## Fluid Mechanics – Boundary Layer

Fluid mechanics is the field that studies the properties of fluids in various states.  Fluid dynamics studies the forces on a liquid or a gas during motion.  Osborne Reynolds, an Irish innovator, popularized this dynamic with a dimensionless number, Re. This number determines the state in which the fluid is moving; laminar, transitional, or turbulent.  For compressed air, a value of Re < 2300 will indicate a laminar air flow while the value of Re > 4000 will be in the range of turbulent flow.  Equation 1 below shows the relationship between the inertial forces of the fluid as compared to the viscous forces.

Equation 1:

Re = V * Dh / u

Re – Reynolds Number (no dimensions)

V – Velocity (feet/sec or meters/sec)

Dh – hydraulic diameter (feet or meters)

u – Kinematic Viscosity (feet^2/sec or meter^2/sec)

To dive deeper into this, we can examine the boundary layer.  The boundary layer is the area that is near the surface of the object.  This could refer to a wing on an airplane or a blade in a turbine.  In this blog, I will target the boundary layer inside pipes, tubes, and hoses that are used to transport fluids.  The profile across the area (reference diagram below) is a velocity gradient.  The boundary layer is the distance from the wall or surface to 99% of the maximum velocity of the fluid stream.  At the surface, the velocity of the fluid is zero because the fluid is in a “no slip” condition.  As we move away from the wall, the velocity starts to increase.  The boundary layer thickness measures that area where the velocity is not uniform.  If you reach 99% of the maximum velocity very close to the wall of the pipe, the air flow is turbulent.  If the boundary layer reaches the radius of the pipe, then the velocity is fully developed, or laminar.  Mathematically, laminar flow equations can be calculated, but turbulent flows require theories and experimental data to determine.

As an analogy, imagine an expressway as the velocity profile, and the on-ramp as the boundary layer.  If the on-ramp is long and smooth, a car can reach the speed of traffic and merge without disrupting the flow.  This would be considered Laminar Flow.  If the on-ramp is curved but short, the car has to merge into traffic at a much slower speed.  This will disrupt the flow of some of the traffic.  I would consider this as the transitional range.  Now imagine an on-ramp to be very short and perpendicular to the expressway. As the car goes to merge into traffic, it will cause chaos and accidents.  This is what I would consider to be turbulent flow.

In a compressed air system, similar things happen within the piping scheme.  Valves, tees, elbows, pipe reducers, filters, etc. are common items that will disrupt the flow.  Let’s look at a scenario with the EXAIR Digital Flowmeters.  In the instruction manual, we require the flow meter to be placed 30 pipe diameters from any disruptions.  The reason is to get a laminar air flow for accurate flow measurements.  In order to get laminar flow, we need the boundary layer thickness to reach the radius of the pipe.

Why is this important to know?  In many compressed air applications, the laminar region is the best flow to generate a strong force; efficiently and quietly.  Allowing the compressed air to have a more uniform boundary layer will optimize your compressed air system.  And for the Digital Flowmeter, it helps to measure the flow accurately and consistently.  If you would like to discuss further how to reduce “traffic jams” in your process, an EXAIR Application Engineer will be happy to help you.

John Ball
Application Engineer
Email: johnball@exair.com

## Laminar Flow Compared to Turbulent Flow

Fluid mechanics is the field that studies the properties of fluids in various states.  There are two main areas; fluid statics and fluid dynamics.  Fluid dynamics studies the forces on a fluid, either as a liquid or a gas, during motion.  Osborne Reynolds, an Irish innovator, popularized this dynamic with a dimensionless number, Re. This number determines the state in which the fluid is moving; either laminar flow, transitional flow, or turbulent flow.  Equation 1 below shows the relationship between the inertial forces of the fluid as compared to the viscous forces.

