Fluid Network Studio

Fan and duct, a worked operating-point example

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 between the inlet and 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.

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.