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HVAC Design Simulator

HVAC Duct Sizing Simulator — Rectangular Duct Pressure Drop

From flow rate, width, height, and length, compute in real time the hydraulic diameter, mean velocity, unit-length pressure drop, and total pressure drop of a rectangular duct. Useful for sizing HVAC ducts and estimating fan static pressure.

Parameters
Flow rate Q
m³/s
Duct width a
mm
Duct height b
mm
Duct length L
m

Air properties fixed at rho = 1.20 kg/m^3, mu = 1.8e-5 Pa s. Sheet-metal duct roughness epsilon = 0.09 mm.

Results
—
Mean velocity V
—
Hydraulic diameter D_h
—
Unit-length pressure drop ΔP/L
—
Total pressure drop ΔP
Rectangular duct (oblique view)

3D-style oblique view of a duct of size a × b × L. Yellow arrows show inflow / outflow with the current flow rate Q.

Velocity V vs unit-length pressure drop ΔP/L

X = V (m/s) / Y = ΔP/L (Pa/m). Green band = HVAC recommended 3-8 m/s. Yellow dot = current operating point.

Theory & Key Formulas

Rectangular-duct pressure drop is computed by replacing the pipe diameter in the Darcy-Weisbach equation with the hydraulic diameter $D_h$ and using the Swamee-Jain explicit formula for the friction factor.

Hydraulic diameter and mean velocity:

$$D_h = \frac{2ab}{a+b},\qquad V = \frac{Q}{a\,b}$$

Reynolds number and Swamee-Jain formula:

$$Re = \frac{\rho V D_h}{\mu},\qquad f = \frac{0.25}{\left[\log_{10}\!\left(\dfrac{\varepsilon/D_h}{3.7} + \dfrac{5.74}{Re^{0.9}}\right)\right]^2}$$

Unit-length and total pressure drop:

$$\frac{\Delta P}{L} = f\,\frac{\rho V^2}{2\,D_h},\qquad \Delta P_\text{total} = \frac{\Delta P}{L}\cdot L$$

Here $a,b$ are duct width and height [m], $L$ is duct length [m], $Q$ is flow rate [m³/s], $\rho = 1.20$ kg/m³ (air), $\mu = 1.8\times 10^{-5}$ Pa·s, and $\varepsilon = 0.09$ mm (sheet-metal duct).

What is the HVAC Duct Sizing Simulator?

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My HVAC assignment asks me to size a duct, but how do I compute pressure drop in a rectangular duct? My textbook only covers round pipes.
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The trick is to use the hydraulic diameter to map it onto the pipe formula. For a rectangular duct of width a and height b, define $D_h = 2ab/(a+b)$ as the equivalent diameter, then treat it as a round pipe. The Darcy-Weisbach equation $\Delta P = f(L/D_h)(\rho V^2/2)$ then gives the pressure drop with engineering accuracy of a few percent.
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That simple? Why does the cross-section shape not matter much?
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In turbulent flow the thin boundary layer near the wall dominates friction, so what counts is not the overall cross-section shape but how much of the perimeter is wetted by the flow — that is exactly 4A/P, the hydraulic diameter. Laminar flow needs a small shape correction, but typical HVAC ducts at 3-8 m/s have Re of tens to hundreds of thousands, fully turbulent, so this approximation is plenty.
🙋
Where does the 3-8 m/s recommended range come from?
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The lower bound is where ducts get so fat that construction cost and space explode, and the upper bound is where pressure drop and noise become intolerable. For example raising V from 5 to 10 m/s makes ΔP/L roughly 4 times bigger and roughly quadruples fan power, while noise and vibration become audible in occupied rooms. In practice, main ducts at 5-7 m/s and room branches at 3-4 m/s is the standard playbook.
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For the same flow rate, does it matter whether I make the width or the height larger?
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Great question. For a fixed area A = ab, a square (a = b) maximizes D_h, while a very elongated aspect ratio (say 10:1) shrinks D_h and raises pressure drop. For instance 400×300 mm and 600×200 mm both have area 0.12 m^2, but D_h is 343 mm versus 300 mm and the latter has about 14% higher pressure drop. Try swapping a and b in the sliders to feel this effect.

