Stack gas velocity and volumetric flow rate
EPA Method 2, 40 CFR Part 60, Appendix A-1
Method 2 turns a small pressure difference across a pitot tube into the speed of the gas, then multiplies by the stack area to get the flow rate. Every pounds-per-hour result in a test depends on it.
- Answers
- How fast is the gas moving, and how many dry standard cubic feet leave the stack each hour?
- Equipment
- Type S pitot tube, inclined manometer, thermocouple and readout, barometer
- Produces
- Average stack gas velocity v_s and dry standard flow rate Q_{sd}
- Feeds into
- Method 5 isokinetic sampling and every mass emission rate
How a pitot tube reads velocity
A pitot tube compares two pressures. One opening faces straight into the gas stream, so the gas stops against it and the pressure there rises by the velocity pressure. The other opening faces away from the flow. The difference between the two, called the velocity head or \Delta p, is read on a manometer in inches of water.
Velocity pressure is the kinetic energy of the gas per unit volume, \tfrac{1}{2}\rho v^2. Double the velocity and \Delta p goes up four times. That is why velocity depends on the square root of \Delta p, and why lighter or hotter gas reads a smaller \Delta p at the same speed.
A standard (Prandtl) pitot tube reads true velocity pressure and has a coefficient close to 0.99, but its tiny static-pressure holes plug quickly in dusty, wet stack gas. The Type S (Stausscheibe) pitot has two large openings facing in opposite directions. It resists plugging, fits through a sampling port, and rides alongside a Method 5 probe. Its downstream opening sits in the low-pressure wake behind the tube, so it reads a larger \Delta p than a standard pitot at the same velocity. Its coefficient is correspondingly lower, typically about 0.84.
Pitot tube and inclined manometer
Change the gas velocity and temperature, and compare the two pitot types.
Gas assumed at 29.92 in. Hg with a wet molecular weight of 29.0. Only Δp is ever measured; the split between the two openings is shown to explain why a Type S reads high. Notice that hotter gas reads a smaller Δp at the same velocity because it is less dense.
The pitot coefficient
The coefficient C_p converts what a pitot reads into what an ideal pitot would read. A Type S tube built and maintained to the geometric specifications in Method 2 may be assigned a baseline coefficient of 0.84 without calibration. Bent, damaged, or nonstandard tubes have to be calibrated.
Calibration is done in a wind tunnel against a standard pitot of known coefficient. The two are read at the same point and velocity, one after the other. Each face of the Type S, labeled side A and side B, is calibrated facing upstream, and the two sides must give nearly the same coefficient so the tube reads the same whichever way it is installed.
Type S coefficient from a calibration against a standard pitot
- C_{p(std)}
- coefficient of the standard pitot, about 0.99
- \Delta p_{std},\ \Delta p_s
- readings of the standard and Type S pitots at the same point and velocity
When the pitot is mounted on a sampling probe, Method 2 also sets minimum spacings between the pitot, the sampling nozzle and the thermocouple, so that none of them disturbs the flow the others see. A probe assembly that does not meet those spacings is calibrated as an assembly.
Taking a velocity traverse
- Level and zero the manometer. An inclined manometer is printed for a gauge oil of a specific density, so use the fluid its scale was made for.
- Leak check the pitot lines. Blow into the impact opening until the manometer reads at least 3 in. H₂O, close it off, and make sure the reading holds steady for at least 15 seconds. Do the same on the other side using suction.
- Read the barometric pressure at the sampling elevation. If you use a nearby weather station, remember it reports pressure corrected to sea level; take off about 0.1 in. Hg for every 100 ft of elevation.
- Measure the stack static pressure. With the pitot turned sideways so neither opening faces the flow, disconnect one line and read the other against the atmosphere. One reading near the center is usually enough.
- Traverse. At each Method 1 point, let the reading settle, then record \Delta p and the stack temperature.
- Leak check again when the traverse is done. A failed post-test leak check means the readings cannot be trusted.
Temperature matters as much as Δp
Velocity depends on the square root of the absolute stack temperature. The thermocouple must be accurate to within 1.5% of the minimum absolute stack temperature, and it should sit close to the pitot openings without touching them.
