Isokinetic Sampling Rate

Sampling a gas for particulate is not like sampling it for a gas, because particles have inertia and gas does not. If the sampling nozzle draws gas in at exactly the velocity the stack gas is already travelling, the streamlines run straight into the nozzle undisturbed and the sample carries the same particle size distribution as the stack. That condition is isokinetic, and it is arithmetically trivial: $Q_n = v_s A_n$. A 0.5 cm² nozzle in a stream moving 20 m/s needs $20 \times 5 \times 10^{-5} = 1 \times 10^{-3}$ m³/s, which is 1 L/s or 60 L/min at the nozzle.

Get it wrong and the bias has a predictable sign, which is the part worth internalising. Sample too slowly, sub-isokinetically, and gas spills around the outside of the nozzle rather than entering it; the fine particles follow the gas away, but the heavy ones cannot turn in time and carry straight in, so the sample is enriched in coarse particles and the reported loading is too HIGH. Sample too quickly and the nozzle pulls in gas from the sides that the coarse particles refuse to follow, diluting the sample and reporting a loading that is too LOW. The magnitude depends on the Stokes number, so the bias is negligible for particles under about a micrometre and severe above ten. This is also why gaseous sampling has no isokinetic requirement at all: molecules have no inertia to speak of and go where the gas goes.

EPA Method 5 and its relatives build the whole test around holding this condition, and accept a run only if the isokinetic ratio falls between 90 and 110 %. The velocity is not one number, though. Method 1 lays out a traverse of sampling points across the duct, Method 2 measures the local velocity at each one with a pitot tube, and the sampling rate has to be RESET at every point, because the velocity near the wall can be well below the velocity at the centre. Setting the pump once from the average velocity and leaving it there is the classic field error and it fails the run.

The equation above is the physics; the working form in the method is longer, and it is worth knowing why. The pump and dry gas meter sit downstream of the filter, the impingers and the ice bath, so they measure a cooler, drier, differently pressured gas than the nozzle sees. The full Method 5 nozzle equation therefore carries corrections for meter temperature and pressure, for the stack moisture removed in the impingers, and for the pitot coefficient — all of which convert the flow at the meter into the flow at the nozzle. Nomographs did this on site for decades and calculators do it now. Nozzles themselves come in fixed button sizes, so the practice is to compute the ideal bore, pick the nearest available button, and then adjust the pump rate to hold isokinetic rather than machining a nozzle to a calculated diameter.