OpenSpecEngineering

Finds the pressure loss of a run of round or rectangular duct: the friction loss of the straight duct plus the losses of its fittings. HVAC designers use it to add up the losses along the critical path of a duct system, which the fan must overcome.

Equations

Δp = f·(L/D_h)·p_v + ΣC·p_v     p_v = ρV²/2

Δp is the total pressure loss of the run, L its length and V = Q/A the mean velocity for an airflow Q through a duct of cross-section A. p_v is the velocity pressure and ρ the air density. The first term is the straight-duct friction loss (Darcy–Weisbach); the second is the fitting loss [1]. f is the Darcy friction factor from the Colebrook equation [2],

1/√f = −2·log₁₀(ε/(3.7D_h) + 2.51/(Re·√f))

with ε the duct roughness and Re = ρVD_h/μ the Reynolds number, μ being the air viscosity. Below Re = 2300 the flow is laminar and f = 64/Re. D_h is the diameter of a round duct, or the hydraulic diameter 4A/P of a rectangular one, where P is the perimeter. Picking a duct material fills in ε [1]. The density and viscosity fill in as ASHRAE standard air, dry air at 20 °C and 101.325 kPa [1].

ΣC is the sum of the loss coefficients of the run’s elbows, transitions, dampers and other fittings, taken from fitting loss tables such as those in [1].

Limits and common mistakes

• Each C must be referred to this duct’s velocity pressure. A coefficient a table gives at a different section, such as the outlet of a transition or the branch of a tee, must be converted first, or its loss entered on its own run.
• The run must have one size and one airflow. Split a system into sections wherever the size or the flow changes, and add the sections along the path.
• For a rectangular duct, the page also shows Huebscher’s equivalent round duct D_e. That is the round duct with the same friction at the same airflow; it is not D_h, which is used only inside the friction equation.

Worked example

A 24 × 12 in. galvanized duct with longitudinal seams carries 2,400 CFM for 80 ft. The run has two elbows (C = 0.4 each) and a balancing damper (C = 0.4). Find its pressure loss.

1. Enter Airflow Rate 2400 CFM and choose Duct Shape Rectangular.
2. Enter Duct Width 24 in, Duct Height 12 in and Duct Length 80 ft.
3. Choose Duct Material Medium smooth — galvanized steel, longitudinal seams (0.09 mm). Leave the air at standard air.
4. Enter Sum of Fitting Loss Coefficients 1.2 and press Solve. The Solution shows: Total Pressure Loss (Δp, US): 0.203202 in. w.g.
   Friction Loss (straight duct): 23.7702 Pa
   Fitting Loss (ΣC·p_v): 26.8453 Pa
   Friction Rate (Δp/L, US): 0.119286 in. w.g./100 ft
   Air Velocity (V, US): 1,200 ft/min
   Velocity Pressure (p_v, US): 0.0898115 in. w.g.

Check: 2,400 CFM through 2 ft² is 1,200 ft/min, and the standard-air rule p_v = (V/4005)² gives (1,200/4,005)² = 0.0898 in. w.g. The fittings add 1.2 × 0.0898 = 0.108 in. w.g., more than the 80 ft of straight duct. In a short run, the fittings often decide the loss.