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

 

Deflated Footballs? What’s the Big Deal, We Talk Air Pressure Everyday

This week we prepare for the professional football championship game, that phrase is trademarked within the Woerner household. For a few years, we have had my friends from college over for guacamole, chicken wings, French fries, and beverages. This year our small family is now three, so we are in for a quiet evening at home. My son will most likely be asleep at kick off, but my wife and I might stay awake for the end of the first quarter. Even with the small amount of people that we will watch the game, I will still make a small spread for our family, because tradition. Tradition says, it’s Super Bowl Week – we buy avocados early in the week so they have time to ripen.

In the build up to the big game, it seems like we always get a very silly story that the media grabs a hold of and just will not let go.  I want to join them. Have you heard about the fact that the footballs that the one of teams used on offense might not have been inflated to the correct pressure. I don’t know that the fotballs were under inflated on purpose, but I also think that LaDainian Tomlinson might have been on to something, when he said “The Patriots live by the saying if you ain’t cheating, you ain’t trying.”

That was a long introduction into my blog today about pressure. The NFL Rule Book states,

“The ball shall be made up of an inflated (12 1/2 to 13 1/2 pounds) urethane bladder enclosed in a pebble grained, leather case (natural tan color) without corrugations of any kind. It shall have the form of a prolate spheroid and the size and weight shall be: long axis, 11 to 11 1/4 inches; long circumference, 28 to 28 1/2 inches; short circumference, 21 to 21 1/4 inches; weight, 14 to 15 ounces.”

From an engineering perspective this is ambiguous at best. If I read this with no knowledge of football, I would have no idea how to test whether the ball is inflated. The rule states that the ball should be an inflated urethane bladder. Then in the parenthetical phrase it lists 12 1/2 to 13 1/2 pounds. Last time I checked pounds is a measure of weight. If I received this specifications, I would put the ball on a scale to weigh it. Using some common sense a quarterback isn’t going to be able to throw a 12 pounds ball, like a bullet, 10 yards. Let alone 60 yards for that deep bomb.

If I was writing the rule book, it would read that “the ball shall be inflated to a pressure of 12 1/2 to 13 1/2 pounds per square inch gauge pressure.” With this wording there is a clear standard to be met for football to be worthy for use.

What Is Gauge Pressure?

Gauge pressure is the pressure determined by a gauge or instrument. The term is used to differentiate pressure registered by a gauge from absolute pressure. Absolute pressure is determined by adding gauge pressure to atmospheric (aka barometric) pressure. Barometric pressure can be calculated based on elevation or measured by a barometer.

What is Atmospheric Pressure?

Andrew Gatt
This bottle was sealed at 10,000 ft above sea level then moved to the beach. At the beach the bottle spontaneously crushed by the increased atmospheric pressure

 

Atmospheric pressure is the force per area that the air around us compresses our world. Above is a photo with a simple illustration of atmospheric pressure. At roughly 10,000 feet above sea level, the bottle is sealed trapping the atmospheric pressure inside the bottle. As the bottle drops in elevation, the pressure outside the bottle rises compressing bottle and the air inside.

When do I use Gauge Pressure?

Gauge pressure is used in a majority of industrial applications. For instance, EXAIR’s air nozzle performance is based on 80 Pounds per Square Inch Gauge (PSIG). No matter what elevation the air nozzles are used the flow rate and the force of the nozzle will be the same as long as the gauge at the inlet to the nozzle reads 80 PSIG.

When do I use Atmospheric Pressure?

I seldom use atmospheric pressure by itself. I often use atmospheric pressure in conjunction with gauge pressure. Meteorologists reference atmospheric pressure when referring to low pressure or high pressure weather systems.

When do I use Absolute Pressure?

In one word: calculations. Absolute pressure is equal to gauge pressure plus atmospheric pressure. In a majority of formulas or calculations, absolute pressure is used. Specifically, whenever you are using pressure to multiply, divide, or raise to a power, absolute pressure is used. There may be exceptions, but I would need to be very familiar with the formula, before I would only use gauge pressure to multiply. For instance, if you need to calculate the air usage at of an air nozzle at a different pressure (as seen in this earlier blog), you would use the absolute pressure. The flow through a nozzle is governed by Bernoulli’s principle.

Dave Woerner
Application Engineer
@EXAIR_DW
DaveWoerner@EXAIR.com

 

Photo Courtesy of Andrew Gatt. Creative Commons License