Worked example: a circular air-duct run
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 .
A fan and a duct settle at one operating point: the flow where the pressure the fan can develop equals the pressure the duct takes to pass it. This worked example is an inline fan driving air along a spiral duct with a balancing damper, solved in the gas phase, and it is the clearest picture of how a fan and its system meet.
The setup
An inline duct fan draws air at 20 degrees Celsius from the atmosphere and discharges back to atmosphere at the far end, so there is no static pressure difference across the run. The fan has a pressure-rise curve from 250 Pa at shut-off down to 60 Pa at 150 L/s, referenced to a density of 1.2 kg/m3. The duct is 40 m of DN250 galvanised spiral (0.09 mm roughness), split by an open butterfly damper with a loss coefficient of 0.3.
The physics and the method
This is a compressible-gas solve, though at these low duct pressures the air behaves nearly incompressibly. Because both ends sit at atmospheric pressure, the entire fan pressure rise is spent on friction along the duct plus the loss across the damper. Fluid Network Studio places the fan on its own pressure-rise curve, scaled from the reference density to the inlet air density, and finds the flow where that curve crosses the duct resistance. That crossing is the operating point, and the fan's pressure-flow chart shows it directly.
The damper is the control. Closing it raises its loss coefficient, steepens the resistance curve, and walks the operating point up the fan curve to a lower flow and a higher fan pressure. That is duct balancing in one move, and re-solving after each change shows the new operating point.
The solved result
The fan delivers 164.8 L/s against 25.61 Pa, and the whole run is remarkably cheap in pressure:
| Quantity | Value |
|---|---|
| Operating flow at the fan inlet | 164.8 L/s, which is 593.1 m3/h |
| Fan pressure rise at duty | 25.61 Pa |
| Mass flow through the duct | 0.1984 kg/s |
| Velocity in the DN250 duct | 3.356 m/s |
| Air density | 1.204 kg/m3 |
| Reynolds number | 55 820 |
| Darcy friction factor on the spiral duct | 0.0217 |
The static pressure falls in three steps from the fan to the open end:
| Point | Gauge pressure (Pa) | Drop to the next point (Pa) |
|---|---|---|
| Fan discharge | 25.61 | 2.95 over the first 5 m of duct |
| Damper inlet | 22.66 | 2.04 across the damper |
| Damper outlet | 20.62 | 20.62 over the last 35 m of duct |
| Discharge to atmosphere | 0 | - |
The balancing damper is fully open and it costs only 2.04 Pa of the 25.61 Pa total, under a tenth. In other words the damper's whole authority is still in reserve. That is the number to have in front of you before you start balancing a system, because a damper that is already contributing most of the resistance when open has nothing left to trim with. Everything else is duct: 23.57 Pa over 40 m of DN250 spiral, or roughly 0.6 pascals per metre, which is a light, generously sized run.
One honest caveat about the fan. The duty of 164.8 L/s sits past the last entered curve point at 150 L/s, so the pressure the fan is credited with there is a short extrapolation of the quadratic fitted through the four entered points rather than a reading from the data. It is a modest extrapolation and the fan chart shows exactly where the marker sits relative to the entered points, but if this were your fan you would want a curve point out at the duty before you signed off the selection.
Every number above is solver output rather than a hand calculation. Open the example, press Solve, and check the pressure profile down the duct.
What you learn
Solving the example gives the airflow the fan delivers, the pressure drop split between the duct and the damper, and the operating point on the fan chart. Raise the damper's loss coefficient and re-solve to see the flow fall as the operating point climbs the curve. The single-duct pressure-drop calculation is on the rectangular duct pressure drop calculator, and the fan and duct example explores the same fan-meets-system idea on a rectangular duct.
Compressible gas, with fans and compressors, is part of the Advanced plan, A$39/month or A$390/year.
Open this example in FNS and close the damper to walk the operating point up the fan curve.