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
Twitter: @EXAIR_EK

Entrainment: What is it?

By definition, entrainment is a form of the verb, entrain, which is fluid that is swept along into an existing moving flow.   Whenever there is a discussion about fluid dynamics, the 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 incompressible fluids, but under certain conditions, it can be significant for gas flows as well.  I would like to discuss how EXAIR uses the Bernoulli’s equation for entrainment to maximize efficiency within your compressed air system.

This relationship between pressure as compared to flow and velocity came to be known as the 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. Bernoulli realized that the sum of kinetic energy, flow energy, and potential energy is a constant during steady flow.  He wrote the equation like this:

Equation 1:

P/r + V2/2 + gz = constant

P – Pressure

r – density

V – velocity

g – gravitational constant

z – height difference

 

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.

Since we know the criteria to apply the Bernoulli’s equation with compressed air, let’s look at some EXAIR products.  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.  Remember from the equation above, as the velocity increases, the pressure has to decrease.  When the pressure decreases, the surrounding air will move toward the low pressure.  That low pressure will sweep the ambient air into the air stream; called entrainment.

Compressed air is expensive, but the ambient air is free.  The more ambient air we can entrain, the more efficient the blowing device is.  As an example, 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.  By adding mass to the flow stream, it will reduce the compressed air usage, saving you money, and allow for better cooling and a stronger blowing force.  For a drilled pipe, the amplification ratio is generally only two to three times.

We use this principle for many of our products like the Air Amplifiers, Safety Air Guns, Air Nozzles, Air Knives, and Gen4 Static Eliminators. Daniel Bernoulli was able to find a relationship between velocities and pressures, and EXAIR was able to use 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
Twitter: @EXAIR_jb

 

  1. Wikipedia https://en.wikipedia.org/wiki/Bernoulli%27s_principle

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:

The high speed of the air exiting the (left to right) the Air Wipe, Super Air Knife, Super Air Nozzle, and Air Amplifier creates a low pressure (just like Daniel Bernoulli said) that causes entrainment of an enormous amount of air from the surrounding environment.  This maximizes flow while minimizing consumption of your compressed air.

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 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.

Super Air Nozzle air entrainment

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