Fluid mechanics is the field that studies the properties of fluids in various states. 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. For compressed air, Re < 2300 will have laminar flow while Re > 4000 will have turbulent flow. Equation 1 below shows the relationship between the inertial forces of the fluid as compared to the viscous forces.
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 will need to 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 from a turbine. In this blog, I will target pipes, tubes, and hoses that are used for transporting 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 distance 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.
The calculation is shown in Equation 2.
d = 5 * X / (Re1/2)
d – Boundary layer thickness (feet or meter)
X – distance in pipe or on surface (feet or meter)
Re – Reynolds Number (no dimensions) at distance X
This equation can be very beneficial for determining the thickness where the velocity is not uniform along the cross-section. 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 affect 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. So, let’s see how that number was calculated.
Within the piping system, high Reynold’s numbers generate high pressure drops which makes the system inefficient. For this reason, we should keep Re < 90,000. As an example, let’s look at the 2” EXAIR Digital Flowmeter. The maximum flow range is 400 SCFM (standard cubic feet per min). In looking at Equation 2, the 2” Digital Flowmeter is mounted to a 2” Sch40 pipe with an inner diameter of 2.067” (52.5mm). The radius of this pipe is 1.0335” (26.2 mm) or 0.086 ft (0.026m). If we make the Boundary Layer Thickness equal to the radius of the pipe, then we will have laminar flow. To solve for X which is the distance in the pipe, we can rearrange the terms to:
X = d * (Re)1/2 / 5 = 0.086ft * (90,000)1/2 / 5 = 5.16 ft or 62”
If we look at this number, we will need 62” of pipe to get a laminar air flow for the worse-case condition. If you know the Re value, then you can change that length of pipe to match it and still get valid flow readings. From the note above, the Digital Flowmeter will need to be mounted 30 pipe diameters. So, the pipe diameter is 2.067” and at 30 pipe diameters, we will need to be at 30 * 2.067 = 62”. So, with any type of common disruptions in the air stream, you will always get good flow data at that distance.
Why is this important to know? In many compressed air applications, the laminar region is the best method 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 correctly 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.