From Δp to flow rate
Four equations take you from the field data sheet to a flow rate. First, the absolute pressure inside the stack and the molecular weight of the wet gas:
Absolute stack pressure
- P_{bar}
- barometric pressure, in. Hg
- P_g
- stack static pressure, in. H₂O (negative on most induced-draft stacks); 13.6 converts in. H₂O to in. Hg
Wet molecular weight of the stack gas
Average stack gas velocity
- K_p
- 85.49 ft/s · [(lb/lb-mol)(in. Hg) / ((°R)(in. H₂O))]½
- (\sqrt{\Delta p})_{avg}
- average of the square roots of the Δp readings
- T_{s(abs)}
- average absolute stack temperature, °R (°F + 460)
Dry volumetric flow rate at standard conditions
- A
- cross-sectional area of the stack at the sampling location, ft²
- T_{std},\ P_{std}
- 528 °R (68 °F) and 29.92 in. Hg
- Q_{sd}
- dry standard cubic feet per hour (dscf/hr)
Velocity and flow calculator
Every slider feeds the equations below, with the numbers filled in.
Actual flow is at stack temperature, pressure and moisture (acfm). Dry standard flow removes the water and corrects to 68 °F and 29.92 in. Hg, which is the basis emission limits use.
Average the square roots, not the readings
Because velocity follows \sqrt{\Delta p}, the average velocity comes from the average of the square roots. If you average the \Delta p readings first and take the root afterward, you always overstate the velocity whenever the readings differ across the stack. The more uneven the profile, the bigger the error, and it carries straight through to the flow rate and the emission rate.
A 12-point velocity traverse
Pick a profile, or type your own readings into the table.
Fixed conditions for this traverse: 84 in. stack, Cp 0.84, Pbar 29.40 in. Hg, Pg −0.60 in. H₂O, Md 30.10, Bws 10.5%. Temperatures are averaged as read, then converted to absolute.
Where the other inputs come from
- Dry molecular weight comes from Method 3. For a source emitting essentially air, such as a ventilation exhaust, Method 2 lets you skip the analysis and use 29.0.
- Moisture comes from Method 4, usually run as part of the Method 5 train. An estimate is fine for setting up, but final results use the measured value.
- Traverse points come from Method 1, including the cyclonic flow check. Method 2 assumes the gas moves straight up the stack.
Small errors in each input reach the velocity in different proportions. Because most inputs sit under a square root, their effect is roughly halved:
| Input | Change | Velocity changes by |
|---|---|---|
| Δp readings | 10% high | +4.9% |
| Absolute stack temperature | 10% high | +4.9% |
| Wet molecular weight | 3% high | −1.5% |
| Pitot coefficient | 0.85 instead of 0.84 | +1.2% |
| Stack pressure | 1 in. Hg high | about −1.7% |
When Method 2 needs help
- Methods 2F and 2G use three-dimensional and two-dimensional probes that measure the angle of the flow as well as its speed. They are used where the gas does not travel straight up the stack, often for flow monitor audits at power plants.
- Method 2H corrects for the slower gas near the walls of circular stacks, which a standard traverse can under-sample.
- Method 2C covers small stacks and ducts using a standard pitot tube, and Methods 2A and 2D measure flow in pipes and small ducts with gas meters and rate meters.
Acceptance criteria
Method 2 at a glance
- A Type S pitot meeting the geometric specifications may use Cp = 0.84; otherwise calibrate it against a standard pitot.
- On calibration, the side A and side B coefficients must agree closely; check the current method text for the exact limits.
- Pitot leak checks before and after the traverse: at least 3 in. H₂O held steady for at least 15 seconds on each side.
- Temperature measured to within 1.5% of the minimum absolute stack temperature.
- Traverse at the Method 1 points, after an acceptable cyclonic flow check.
- Very low Δp readings, a few hundredths of an inch, need a more sensitive gauge; Method 2 gives a test for when.
Field mistakes that cost runs
Averaging Δp instead of √Δp
The spreadsheet column labeled “average Δp” is the wrong number. Average the square roots, square the result only if you need an equivalent Δp.
A plugged or wet pitot line
Particulate or condensate in a pitot line makes readings sluggish or drift toward zero. Watch for a manometer that stops responding when you move between points, and blow the lines back.
Getting the static pressure sign wrong
Most stacks behind an induced-draft fan run below atmospheric pressure, so P_g is negative. Entering −1.5 in. H₂O as +1.5 shifts the stack pressure by about 0.2 in. Hg.
A pitot that is not square to the flow
The openings must face straight up and down the stack. A tube that is rotated, pitched, or bent reads low and nothing on the data sheet will show it.