## 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

## Fluidics, Boundary Layers, And Engineered Compressed Air Products

Fluidics is an interesting discipline of physics.  Air, in particular, can be made to behave quite peculiarly by flowing it across a solid surface.  Consider the EXAIR Standard and Full Flow Air Knives:

If you’ve ever used a leaf blower, or rolled down the car window while traveling at highway speed, you’re familiar with the power of a high velocity air flow.  Now consider that the Coanda effect can cause such a drastic redirection of this kind of air flow, and that’s a prime example of just how interesting the science of fluidics can be.

EXAIR Air Amplifiers, Air Wipes, and Super Air Nozzles also employ the Coanda effect to entrain air, and the Super Air Knife employs similar precision engineered surfaces to optimize entrainment, resulting in a 40:1 amplification ratio:

As fascinating as all that is, the entrainment of air that these products employ contributes to another principle of fluidics: the creation of a boundary layer.  In addition to the Coanda effect causing the fluid to follow the path of the surface it’s flowing past, the flow is also affected in direct proportion to its velocity, and inversely by its viscosity, in the formation of a boundary layer.

This laminar, lower velocity boundary layer travels with the primary air stream as it discharges from the EXAIR products shown above.  In addition to amplifying the total developed flow, it also serves to attenuate the sound level of the higher velocity primary air stream.  This makes EXAIR Intelligent Compressed Air Products not only as efficient as possible in regard to their use of compressed air, but as quiet as possible as well.

If you’d like to find out more about how the science behind our products can improve your air consumption, give me a call.