Equation 1:  Re = V * Dh/u

Re – Reynolds Number (no dimensions)

V – Velocity (feet/sec or meters/sec)

Dh – hydraulic diameter (feet or meters)

u – Kinematic Viscosity (feet^2/sec or meter^2/sec)

The value of Re will mark the region in which the fluid (liquid or gas) is moving.  If the Reynolds number, Re, is below 2300, then it is considered to be laminar (streamline and predictable).  If Re is greater than 4000, then it is considered to be turbulent (chaotic and violent).  The area between these two numbers is the transitional area where you can have eddy currents and some non-linear velocities.  To better show the differences between each state, I have a picture below that shows water flowing from a drain pipe into a channel.  The water is loud and disorderly; traveling in different directions, even upstream.  With the high velocity of water coming out of the drain pipe, the inertial forces are greater than the viscous forces of the water.  This indicates turbulent flow with a Reynolds number larger than 4000.  As the water flows into the mouth of the river, the waves transform from a disorderly mess into a more uniform stream.  This is the transitional region.  A bit further downstream, the stream becomes calm and quiet, flowing in the same direction.  This is laminar flow.  Air is also a fluid, and it will behave in a similar way depending on the Reynolds number.

Why is this important to know?  In certain applications, one state may be better suited than the other.  For mixing, suspension and heat transfer; turbulent flows are better.  But, when it comes to effective blowing, lower pressure drops and reduced noise levels; laminar flows are better.  In many compressed air applications, the laminar region is the best method to generate a strong force efficiently and quietly.  EXAIR offers a large line of products, including the Super Air Knives, Super Air Amplifiers and Super Air Nozzles that utilizes that laminar flow for compressed air applications.  If you would like to discuss further how laminar flows could benefit your process, an EXAIR Application Engineer will be happy to help you.

John Ball
Application Engineer
Email: johnball@exair.com

## 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

## Henri Coanda: Founder of The Coanda Effect (1886-1972)

EXAIR uses the Coanda effect in many of our products. Henri Coanda is an important figure in the world of fluid dynamics and aerodynamics.

Henri Coanda was a prominent Romanian Inventor and aerodynamics pioneer is known for the creation of the Coanda-1910 experimental plane as well as discovering the Coanda effect. On June 7, 1886 Henri was born in Bucharest Romania to General Constantin Coanda and Aida Danet. In 1899 Henri’s father who desired him to have a military career had him transfer to a Military High School for additional years of schooling, where he graduated with the rank of Sergeant Major. Continuing his studies, he went on to technical school back in Bucharest for Artillery, Military, and Naval Engineering. In 1904 he was sent to an artillery regiment in Germany where he would enroll in Technische Hochshule. Henri did not give up on studying and in 1907 went to Montefiore Institute in Liege, Belgium, where he met Gianni Caproni.

In 1910 Henri and Gianni began a partnership to construct an experimental aircraft which was later called the Coanda-1910. The Coanda-1910 was unlike any other aircraft of its time as it had no propeller; instead it sported an oddly shaped front end with built-in rotary blades arranged in a swirl pattern. These blades were driven by an internal turbine screw that would suck air in through the turbine while exhausting the gases out of the rear, propelling the plane forward. This initial jet engine was quite impressive for the time, but sadly nobody believed it would ever fly and is believed that it never did achieve flight. Coanda is not credited with the invention of the jet engine, but his technology spurred the future of aviation into the future.

During World War 2 Henri spent his time developing the turbo-propeller drive system from his 1910 Biplane. After World War 2 had ended Henri began furthering his research on the Coanda Effect which would become the basis for several investigations into entrained and augmented flow of fluids. Later on in 1969 Henri would spend the last of his days in Romania serving as Director of the Institute for Scientific and Technical Creation. Coanda died on November 25, 1972 in his home town of Bucharest.

Here at EXAIR we have taken Henri Coanda’s, Coanda Effect and applied it to a number of our products to help amplify total airflow and save on compressed air.  The most notable product lines are our Air Amplifiers, Air Nozzles, and Air Knives – which are some of the most efficient products of their kind. These products can help lower your compressed air demand.

If you have any questions about compressed air systems or want more information on any of EXAIR’s products, give us a call, we have a team of Application Engineers ready to answer your questions and recommend a solution for your applications.

Cody Biehle
Application Engineer
EXAIR Corporation
Visit us on the Web