Compressor and line, a worked set-ratio 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 compressor feeding a discharge line, the building block of any system that needs to raise pressure rather than just move air. It is a built-in network in Fluid Network Studio, so you can open it, solve it, and read the discharge temperature and shaft power without building anything first.
The scenario
A compressor takes air at a suction pressure and raises it to a set pressure ratio. The compressed air then travels down a line to a delivery point held at a fixed pressure. Two questions matter here that do not arise with a fan. First, how hot does the air get when you compress it, because discharge temperature drives material limits and any aftercooling you might need. Second, how much shaft power does the duty take. This example answers both.
The real setup
The example uses these parameters exactly as built:
- A suction boundary at 200 kPa absolute (about 1 bar gauge against the default atmosphere).
- A compressor between the suction and a junction, set to a pressure ratio of 2.0, so it lifts the air to 400 kPa absolute. Isentropic efficiency 0.75.
- A line, 150 m long, 60 mm internal diameter, roughness 4.6e-5 m, from the junction to the delivery point.
- A delivery boundary at 300 kPa absolute.
- Working fluid set to the gas phase, air at 15 degrees C, gas constant 287.05 J/kg.K, viscosity 1.81e-5 Pa.s.
The physics and method
The compressor is a set-point machine, not a curve-driven one. You fix the ratio and the solver makes it hold. Internally it splits the network at the machine and runs a bracketed root-find on the suction-side flow so the delivered pressure lands where the downstream line and boundary demand. The discharge temperature comes from the isentropic relation corrected by the efficiency you set, so a less efficient machine reports a hotter discharge for the same ratio. The downstream line is solved by the compressible gas kernel in absolute pressure, in pressure-squared, with the Churchill friction factor. The network solves isothermally, and the compressor reports its outlet temperature alongside the hydraulic result.
The solved result
The system settles at 0.3716 kg/s, and the air leaves the compressor at 99.15 degrees Celsius:
| Quantity | Value |
|---|---|
| Mass flow | 0.3716 kg/s |
| Suction pressure | 200.0 kPa absolute, 98.67 kPa gauge |
| Discharge pressure | 400.0 kPa absolute, 298.7 kPa gauge |
| Pressure ratio achieved | 2.00 |
| Delivery pressure at the far end | 300.0 kPa absolute, 198.7 kPa gauge |
| Isentropic discharge temperature | 78.11 degC |
| Actual discharge temperature at 75 % isentropic efficiency | 99.15 degC |
| Shaft power | 31.43 kW |
| Velocity at the line inlet | 27.18 m/s |
| Velocity at the line outlet | 36.24 m/s |
| Density at the line inlet | 4.836 kg/m3 |
| Density at the line outlet | 3.627 kg/m3 |
| Reynolds number in the line | 435 700 |
Two numbers on this page pay for the whole exercise. The first is the gap between 78.11 and 99.15 degrees Celsius. A perfect machine would deliver this 2:1 compression at 78.11 degrees, and the 21 K on top of that is the inefficiency alone, turned into heat in the air. Specify a less efficient compressor and the discharge gets hotter for exactly the same duty, which is what drives aftercooler sizing and material limits downstream.
The second is what happens to that pressure. The compressor adds 200 kPa and the 150 m of 60 mm line gives 100 kPa of it straight back to friction, so half the compression work is spent moving the air rather than delivering it at pressure. On a set-ratio machine the line does not change the discharge pressure, it changes the flow, and the flow is what sets the 31.43 kW of shaft power. Widen that line and the same compressor does more useful work for the same ratio.
These are solver figures, not hand estimates, and they are reproducible. Open the example, press Solve, and select the compressor to read the discharge temperature and power directly.
What the solver computes and what you learn
Solve it and you get the flow the system settles at, the pressure along the line, and on the compressor itself the discharge temperature and the shaft power. The lesson is that the compressor and the line are coupled. The 2:1 ratio sets the discharge pressure, but the line and the 300 kPa delivery boundary decide the flow, and the flow in turn sets the power. Reading the discharge temperature is the quickest way to check whether you need aftercooling before the air enters the line.
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 fans versus compressors and sizing the downstream pipe to match. 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 pressure ratio to watch the discharge temperature respond.