Frequently Asked Questions

The Swamee-Jain formula (1976) is an explicit approximation to the Colebrook equation and stays within about 1% of the Colebrook solution over 5e3 ≤ Re ≤ 1e8 and 1e-6 ≤ epsilon/D ≤ 1e-2. Typical HVAC ducts (Re about 1e4-1e6, epsilon/D about 1e-4-1e-3) fall fully inside this range. The ASHRAE Duct Fitting Database and SHASE design manuals also adopt equivalent explicit formulas, so it works directly in spreadsheets and is the everyday workhorse for hand and CAD calculations.
For the same flow area, a round duct gives a larger D_h and lower pressure drop (round D_h = D is always larger than the rectangular equivalent). Round (especially spiral) duct also wins on cost and air-tightness. Rectangular duct, however, fits much more efficiently into a height-limited ceiling space. A common practical solution is a hybrid layout: spiral round for the long main runs above corridors, and rectangular for branches within the ceiling of each room.
No. This tool computes only the friction loss in straight duct. The required fan static pressure also includes losses from elbows, branches, dampers, coils (filters, chilled/hot-water coils, humidifiers), and outlet diffusers. A typical order-of-magnitude split is "duct friction : equipment : outlets ≈ 1:1:1," so the external static pressure of the fan is often 2-3 times the duct-friction ΔP from this tool. For the final number, add each fitting using ASHRAE / SHASE fitting databases.
Pressure drop changes because air density rho and viscosity mu change. This tool assumes 20°C standard air (rho = 1.20 kg/m^3, mu = 1.8e-5 Pa s). For typical conditioned air downstream of coils (5-40°C), the values are within a few percent of the tool's output. For smoke-extraction ducts above 200°C, rho drops to about 0.74 kg/m^3, so ΔP drops in the same proportion. A common quick correction is to multiply ΔP by 273 / (273 + T°C), using the ideal-gas approximation rho ∝ 1/T.

Real-World Applications

Office and commercial HVAC duct design: This tool maps directly to the initial planning of ceiling-space HVAC ducts in offices and shops. From a required flow rate you pick a cross-section based on ASHRAE / SHASE recommended velocities, then estimate the pressure drop from the duct length. That is exactly the internal logic of "equal-friction" and "equal-velocity" sizing methods, the backbone of HVAC duct design. For an office main duct, a typical target is ΔP/L ≈ 1 Pa/m; in this tool you can scrub the sliders until the readout lands on that target to back-solve the cross-section.

High-static cleanroom and laboratory systems: Semiconductor and pharmaceutical cleanrooms operate with external static pressures of 500-1500 Pa because of HEPA filtration. Designers add filter loss (e.g. final 250 Pa) on top of friction-style straight-duct loss, of the kind this tool produces, when selecting fans. Velocities are typically 6-10 m/s, a bit higher than general HVAC, so pushing the slider near the upper end of this tool already gives a feel for the design numbers.

Industrial ventilation and smoke extraction: Smoke ducts are sized at the maximum design flow with the density-drop from elevated temperature taken into account. Residential and small-building local ventilation often uses flexible ducts (large epsilon), so ΔP/L can be 2-5 times the value this tool returns for sheet-metal at epsilon = 0.09 mm. Keeping the duct path as short as possible has a very large pay-off in fan power, which the slider sensitivity makes immediately obvious.

Subway and road-tunnel ventilation: Even giant tunnels with cross-sections beyond 50 m^2 are still amenable to the same hydraulic-diameter framework. Velocities of 4-10 m/s over a few kilometers of length lead to total ΔP of several kPa and jet- or axial-fan power in the megawatt range. Early-stage sensitivity studies — a 5% change in cross-section delivers about 20% lower pressure drop — are quickly checked in this tool.

Common Misconceptions and Pitfalls

The most common misconception is to assume that as long as the cross-sectional area is the same, the shape does not matter. Yes, equal area at equal flow gives equal mean velocity, but the hydraulic diameter $D_h = 2ab/(a+b)$ varies strongly with shape. A 400×300 mm duct and a 600×200 mm duct both have area 0.12 m^2, but D_h is 343 mm versus 300 mm, a 13% difference, which carries through directly into ΔP/L (about 14% higher for the latter). Keeping the aspect ratio in roughly 1:1 to 2:1 is a basic rule for fan-power efficiency. Swapping a and b in the sliders makes the effect obvious.

The next is to assume that pressure drop is linear in velocity. In fact the Darcy-Weisbach right-hand side scales with $\rho V^2/2$, and in turbulent flow the friction factor f is a weak function of V (about Re^-0.2), so the effective dependence is ΔP/L ∝ V^1.8 to V^2. Doubling velocity roughly quadruples pressure drop, and the fan power (flow times static pressure) grows by about a factor of 8. Conversely, a 20% larger cross-section pushes V down by 1/1.44 and pressure drop down by about half — the leverage you can see by moving the cross-section sliders.

Finally, remember that this tool computes only straight-duct friction. A real route always has elbows (K = 0.2-0.5), Y-branches (K = 0.5-1.0), dampers, coils, filters, and outlet diffusers. In short ducts these local losses can match or exceed the friction loss. In practice, with dampers fully open, 30-50% of the total static pressure is local loss. For an accurate number you must add each fitting from the ASHRAE Duct Fitting Database or SHASE-S 010. Use this tool only as an "early-stage duct friction lookup" for initial sizing.

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