Compressed air line, a worked pressure-drop example
Written by Haimi Jordaan, MEng (Mechanical), University of Pretoria. Seven years in a specialist engineering analysis and design group across CFD, FEA and DEM. He wrote the solver behind Fluid Network Studio.Published . Last updated .
This worked example is a short compressed air distribution run, the kind you find feeding a tool station or a process header off a plant ringmain. It is one of the built-in networks in Fluid Network Studio, so you can open it, solve it, and change it to match your own system without setting anything up from scratch.
The scenario
A supply point holds the line at about 6 bar gauge. From there the air travels through a length of pipe, passes a junction, then continues through a narrower pipe to a delivery point that draws a fixed mass flow. The question every air system raises is the same one this example answers: how much pressure do you lose along the run, and how fast is the air moving by the time it reaches the end?
The real setup
The example uses these parameters exactly as built:
- Inlet boundary held at 700 kPa absolute (about 6 bar gauge against the default atmosphere of 101.325 kPa).
- A first pipe, 300 m long, 100 mm internal diameter, roughness 4.6e-5 m (clean commercial steel).
- A junction, then a second pipe, 200 m long, 80 mm internal diameter, same roughness.
- An outlet boundary held at 450 kPa absolute.
- Working fluid set to the gas phase, air at 15 degrees C, with gas constant 287.05 J/kg.K and viscosity 1.81e-5 Pa.s.
The draw-off at the outlet works out to roughly 1.15 kg/s of air across that pressure difference.
The physics and method
Air is compressible, so the solver does not treat this like a water pipe. It works in absolute pressure and solves the network in the pressure-squared variable, balancing mass flow at the junction rather than volume flow. The pipe relation is the exact isothermal form, including the acceleration term, with the Churchill friction factor covering laminar and turbulent flow in one expression. Because the density is tied to the local absolute pressure, the model captures the way the gas expands as it loses pressure down the line.
The solved result
The run passes 1.151 kg/s of air, and the pressure profile is strongly lopsided:
| Point | Absolute pressure (kPa) | Gauge pressure (kPa) |
|---|---|---|
| Inlet boundary | 700.0 | 598.7 |
| Junction, where the bore steps down | 631.1 | 529.7 |
| Outlet boundary | 450.0 | 348.7 |
| Pipe | Size | Mass flow (kg/s) | Velocity in (m/s) | Velocity out (m/s) | Density in (kg/m3) | Density out (kg/m3) | Reynolds |
|---|---|---|---|---|---|---|---|
| First run | 300 m of 100 mm | 1.151 | 17.32 | 19.21 | 8.463 | 7.629 | 809 800 |
| Second run | 200 m of 80 mm | 1.151 | 30.02 | 42.10 | 7.629 | 5.440 | 1 012 000 |
Read the two pipes against each other. The first is half again as long as the second and it costs 68.9 kPa, while the shorter second run costs 181.1 kPa. Nearly three quarters of the line's pressure loss happens in the last 200 m, because that is where the bore narrows to 80 mm and the air is already expanded. Velocity tells the same story from the other side: the air enters at 17.32 m/s and leaves at 42.10, two and a half times faster, while its density falls from 8.463 to 5.440 kg/m3. The mass flow is constant along the run, so every kilogram of pressure the line loses has to be paid for in speed.
That climbing velocity is the early warning an air main gives you. Nothing here has tripped the high-velocity advisory, which for air at 15 degrees Celsius fires above about 102 m/s, but the trend from 17 to 42 m/s over 500 m is the shape you learn to look for before a main runs out of capacity.
Every number above is solver output and it is reproducible. Open the example, press Solve, and check the mass balance at the junction.
What the solver computes and what you learn
Solve it and you get the absolute pressure at the junction and the outlet, the mass flow in each pipe, and the velocity and density at each end of each pipe. The lesson is in the velocity. As the duct narrows from 100 mm to 80 mm and the pressure falls, the density drops and the same mass flow has to move faster, so the velocity rises along the run. That climb is the clearest early warning that a main is undersized. A mass-balance residual is reported on every solve, so conservation is shown rather than assumed.
Compressible gas is part of the Advanced plan, so solving this example needs that plan.
Take it further
This example sits behind the compressed air system design page, which covers sizing mains, velocity limits and the gauge-versus-absolute trap in more depth. The glossary explains the terms the solver uses. Fluid Network Studio supports your engineering work and does not replace a qualified engineer, and it makes no claim of compliance with any standard.
Open this example in FNS and change the diameters to match your own air main.