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 the fluid dynamics, we can examine the layer which is next to the surface; the boundary layer.  This could refer to a wing on an airplane, a blade in a turbine, or inside compressed air lines.  In this blog, I will target the boundary layer inside pipes, tubes, and hoses that are used to transport compressed air.  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 you 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 can be calculated, but turbulent flow requires 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.  Now imagine an on-ramp to be 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 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 where 99% of the air speed is represented at the center. 

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

Twitter: @EXAIR_jb

Photo: Smoke by SkitterphotoPixabay license

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