How to Average a Duct Traverse Into CFM

Why this matters

Airflow numbers decide real money and real comfort: whether a new system is delivering its design CFM, whether a cold room is a duct problem or an equipment problem, whether a commissioning report gets signed. A single velocity reading in the middle of a duct is not airflow. Air moves faster in the center than at the walls, so one center reading overstates the flow, and a reading near a wall understates it. A traverse, a grid of readings across the whole section, averaged and multiplied by the area, is how you turn velocity into CFM you can defend. This card is the arithmetic of that traverse: the area, the grid, the average and the multiply, with the errors that throw the answer off the most.

For when a traverse is the right method versus a flow hood or a pressure-based estimate, and for the system-level verification around it, see 'Airflow Measurement and CFM Verification'.

The formula

CFM = average velocity (ft/min) x inside cross-sectional area (sq ft)

Feet per minute times square feet leaves cubic feet per minute. The two inputs are measured separately, and each has its own trap.

Before you drill

Hazard: test holes go in sheet metal duct only, on a section you can see both sides of. Never drill into the furnace or air handler cabinet, a heat exchanger, a coil, or anywhere near a flue or vent connector, where a hole can let combustion products into the airstream. Check behind the spot for wiring and refrigerant lines before the bit goes in, wear eye protection for the chips, and deburr the hole. In an attic, work from boards across the joists, not the drywall between them, and limit time in the heat. Every hole you drill gets a proper duct plug before you leave; an open hole leaks air for the life of the system.

Pick the section. A traverse is only as good as the airflow profile it samples. Choose straight duct as far downstream of elbows, transitions, takeoffs and dampers as the run allows. Close to a fitting, the air is swirling or piled against one side, and no number of points averages that out reliably. Your instrument maker and whatever test procedure you work to give recommended distances; where a project specification calls for ASHRAE Standard 111 or a balancing body's procedure, the edition named in that specification sets the location and point rules, and they bind you through the contract, not by law.

Step 1: the inside area

Measure the inside dimensions, in inches, and convert to square feet.

• Rectangular: area (sq ft) = width (in) x height (in) / 144
• Round: area (sq ft) = 0.7854 x diameter (in) x diameter (in) / 144

The 144 is the square inches in a square foot (12 x 12). Dividing by 12 instead gives an area twelve times too large. See related: Units Carried Through Every Line of a Calculation.

For a 14 by 8 in duct: 14 in x 8 in = 112 sq in, and 112 / 144 = 0.778 sq ft. For a 10 in round duct: 0.7854 x 10 x 10 = 78.54 sq in, and 78.54 / 144 = 0.545 sq ft. The round formula is the circle area in diameter form; see related: Circles in the Field: Area, Circumference and the Diameter Trap.

The lined-duct trap. Duct with internal liner, and duct board, have inside dimensions smaller than the outside. A duct that measures 14 by 8 in outside with 1 in liner on every wall is 12 by 6 in inside: 72 sq in, or 0.500 sq ft. Using the outside 0.778 sq ft on that duct overstates the area by 0.778 / 0.500 = 1.56 times, so the CFM comes out 56 percent high. Push a probe through the hole until it touches the far wall and read the depth; that gives you the real inside height or width.

Step 2: lay out the points

The goal is that each reading represents an equal share of the cross-section, so a plain average is fair.

Rectangular duct, equal-area grid. Divide the section into equal rectangles and read at the center of each. For the 14 by 8 in duct, four columns of 3.5 in and three rows of 2.67 in gives twelve equal rectangles of 9.33 sq in each. The reading points sit at the center of each:

• Across the 14 in width: 1.75, 5.25, 8.75 and 12.25 in from one side.
• Down the 8 in height: 1.33, 4.00 and 6.67 in from the top.

Three holes in the top of the duct, or the side, at the column positions, and the probe marked at the row depths, gets you there. Larger ducts need more points, and the test procedure you are working to sets the minimum; some use a log-Tchebycheff layout rather than equal spacing, which places points closer to the walls to capture the profile better with fewer readings.

Round duct, equal-area rings. Readings go along two diameters at right angles. For an equal-area layout with three rings, the points sit at 0.408, 0.707 and 0.913 of the radius from the center, on each side. Those come from splitting the circle into three rings of equal area and reading at the radius that splits each ring's area in half (the square roots of 1/6, 3/6 and 5/6). For a 10 in duct, radius 5 in, that is 2.04, 3.54 and 4.56 in from the center, which is 0.44, 1.46, 2.96, 7.04, 8.54 and 9.56 in from the near wall along each diameter.

