Introduction
Note: this case study is hypothetical and illustrative — a worked planning scenario using realistic numbers, not a report of an actual job. A two-story, 2,400 sq ft home has a 4-ton air conditioner and a familiar complaint: the upstairs bedrooms never cool down in summer, the system roars at the return grille, and the far bedroom runs 5°F warmer than the thermostat. The ductwork is original to a 1990s install. This study diagnoses the ducts with the friction-rate method, sizes the corrections, and prices the fix.
Follow along with your own numbers in the Duct Size Calculator — enter the CFM, friction rate, and each candidate duct size to reproduce every figure below. The sizing method is fully derived in the formula-explained guide.
The Scenario
| Parameter | Value |
|---|---|
| Home | 2,400 sq ft, two-story |
| Equipment | 4-ton AC, air handler rated 0.50 in. w.c. ESP |
| Total system airflow | 4 × 400 = 1,600 CFM |
| Component losses | Coil 0.15 + filter 0.06 + grilles 0.03 = 0.24 in. w.c. |
| Available static pressure | 0.50 − 0.24 = 0.26 in. w.c. |
| Longest run TEL | 325 ft (measured + fitting equivalents) |
| Design friction rate | (0.26 ÷ 325) × 100 = 0.08 in. w.c./100 ft |
| Existing trunk | 16-in round, rigid metal |
| Existing return | Single 14-in round |
| Far bedroom branch | 6-in flex, compressed and sagging |
Diagnosis: The Existing Ducts by the Numbers
The 16-inch trunk carrying 1,600 CFM
Friction loss in the 16-in trunk at 1,600 CFM: 0.121 in. w.c. per 100 ft — 51% over the 0.08 budget. Velocity: 1,600 CFM through 1.396 ft² = 1,146 FPM — well above the 900 FPM trunk ceiling. Verdict: the trunk alone consumes the pressure budget before air reaches the branches, and it does so noisily. This single undersized trunk explains the weak airflow everywhere downstream.
The single 14-inch return
A 14-in round duct carries only about 906 CFM at the 0.08 friction rate — 57% of the 1,600 CFM the system needs. Forcing 1,600 CFM through it means roughly 1,500 FPM at the grille: the roar the homeowner hears. Verdict: the return is choking the blower — the classic undersized-return failure.
The 6-inch flex bedroom branch
The far bedroom needs 200 CFM. A 6-in duct carries only about 97 CFM at 0.08 — and this run is compressed flex, whose real-world friction is worse than the rated value. The room receives less than half its design airflow. Verdict: undersized and installed in the worst possible material condition.
The Redesign
New trunk: 20-inch round
At 1,600 CFM and 0.08 friction rate, the exact required diameter is 17.6 in → an 18-in duct meets the budget (0.067 in. w.c./100 ft, 905 FPM), but the design rounds up to 20-inch for margin and quiet operation: friction 0.039 in. w.c./100 ft ✓✓, velocity 733 FPM ✓ — comfortably inside the 700–900 FPM trunk band. (Metric: 1,600 CFM = 0.755 m³/s; 20 in = 508 mm; 733 FPM = 3.72 m/s.)
New returns: two 16-inch runs
Splitting the return into two 16-in runs gives each 800 CFM to carry — each 16-in duct handles about 1,290 CFM at 0.08, so 800 CFM runs at 573 FPM ✓, quiet and well within budget. Two returns (one per floor) also fix the closed-bedroom-door pressure problem. Return grille face velocity drops into the 300–500 FPM target — the roar disappears by design, not by luck.
Bedroom branch: 8-inch rigid
The 200 CFM bedroom gets an 8-in rigid metal runout replacing the compressed 6-in flex: 207 CFM capacity at 0.08 ✓, 573 FPM ✓. Short, straight, sealed with mastic — rigid metal beats flex for problem runs because its smooth interior holds the rated friction.
Illustrative Cost of the Fix
Using typical planning ranges from the cost guide (region and access move these): trunk replacement 60 ft of 20-in rigid at $35–$75/ft ≈ $2,100–$4,500; second return run ≈ $500–$1,500; bedroom branch re-run ≈ $200–$500; mastic sealing of remaining joints ≈ $300–$800; permit and inspection ≈ $100–$400. Planning total: roughly $3,200–$7,700. Because the equipment itself is sound, no equipment change is included — this is a duct-only correction, which is exactly when duct replacement beats full system replacement.
Illustrative Outcomes
With the redesign installed and balanced (dampers set room by room, static pressure verified with a manometer against the 0.50 ESP rating):
- Static pressure falls back within the equipment’s rated range — the blower moves its full 1,600 CFM without straining.
- The far bedroom receives its full 200 CFM design airflow instead of under half — the 5°F split is an airflow problem, and airflow problems respond to airflow fixes.
- Noise drops at every grille: trunk velocity falls from 1,146 to 733 FPM, return velocity from ~1,500 to 573 FPM.
- Energy waste shrinks two ways: the blower no longer fights excess static pressure, and sealed, insulated ducts stop leaking conditioned air into the attic.
These are the expected directions of improvement for this illustrative scenario, not measured results — real outcomes depend on installation quality, sealing thoroughness, and commissioning. The pro tips guide covers the commissioning measurements that confirm the fix worked.
Lessons From the Scenario
- One undersized trunk poisons the whole system. Every branch downstream of a choked trunk underperforms — fixing branches without fixing the trunk wastes money.
- Returns are half the system. The single 14-in return was as guilty as the trunk; most diagnoses stop at the supply side and miss it.
- Flex condition matters as much as flex size. The 6-in bedroom run was wrong on paper and worse in the field.
- The friction rate is the diagnostic. Comparing each section’s actual friction against the computed 0.08 budget identified every problem quantitatively — no guesswork.
- Measure first with the estimating guide procedure — TEL with fittings counted is what made the 0.08 budget trustworthy.
Related Guides
- Duct Size Calculator FAQ — quick answers to the most asked duct sizing questions.
- Pro Tips — design and installation judgment from the trade.
- Common Mistakes — the sizing errors this scenario illustrates.
- Duct Sizing Checklist — every step to verify before you buy ductwork.
- DIY vs Pro — when to do this work yourself, and when to hire.
Get Your Number
Run your own home through the same diagnostic: compute your friction rate, check each trunk and branch against it in the Duct Size Calculator, and size the returns with the same rigor as the supplies. Undersized sections reveal themselves as friction numbers over budget and velocities over target — exactly like the ones above. Have a licensed HVAC professional review any redesign before installation, and confirm permit requirements with your local building authority.
Disclaimer: This case study is hypothetical and illustrative — a worked planning scenario, not a report of a real project. Calculator results are planning estimates based on the dimensions you enter. Actual duct sizing depends on your system’s airflow requirements, equipment static pressure, duct material, and local code. Verify with a licensed HVAC professional, and consult your local building authority for code and permit decisions.
