Ducts, Fans and Air Distribution
Duct sizing, friction and fitting losses, fan curves and fan laws, diffusers and balancing.
The air path
The air handler (fan, filters, coils, dampers) pushes air through a trunk duct to branches and then to diffusers in the rooms; return air comes back through a plenum or return duct. The fan has to overcome the friction of every part of the path, and everything else in the design (noise, space, leakage) is traded against that pressure. The duct system for the example office carries 500 L/s (the 425 L/s of the load calculation plus the margin for the neighboring zone).
Sizing round ducts
The common method is equal friction: choose a friction rate (0.8 to 1.2 Pa/m for low-velocity comfort systems) and size every section at that rate. The pressure drop in a round duct is the Darcy–Weisbach equation of Pipe Friction and the Moody Diagram: ΔP ÷ L = f ÷ D × ρ v² ÷ 2, with ρ = 1.2 kg/m³ and a galvanized-steel roughness of 0.09 mm.
| Flow | Round duct for 1 Pa/m | Velocity | Friction |
|---|---|---|---|
| 100 L/s | 186 mm | 3.7 m/s | 1.00 Pa/m |
| 250 L/s | 262 mm | 4.6 m/s | 1.00 Pa/m |
| 500 L/s | 340 mm | 5.5 m/s | 1.00 Pa/m |
| 1 000 L/s | 441 mm | 6.5 m/s | 1.00 Pa/m |
Worked example: the main duct for 500 L/s
- Solving for 1.0 Pa/m gives D = 340 mm and v = 5.5 m/s (Re = 124 148, f = 0.0187).
- Take the standard 355 mm duct: v = 5.1 m/s, friction 0.81 Pa/m, dynamic pressure ρv² ÷ 2 = 15.3 Pa.
- Rule: the friction rate rises with about the 1.9th power of velocity and falls steeply with diameter (roughly as D−4.9), so a one-size-up duct halves the friction.
Typical maximum velocities for comfort systems: main ducts 8 to 10 m/s, branches 4 to 6 m/s, final run-outs 2 to 3 m/s; in quiet rooms (studios, bedrooms) use roughly half. Higher velocities mean smaller ducts and more fan power and noise.
Rectangular ducts
Rectangular ducts fit in ceiling voids. A rectangle gives the same friction at the same flow as a round duct of the equivalent diameter De = 1.30 (a b)0.625 ÷ (a + b)0.25 (not the same area). For 500 × 300 mm: De = 420 mm, so it matches the 355 mm round duct for friction but needs 152 percent of its cross-section. Keep the aspect ratio under 4:1; a flat duct has more perimeter and surface for the same area, and more friction.
Friction, fittings and the system curve
Each fitting adds a loss ΔP = C × ρ v² ÷ 2, where C is the loss coefficient (smooth 90° round elbow 0.2 to 0.3, a mitred elbow without vanes about 1.2, a branch tee 0.3 to 1.0 depending on flow split, a sudden contraction 0.5, a sudden expansion near 1). Equipment adds its own drop: filter 50 to 250 Pa, cooling coil 50 to 150 Pa, diffusers 20 to 50 Pa. The fan pressure is the total at design flow, and varies as flow squared (see Pipe Systems, the same rule).
Worked example: the fan pressure for the 500 L/s system
| Part | Calculation | Pressure (Pa) |
|---|---|---|
| Straight duct | 40 m × 0.81 Pa/m | 32 |
| Four elbows | 4 × 0.25 × 15.3 | 15 |
| One branch tee | 0.5 × 15.3 | 8 |
| Diffusers | catalog | 40 |
| Cooling coil | catalog | 100 |
| Filter (mid life) | catalog | 50 |
| Total | 245 |
So a fan must deliver 500 L/s at about 245 Pa (rounded to 250 Pa in the fan figure below). Add an allowance (10 to 15 percent) for unknowns and leakage.
Fans and the fan laws
A fan’s curve falls with flow and meets the system curve at the operating point. The shaft power is P = Q ΔP ÷ η: 0.5 m³/s × 245 Pa ÷ 0.65 = 189 W (377 W per m³/s). The fan laws relate speed N to flow, pressure and power for the same fan and system:
Q₂ ÷ Q₁ = N₂ ÷ N₁ ΔP₂ ÷ ΔP₁ = (N₂ ÷ N₁)² P₂ ÷ P₁ = (N₂ ÷ N₁)³
At 80 percent speed the flow falls to 400 L/s and the power to 97 W (51 percent of the full-speed value). In a VAV system the fan speed follows the duct pressure, and a 20 percent cut in airflow saves almost half the fan energy. Fan types: forward-curved (small, cheap, low pressure), backward-curved or plug (efficient, up to 70 to 85 percent, higher pressure), axial (high flow, low pressure, noisy) and EC motors for efficiency.
Diffusers and air distribution
A diffuser mixes the supply air with room air so it does not feel like a draft. The throw is the distance at which the air slows to a terminal velocity (usually 0.25 m/s). Rules: choose throw about 0.75 of the distance to the wall, keep the supply difference to 8 to 11 K for cooling (colder air dumps), place the diffuser so the jet attaches to the ceiling (the Coanda effect) and avoid short-circuiting to the return. Displacement ventilation supplies cool air low and slowly (0.2 m/s, 18 to 20 °C), letting the heat plumes carry pollution up to the ceiling; chilled beams use water for most of the cooling and a small air flow for ventilation.
Balancing and commissioning
A system that is calculated well but not balanced will starve the far rooms. Balancing sets the dampers so each outlet gets its design flow, measured with a flow hood or a pitot traverse, and checks the total fan flow, the pressures, the leakage (a sealed duct system leaks under 5 percent, a poor one 20 to 30 percent), the rotation direction and the motor current. Fix the cause (too small a duct, a missing damper) rather than closing the dampers on the near rooms, which wastes fan energy.
Related
- Previous: Ventilation and Indoor Air Quality. Next: Coils, Chillers and Cooling Towers.
- Pipe Friction and the Moody Diagram for the Darcy–Weisbach equation.
- Pipe Flow and Pressure Drop Calculator.
- HVAC and Psychrometrics: the whole guide.
FAQ
What is static pressure?
The pressure that pushes air through resistance, as opposed to the velocity (dynamic) pressure. A fan’s rating is usually total or static pressure at a flow; make sure you compare like with like.
Why do ducts leak, and does it matter?
Joints are rarely perfect. Leakage of 10 to 20 percent is common in old systems and wastes fan and conditioning energy; seal with mastic and test.
What is the equal-friction method’s weakness?
It does not balance the system by itself: the shortest runs get too much pressure. Use balancing dampers or a method that sizes for static regain on large systems.
Can I reduce the airflow by closing a damper?
Yes, but a variable-speed fan with the damper wide open saves much more energy.
References
- ASHRAE, Handbook – Fundamentals, Chapter 21 (duct design) and HVAC Systems and Equipment, Chapter on fans.
- SMACNA, HVAC Systems – Duct Design; CIBSE Guide B3 and Guide C (duct friction data).
- AMCA Standard 210 / ISO 5801 (fan testing) and the fan laws in AMCA Publication 201.
Last reviewed: October 2026. Loss coefficients and fan efficiencies are typical; use the maker’s data.