibrate and make sound when air (being expelled by the lungs when your diaphragm contracts) passes through.  When you sing different notes, you’re actually manipulating the area of air passage.  If you narrow that area, the air speed increases, making the pressure drop, skewing the shape of those folds so that they vibrate at a higher frequency, creating the high notes.  Opening up that area lowers the air speed, and the resultant increase in pressure lowers the vocal folds’ vibration frequency, making the low notes.
• Bonus (because I work for EXAIR) Bernoulli’s Principle application: many EXAIR Intelligent Compressed Air Products are engineered to take advantage of this phenomenon to optimize efficiency:

If you’d like to discuss Bernoulli, baseball, singing, or a potential compressed air application, give me a call.  If you want to talk airplane stuff, perhaps one of the other Application Engineers can help…I don’t really like to fly, but that’s a subject for another blog.

Russ Bowman
Application Engineer
EXAIR Corporation
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## People of Interest: Daniel Bernoulli (2/8/1700-3/17/1782)

Daniel Bernoulli was born in the Netherlands in February of 1700. Mathematics was in his bloodline as the son of renowned Swiss mathematician, Johann Bernoulli. He and Johann’s brother, Jakob, both took jobs as professors at a university in Basel, Switzerland. Fittingly, Johann taught Daniel mathematics at a very young age. Daniel Bernoulli spent some time studying a variety of topics including philosophy, logic, and medicine. Daniel obtained his Bachelor’s Degree at the age of just 15, earning his Master’s Degree just one year later.

Daniel was well-known and was highly regarded among scholars throughout Europe. After spending some time teaching Botany, he switched to physiology topics in 1743. This continued for several years when in 1750 he was appointed to the chair of physics where he taught at Basel for 26 years. During this time, he also received a total of 10 grand prizes from the Paris Academy of Sciences for work he completed in astronomy, a variety of nautical topics, and magnetism.

Daniel is most commonly known for his work in developing what is now called Bernoulli’s Principle, which discusses the relationship between fluid speed and pressure. An increase in the speed of a fluid will occur simultaneously with a decrease in the fluid’s pressure or potential energy.

The air entrainment properties of some of EXAIR’s Intelligent Compressed Air Products can be explained through Bernoulli’s Principle. As high-velocity air exits the nozzle of a Super Air Knife, for example, a low-pressure area is created that speeds up and draws in ambient air at an astonishing rate of 40:1. The same also occurs with the Super Air AmplifiersAdjustable Air Amplifiers, and Air Nozzles. To find out how you can utilize this advantage to save compressed air in your processes, give us a call. An Application Engineer will be happy to help assist you in determining the most suitable products for your application.

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

## People of Interest: Daniel Bernoulli – 2/8/1700 to 3/17/1782

Daniel Bernoulli was born in Groningen, Netherlands on February 8, 1700  and was part of a large family heritage of famous mathematicians – His father Johann Bernoulli, one of the first founders of calculus, his uncle Jacob Bernoulli and his older brother Nicolous. When he was only 7 years old, Daniel began to take an interest in mathematics but his father convinced him that there was no financial gain to be had in mathematics and recommended he focus his studies in business instead. Reluctant at first, Daniel would take his father’s advice under the one condition, that his father would tutor him in calculus and his theories of kinetic energy.

At 13 years old, Daniel attended Basel University where he studied logic and philosophy completing his bachelor’s degree by the age of 15 and earning his master’s degree just 1 year later. Over the years, Daniel’s relationship with his father was strained as a result of him plagiarizing his father’s findings. Eventually, his father passed without reconciling with Daniel. At 24, Daniel became a Professor of Mathematics  at a University in Venice but resigned from the position just 9 years later in 1733.

His most recognized mathematical contribution, Bernoulli’s principle, came in 1938 while performing energy conservation experiments, and he published the results in his book entitled Hydrodynamica . He discovered that when fluid travels through a wide pipe into a smaller, more narrow pipe, the fluid begins to move  faster. He determined that the volume or amount of fluid moving through the pipe remains unchanged but will conform to the shape of the pipe or container as it flows. He concluded that the higher the pressure, the slower the flow of the liquid and the lower the pressure, the faster the liquid flow.

The same principle can be applied to air. As air moves around an obstruction or object, it follows the profile of the part and begins to speed up.

Take for example our Super Air Nozzles. The compressed air exits the nozzle through a series of jets which induces a low pressure around the profile of the nozzle, drawing in ambient air. This entrainment of air, up to 25 times or more, results in a high outlet flow at minimal compressed air consumption.

Many of the products offered by EXAIR incorporate this science which can lead to a more efficient operation by lowering compressed air demand ultimately reducing operating costs. To see how our products can help you save money while increasing process performance, contact an Application Engineer for assistance.

Justin Nicholl
Application Engineer
justinnicholl@exair.com
@EXAIR_JN

Bildnis des Daniel Bernoullius image courtesy of Universitätsbibliothek Leipzig via creative commons license

## Intelligent Compressed Air: Bernoulli’s Principle

Daniel Bernoulli was a Swiss mathematician and physicist born in 1700. He is most known for the Bernoulli principle, published in his book Hydrodynamica in 1739. The Bernoulli’s principle states that an increase in speed of a fluid will result in a decrease in pressure. As a fluid moves from a wider pipe to a narrow one, the fluid begins to move faster. The given volume of the fluid moving from one point to another over a set amount of time will not change. In order for the same amount of fluid to pass through a smaller orifice, it must speed up. This is displayed quite well in the flow of a river. At wide, open spaces the river flows slowly. In areas that become narrow, for example by a canyon wall, the speed of the river’s flow increases dramatically.

The Bernoulli principle also provides an explanation for the lift that is created on an airplane wing. When air encounters an obstacle (in this case an airplane wing), its path will narrow as it flows around the object. As this stream of air speeds up, some of the energy from the random motion of the air molecules must be converted into energy of the stream’s forward flow. Pressure is created by the random motion of these air molecules. Transferring this energy into the stream flow then results in a drop in the air pressure. An airplane wing is shaped so that the air must move faster over it than under it. This causes the slower moving air underneath to exert more pressure on the wing than the air moving across the top. This is referred to as lift and is what allows an airplane to fly.

Temperatures are beginning to creep back up here in Cincinnati and just last week pitchers and catchers for the Cincinnati Reds reported for Spring Training. They’ll also be watching Bernoulli’s principle in action. The oft-dreaded (for batters, anyway) 12-6 curveball occurs due to the way the pitcher forces the ball to spin. Due to way he grips the ball across the laces and imparts this spinning motion, more air pressure forms on the top of the ball. This causes the bottom of the ball to accelerate downwards, resulting in the phenomenon that drives many baseball players crazy as they swing and miss due to a miscalculation of the ball’s position.

Some of EXAIR’s products also utilize the Bernoulli Principle. As the high-velocity air exits the nozzle of a Super Air Knife, a low pressure area is created that draws in surrounding ambient air at a rate of 40:1. The same also occurs with the Super Air Amplifiers, Adjustable Air Amplifiers, and Air Nozzles. If you’d like to discuss the application of any of our Intelligent Compressed Air Products, give an Application Engineer a call today.

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