Fan and duct, a worked operating-point 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 low-pressure air-moving problem rather than a high-pressure one, a fan pushing air through a duct. It is a built-in network in Fluid Network Studio, so you can open it, solve it, and read the fan operating point directly. It shows how a fan finds its duty against a duct, which is the central question in ventilation, combustion-air and low-pressure conveying design.
The scenario
A fan draws air from the atmosphere and pushes it along a duct that discharges back to the atmosphere. With both ends open to the air, the only thing the fan works against is the friction of the duct. Where does the flow settle? At the single point where the pressure the fan can produce exactly matches the pressure the duct demands at that flow. That is the operating point, and finding it is what this example is about.
The real setup
The example uses these parameters exactly as built:
- An inlet boundary at 0 gauge (atmosphere) and an outlet boundary at 0 gauge.
- A fan component with its inlet at the atmosphere boundary and its outlet at a junction, carrying a pressure-rise versus flow curve through three points: 500 Pa at zero flow, 320 Pa at 0.03 m3/s, and 0 Pa at 0.05 m3/s. Reference density 1.2 kg/m3.
- A duct, 60 m long, 100 mm diameter, roughness 1.5e-4 m, from the junction to the outlet.
- Working fluid set to the gas phase, air at 20 degrees C, gas constant 287.05 J/kg.K, viscosity 1.81e-5 Pa.s.
The physics and method
The fan is modelled from its curve. Fluid Network Studio fits a quadratic pressure-rise versus flow relation through the three curve points, then scales it to the inlet air density using the affinity laws so the curve reflects the actual gas rather than the reference condition. The duct resistance comes from the compressible gas kernel: the solver works in absolute pressure, in the pressure-squared variable, with the Churchill friction factor. The flow advances until the fan rise and the duct loss agree, which is the network's way of intersecting the fan curve with the system curve.
The solved result
The fan and the duct meet at 37.37 L/s and 221.4 Pa:
| Quantity | Value |
|---|---|
| Operating flow at the fan inlet | 37.37 L/s, which is 134.5 m3/h |
| Fan pressure rise at duty | 221.4 Pa |
| Mass flow through the duct | 0.0450 kg/s |
| Air density at the fan inlet | 1.204 kg/m3 |
| Static pressure at the fan discharge | 221.4 Pa gauge, 101.5 kPa absolute |
| Velocity at the duct inlet | 4.748 m/s |
| Velocity at the duct outlet | 4.758 m/s |
| Reynolds number in the duct | 31 650 |
| Darcy friction factor | 0.0271 |
| Entered curve range | 0 to 50 L/s, so this duty is inside the data |
The fan gives 221.4 Pa, a little under half its 500 Pa shut-off rise, at three quarters of the 50 L/s free-delivery flow. Because both ends of the run sit at atmosphere, there is no static component at all and every one of those 221.4 pascals is spent on 60 m of 100 mm duct. That is what makes this the cleanest possible picture of a fan meeting its system: move the duct and the whole pressure rise moves with it.
Notice how little the air changes state along the way. Velocity climbs only from 4.748 to 4.758 m/s and density is effectively constant, so at this pressure the compressible kernel is producing an almost incompressible answer. That is the correct result and a useful reassurance: a low-pressure ventilation duct does not need a compressible treatment, but running one costs nothing and tells you when you have left that regime.
The duty also sits inside the entered fan curve, between the 0 and 50 L/s points, so it is an interpolation of the fitted characteristic rather than an extrapolation past its end.
Every figure is solver output. Open the example, press Solve, and read the operating-point marker on the fan chart.
What the solver computes and what you learn
Solve it and the network settles at the operating flow and the matching pressure rise. Select the fan and you see its Delta-p versus Q chart with the operating-point marker placed on the curve, so you can read where on its characteristic the fan is actually working. The lesson is that a fan does not have a single flow, it has a curve, and the duct decides which point on that curve you get. Make the duct longer or narrower and the resistance line steepens, the marker slides back up the curve, and the flow drops. That is the trade-off every ventilation sizing exercise turns on.
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 where each suits. The glossary explains the operating point and the other 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 duct length to watch the operating point move.