## Daniel Bernoulli, Entraining EXAIR Products

Daniel Bernoulli was born February 8, 1700 in Groningen in the Netherlands and was the son of Johann Bernoulli an early developer of calculus. It is believed that Daniel did not have a good relationship with his father. This mainly stemmed from the both of them entering the same scientific contest at the University of Paris. The two tied and his father Johann took exception to being compared to his son as “equal” and could not accept the shame and banned Daniel from his home. Daniel tried to reconcile their difference but his father carried this grudge to his death.

Earlier in Daniels life his father convinced Daniel to study business as there was no income incentive to study mathematics but against his will Daniel did choose the study of business. His father then convinced Daniel to study medicine but Daniel still wanted to study mathematics and agreed to study medicine under the condition that his dad teach him mathematics privately. Daniel completed his bachelors degree at the age of 15 and his masters degree when he was 17. Daniel then went on to study medicine and received his PhD in anatomy and botany from the Universities of Basel, Heidelberg and Strasbourg.

Daniel Bernoulli was very accomplished but mostly known for Bernoulli’s principle. Bernoulli’s principle is 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 Venturi effect, published in 1797 by Giovanni Venturi, applies Bernoulli’s principle to a fluid that flows through a tube with a constriction in it. The Venturi tube provides a handy method for mixing fluids or gases, and is popular in carburetors and atomizers, which use the low pressure region generated at the constriction to pull the liquid into the gas flow. It also offers a particularly clear example of the Bernoulli principle.

For example, above is how a Super Air Wipe works. Compressed air flows through an inlet (1) of the Air Wipe into an annular chamber (2). It is then throttled through a small ring nozzle (3) at high velocity. This primary airstream adheres to the Coanda profile (4), which directs it down the angled surface of the Air Wipe. A low pressure area is created at the center (5) inducing a high volume flow of surrounding air into the primary airstream. As the airflow leaves the Air Wipe, it creates a conical 360° ring of air that attaches itself to the surface of the material running through it (6), uniformly wiping the entire surface with the high velocity airflow.

EXAIR incorporates the Bernoulli Principle with our engineered products which entrain air such as our Super Air Knives, Super Air Wipes, Air Amplifiers and Static Eliminating products to name a few. We have several Applications Engineers that will appreciate your call to discuss our products. If you have an application or question please call 800.903.9247 or visit us on our website www,EXAIR,com and let us help you.

Eric Kuhnash
Application Engineer
E-mail: EricKuhnash@exair.com

## 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

## 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