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Reynolds number
Reynolds number is a dimensionless fluid dynamics flow parameter represented by the following symbolic formula: (h < D/:). In this symbolic formula, “h” is a characteristic length, such as a pipe length, “<” is the fluid velocity, “D” is the fluid density, and “:” is the dynamic viscosity.
Fluid dynamics is a branch of mathematics and physics that studies and describes how liquids and gases flow. The Reynolds number helps predict whether the flow through a system will be laminar or turbulent. Engineers harness it to design equipment and flow systems for ideal efficiency.
Engineers for industrial air compressor systems employ the Reynolds number to create an ideal flow model for moving air through the compressor and the connected pipes.
FAQs
The symbolic formula for the Reynolds number is h < D/:. To perform a calculation, you can use this formula:
Re = ρvd/µ
Here’s what the symbols represent:
- Re: The Reynolds number
- ρ: The density of the air in pound-mass per cubic foot (lbm/ft3)
- v: The mean velocity in feet per second
- d: The pipe diameter in feet
- µ: The dynamic viscosity of air in pound-mass per foot second (lbm/ft·s)
You can use values you’ve determined to find the Reynolds number for a particular air compressor system. For example, let’s say these are the values you’ve collected:
- Air density: 0.075 lbm/ft3 (typical density at room temperature and atmospheric pressure)
- Velocity: 2 ft/s
- Pipe diameter: 2 inches (0.167 ft)
- Dynamic viscosity: 2.7 × 10⁻⁵ lbm/ft·s
Put these values into the equation, like so:
Re = (0.075 lb/ft3 x 2 ft/s x 0.167 ft)/(2.7 × 10⁻⁵ lbm/ft·s)
Once you solve the equation, you get a Reynolds number value of about 928. For reference, a higher number indicates more turbulent flow. A value of 2,300 or lower is laminar, and 4,000 or more is turbulent. Anything in between is called transitional flow.
The Reynolds number tells you whether the flow is laminar or turbulent. In laminar flow, the velocity and pressure remain constant, and the fluid layers stay parallel without mixing or disrupting one another. In turbulent flow, irregularities or obstructions in the path of a fluid cause the layers to cross paths. As they do, the direction and magnitude of flow vary unpredictably.
The Reynolds number helps you determine how air behaves in various situations, including within air compressor pipe systems. This knowledge is vital because turbulent flow causes a pressure drop, damages the system and creates higher operational costs.
You can use the Reynolds number during the design process to reduce air turbulence. Engineers calculate this value for various pipe diameters and flow rates to balance cost while reducing turbulence. They also select valves and fittings that create minimal air disruption.
Pipe systems with many bends or kinks create more turbulence, which causes the pressure to drop. The chaotic movement of the air generates pipe friction and uses up the compressed air’s energy.
It’s essential to account for this value during the design phase because you can’t avoid it by increasing the pressure in an air compressor. Increasing the pressure will only increase turbulence, further reducing the compressor’s output pressure. Energy usage will spike during the process, and your air compressor will endure more wear.
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