Stack Exit Velocity

This is nothing more than continuity, $Q = vA$, with the area of a circle written out, and it earns its own page because everything downstream of a stack depends on the answer. Twelve cubic metres a second through a 1.2 m bore gives $4 \times 12/(\pi \times 1.44) = 10.61$ m/s. The one thing to be careful of is which twelve. Fan curves, permits and CEM reports quote flow on at least three different bases: actual cubic metres per second at stack conditions, standard cubic metres at 20 or 25 °C, and dry standard cubic metres with the moisture stripped out. Exit velocity is a physical speed and takes the ACTUAL flow. A boiler stack at 200 °C moves about 1.6 times the volume its standard flow suggests, so using the standard number here under-states the velocity by that same factor and quietly under-states plume rise along with it.

The number to compare the answer against is the wind, not a table. Stack-tip downwash occurs when the exit velocity is less than about 1.5 times the wind speed at the stack top: the plume fails to escape the low-pressure wake immediately behind the stack, gets pulled down into it, and effectively loses part of the height that was paid for. Briggs handled this by subtracting a downwash allowance from the physical stack height, and the practical consequence is that a tall stack with a lazy exit can perform worse than a shorter one with a brisk exit. Industrial designs generally land between 15 and 20 m/s at full load, which clears the wind on all but the worst days.

Part-load is where this bites in the field. A stack sized for 18 m/s at full fire runs at 7 m/s when the boiler modulates down to 40 %, and the downwash condition it comfortably passed on the design sheet fails on an ordinary Tuesday in April. The cheap remedy is a tapered exit cone, which raises the velocity at the tip without touching the fan or the ductwork; it costs a little static pressure and it is very much cheaper than adding steel. The expensive remedy is more height. Doing nothing is common and is why so many buildings have a fume complaint that only appears at part load.

Two more habits worth keeping. Velocity pressure rises with the square of this number and stack noise with roughly its sixth power, so the temptation to solve every dispersion problem by cranking up exit velocity is paid for continuously in fan power and sometimes in a noise complaint. And when the number is going into a Method 5 sampling plan rather than a dispersion model, remember this equation gives the AVERAGE velocity: the local velocity at a traverse point near the wall can be 20 % below it, which is exactly why the sampling rate has to be reset at every point rather than computed once from the mean.