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💨 Duct Design Calculator — Darcy–Weisbach + Fittings
Now with a Design Target for max velocity, inline “What to enter?” tooltips, and a pressure-drop sparkline that steps at each fitting.
1) Fluid, Units & Duct Geometry
Design Target — Max Velocity
2) Fittings Losses
Recommended defaults & tips
3) Results
Results will appear here. We report straight‑duct friction (Darcy–Weisbach) and additional fitting losses, then total static pressure.
What’s happening under the hood?
Designing Ductwork Using Bernoulli’s Equation: A Step‑by‑Step Guide
Use Bernoulli’s energy balance (with friction & fittings) to size ducts, estimate losses, and ensure terminals receive the pressure they need. This article is calculator‑free for clean reading — the interactive tool can be embedded as a separate block.
1) Bernoulli — a quick refresher
Concept Bernoulli’s equation is an energy balance along a streamline. For an incompressible fluid (like air at low speeds in HVAC) with fan work and head losses, the practical form is:
p/ρg + α·V²/2g + z + hfan = p/ρg + α·V²/2g + z + hloss
In horizontal ducts, elevation z barely changes. The fan adds head, while friction and fittings take it away. We track two helpful lines:
- EGL (Energy Grade Line): p/ρg + V²/2g + z
- HGL (Hydraulic Grade Line): p/ρg + z
3) Step‑by‑step duct design
- Collect Inputs. Flow Q, path length L, fittings (elbows, tees, dampers), material/roughness, terminal pressure requirement (e.g., diffuser needs pterm).
- Pick a target velocity. Trunks ≈ 5–6 m/s, branches ≈ 3.5–4.5 m/s, terminals ≈ 1.5–2.5 m/s. With Q = V·A, choose a trial size.
- Compute velocity pressure. VP = ρ·V²/2. This is the “kinetic energy” term in Bernoulli.
- Estimate friction. Darcy–Weisbach: Δpduct = f·(L/Dh)·(ρV²/2). Get f via Swamee–Jain (needs Reynolds number and relative roughness).
- Add fitting losses. Δpfit = ΣK·(ρV²/2). Or convert to equivalent length Leq = Σ(K·Dh/f) and add to L.
- Apply Bernoulli. Required start static = terminal static + Δpduct + Δpfit. Check against fan capability; iterate on duct size/layout to hit targets.
Typical K‑values (rule‑of‑thumb — verify from catalogues/ASHRAE)
| Fitting | Approx. K | Note |
|---|---|---|
| 90° Elbow | ~1.3 | Long‑radius & vanes reduce K |
| VCD (part‑open) | ~2.0 | Depends on blade angle |
| VAV box | ~1.0 | Use manufacturer data |
| Fire damper | ~3.0 | Blade/curtain type varies |
| Entry | ~0.5 | Rounded entry lowers K |
| Exit | ~1.0 | Diffuser cone lowers K |
| Tee — through run | ~1.8 | Geometry dependent |
| Tee — branch | ~2.5 | Geometry dependent |
Always prefer tested K‑values from the product submittal when available.
4) Worked example (paper‑based)
Find: Required start static pressure.
- Area A = 0.6×0.35 = 0.210 m²; Perimeter P = 2(0.6+0.35)=1.9 ⇒ Dh = 4A/P ≈ 0.442 m.
- Velocity V = Q/A = 0.8/0.210 ≈ 3.81 m/s (good for a trunk/large branch).
- Re = V·Dh/ν ≈ 3.81×0.442 / 1.5e‑5 ≈ 112,000 (turbulent).
- Relative roughness ε/D ≈ 152e‑6 / 0.442 ≈ 3.44e‑4; Swamee–Jain ⇒ f ≈ 0.020 (approx.).
- Velocity pressure ρV²/2 ≈ 1.21×(3.81²)/2 ≈ 8.8 Pa.
- Straight‑duct drop Δpduct = f(L/D)·(ρV²/2) ≈ 0.020×(40/0.442)×8.8 ≈ 15.9 Pa.
- ΣK = 4(1.3)+2(2.0)+3.0+1.0 = 12.2 ⇒ Δpfit = ΣK·(ρV²/2) ≈ 12.2×8.8 ≈ 107.4 Pa.
- Total drop Δp = 15.9 + 107.4 ≈ 123.3 Pa.
- Required start static = terminal (50 Pa) + total drop (123.3 Pa) = ≈ 173 Pa.
This hand calc mirrors what a calculator would do. Use your dedicated calculator block for rapid iterations.
5) Printable design checklist
- ✔ Define Q and target velocity band per section (trunk/branch/terminal).
- ✔ Choose trial size → compute V and check noise/comfort band.
- ✔ Estimate f via Re + roughness; confirm material.
- ✔ Count fittings and estimate ΣK (or use equivalent lengths).
- ✔ Apply Bernoulli: terminal static + losses = required start static.
- ✔ Iterate on size/layout until requirements are met with margin.
- ✔ Validate against fan curve and balancing needs.