Step 3: read each point, as a velocity

Hold the probe square to the airflow at each mark and let the reading settle. If it wanders, watch it for several seconds and write the middle of the swing. Record every point, including the low ones near the walls. Those are real air moving slowly, and dropping them pushes the average up.

If you are using a pitot tube, convert each reading to velocity before averaging. A pitot tube reads velocity pressure (VP, in inches of water column), and velocity goes with the square root of VP. For standard air (0.075 lb per cu ft, roughly sea level and room temperature), velocity (ft/min) = 4005 x square root of VP (in. w.c.).

Averaging the pressures first and converting once gives a higher number than the true average, because the square root of an average is always at least the average of the square roots. Two points show it:

• Point A, VP 0.02 in. w.c.: 4005 x 0.1414 = 566 ft/min
• Point B, VP 0.04 in. w.c.: 4005 x 0.2000 = 801 ft/min
• Right: average the velocities, (566 + 801) / 2 = 684 ft/min
• Wrong: average the VPs, 0.03 in. w.c., then 4005 x 0.1732 = 694 ft/min

Ten ft/min high on two points, about 1.5 percent; across a full grid with a steep profile, more. A digital anemometer that reads velocity directly avoids the issue, but check whether yours averages in velocity or pressure when it computes its own mean.

The constant 4005 holds for standard air only. At altitude, or in hot supply air, air is less dense, and the same velocity pressure means a higher true velocity. Using 4005 there understates the flow. Apply the density correction your instrument's manual gives, and note on the sheet that you did.

Step 4 and 5: average, then multiply

Here is the full sheet for the 14 by 8 in duct, read with a velocity probe.

DUCT TRAVERSE SHEET
Duct: 14 x 8 in inside, sheet metal, unlined
Area: 14 x 8 = 112 sq in / 144 = 0.778 sq ft
Grid: 4 columns x 3 rows, equal area

Velocity, ft/min
            col 1   col 2   col 3   col 4   row sum
            1.75in  5.25in  8.75in  12.25in
row 1 1.33   640     720     730     650     2740
row 2 4.00   680     780     790     690     2940
row 3 6.67   620     710     720     670     2720
                                    total    8400
Points: 12
Average: 8400 / 12 = 700 ft/min
CFM: 700 ft/min x 0.778 sq ft = 544 CFM

Check the row sums before the total: 640 + 720 + 730 + 650 = 2740, 680 + 780 + 790 + 690 = 2940, 620 + 710 + 720 + 670 = 2720, and 2740 + 2940 + 2720 = 8400. A miscopied row is the commonest error on a traverse sheet, and it is invisible in the final CFM.

Then the multiply: 700 ft/min x 0.778 sq ft (112 / 144 unrounded) = 544.4 CFM, written as about 544 CFM.

The center-reading error, from these numbers. Had you taken only the single highest center reading, 790 ft/min, the CFM would be 790 x 112 / 144 = 614 CFM, 13 percent high. The edges of this grid run 620 to 690 ft/min against 780 to 790 in the middle, and that is a fairly flat profile. A duct closer to a fitting is less forgiving.

Verify before you write it on the report

1. Rough check the product. 700 ft/min through a bit more than three quarters of a square foot is a bit over 500 CFM. If your sheet says about 6,530, the area was divided by 12 instead of 144; if it says 5,440 or 54, a decimal slipped.
2. Look at the shape of the grid. Readings should be lower at the walls and higher in the middle, roughly symmetrical. If one side runs far higher than the other, the section is too close to a fitting or a damper. Move the traverse if you can; if you cannot, write that the profile was skewed so nobody treats the number as tighter than it is.
3. Compare with what the system should be doing. Add up traverses on the branches and compare with a traverse on the trunk, or with the equipment's expected airflow at the measured static pressure. A branch total far above the trunk means one of the areas is wrong, often a lined duct figured on outside dimensions.
4. Repeatability. If the number matters, run the grid a second time. Two passes within a few percent of each other give you a number you can stand behind. Two passes that disagree widely mean the flow is unsteady or the probe is not being held square.

References

• Airflow Measurement and CFM Verification (library card)
• ASHRAE Standard 111, Measurement, Testing, Adjusting and Balancing of Building HVAC Systems, in the edition a project specification names
• Instrument manufacturer documentation for the probe in use (density correction, averaging method)
• See related: Units Carried Through Every Line of a Calculation
• See related: Averaging Readings: Mean, Median and Weighted