## The Bernoulli Principle

When catapults would hurl stones and projectiles at castles there weren’t thinking of how the stones flew or what could make them fly better, often they went with the “Tim Taylor method” of MORE POWER.  It wasn’t until thousands of years later that mathematicians started to talk about gases and liquids and how they react to different scenarios. Things like how does air react to a stone being launched through it. Johann Bernoulli played a significant role and calculated a lot of this out throughout his life and discovered what is now called the Bernoulli Principle.

Bernoulli discovered that when there is an increase in the speed of a fluid, a simultaneous decrease in fluid pressure occurs at the same time. This is what explains how a plane’s wing shape matters. It also can showcase how a curveball coming into the strike zone can fall out and cause an outlandish “STTTeeerriike Three” from the umpire. It is also sometimes confused with the Coandă effect. While both effects have a tremendous impact on our modern lives, the best way I have learned these effects is through videos such as the one below.

As mentioned within the video, there are numerous effects that can closely relate to the Bernoulli effect, the best example I see is the curveball which when implemented correctly can cause a very upset batter, while the pitcher has the game of his or her career.

If you would like to talk about some scientific discoveries that have you puzzled, or if you want to figure out how we can use one of these effects to help your application, contact us.

Brian Farno
Application Engineer
BrianFarno@EXAIR.com
@EXAIR_BF

## Robert Boyle And The Scientific Method

How do we know something is true? In grade school, you may remember being taught a process by which an observation elicits a question, from which a hypothesis can be derived, which leads to a prediction that can be tested, and proven…or not) These steps are commonly known as the Scientific Method, and they’ve been successfully used for thousands of years, by such legendary people of science as Aristotle (384 – 322 BC,) Roger Bacon (1219 – 1292,) Johannes Kepler (1571-1630,) Galileo Galilei (1564-1642) and right up to today’s scientists who run the CERN Large Hadron Collider.  The collider is the largest machine in the world, and its very purpose is the testing and proving (or not) of hypotheses based on questions that come from observations (often made in the LHC itself) in ongoing efforts to answer amazingly complex questions regarding space, time, quantum mechanics, and general relativity.

The Scientific Method is actually the reason (more on this in a minute) for the name of a fundamental law of physics: Boyle’s Law.  It states:

“For a fixed amount of an ideal gas kept at fixed temperature, pressure and volume are inversely proportional.”

And can be mathematically represented:

PV=k, where:

• P = is the pressure of a gas
• V = is the volume of that gas, and
• k = is a constant

So, if “k” is held constant, no matter how pressure changes, volume will change in inverse proportion.  Or, if volume changes, pressure will change in inverse proportion.  In other words, when one goes up, the other goes down.  It’s also quite useful in another formulaic representation, which allows us to calculate the resultant volume (or pressure,) assuming the initial volume & pressure and resultant pressure (or volume) is known:

P1V1=P2V2, where:

• P1  and P2 are the initial, and resultant, pressures (respectively) and
• V1  and V2 are the initial, and resultant, volumes (respectively)

This is in fact, what happens when compressed air is generated, so this formula is instrumental in many aspects of air system design, such as determining compressor output, reservoir storage, pneumatic cylinder performance, etc.

Back to the reason it’s called “Boyle’s Law” – it’s not because he discovered this particular phenomenon.  See, in April of 1661, two of Robert Boyle’s contemporaries, Richard Towneley and Henry Power, actually discovered the relationship between the pressure and volume of a gas when they took a barometer up & down a large hill with them.  Richard Towneley discussed his finding with Robert Boyle, who was sufficiently intrigued to perform the formal experiments based on what he called “Mr Towneley’s hypothesis.”  So, for completing the steps of Scientific Method on this phenomenon – going from hypothesis to law –  students, scientists, and engineers remember Robert Boyle.

Russ Bowman
Application Engineer
EXAIR Corporation
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IMGP6394 image courtesy of Matt Buck, Creative Commons License

## The Theory of the Vortex Tube

There are many theories regarding the dynamics of a vortex tube and how it works. Many a graduate student has studied them as part of their research requirements.

The Vortex Tube was invented by accident in 1928, by George Ranque, a French physics student. He was performing experiments on on a vortex-type pump that he had developed and noticed that warm air exhausted from one end and cold air from the other! Ranque quickly stopped work on the pump, and started a company to take advantage of the commercial possibilities for this odd little device that produced both hot and cold air, using only compressed air, with no moving parts. The company was not successful, and the vortex tube was forgotten until 1945 when Rudolph Hilsch, a German physicist, published a widely read paper on the device.

A vortex tube uses compressed air as a power source, has no moving parts, and produces hot air from one end and cold air from the other. The volume and temperature of the two air streams is adjustable with a valve built into the hot air exhaust.  Temperatures as low as -50°F (-46°C) and as high as 260°F (127°C) are possible.

Here is one widely accepted explanation of the physics and the phenomenon of the vortex tube.

Compressed air is supplied to vortex tube and passes through nozzles that are tangent to to an internal counterbore (1). As the air passes through it is set into a spiraling vortex motion (2) at up to 1,000,000 rpm. The spinning stream of air flows down the hot tube in the form of a spinning shell, like a tornado (in red). The control valve (4) at the end allows some of the warmed air to escape (6) and what does not escape reverses direction and heads back down the tube as a second vortex (in blue) inside of the low pressure area of the larger warm air vortex. The inner vortex loses heat and exits the through the other end of as cold air (5).

It is thought that that both the hot and cold air streams rotate in the same direction at the same angular velocity, even though they are travelling in opposite directions. A particle of air in the inner stream completes one rotation in the same amount of time that an air particle in the outer stream. The principle of conservation of angular momentum would say that the rotational speed of the inner inner vortex should increase because the angular momentum of a rotating particle (L) is equal to the radius of rotation (r) times its mass (m) times its velocity (v).  L = r•m•v.  When an air particle moves from the outer stream to the inner stream, both its radius (r) and velocity (v) decrease, resulting in a lower angular momentum. To maintain an energy balance for the system, the energy that is lost from the inner stream is taken in by the outer stream as heat. Therefore, the outer vortex becomes warm and the inner vortex is cooled.

At EXAIR, we have harnessed the cooling power of the vortex tube, and it can be found and utilized in such products as Spot Coolers, Cabinet Coolers, and the Vortex Tube themselves.

Harnessing the cooling power of the vortex tube

If you have questions about Vortex Tubes, or would like to talk about any of the EXAIR Intelligent Compressed Air® Products, feel free to contact EXAIR and myself or any of our Application Engineers can help you determine the best solution.

Brian Bergmann
Application Engineer
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