Before any plume, the stack. Three relations answer almost everything a designer asks of one.

Exit velocity: $v_s = \dfrac{4Q_v}{\pi d^{2}}$ — v-s equals four Q-v over pi d squared. $Q_v$ is the actual volumetric flow at stack conditions in m³/s, $d$ is the inside diameter at the exit in metres, and $v_s$ is the answer in m/s. The word actual is load-bearing: a stack at 200 °C moves about 1.6 times the volume of its own standardised flow, and mixing the two is the commonest error on a test report. Design practice keeps $v_s$ above about 6 m/s and above 1.5 times the wind at the top — below that the plume is dragged into the stack's own wake, which is stack-tip downwash, and it arrives at ground level far sooner than any calculation predicted.

Draft: $\Delta p = h\,g\,(\rho_a - \rho_s)$ — delta-p equals h g, rho-a minus rho-s. $h$ is the height of the gas column in metres, $\rho_a$ — rho-a — is the ambient air density outside (about 1.2 kg/m³ at 20 °C) and $\rho_s$ the stack gas density inside (0.5–0.8 kg/m³ hot). The answer is in pascals. It is the DIFFERENCE that lifts, which is why a cold flue backdrafts on a winter morning until it is warmed through, and the same equation is why a tall building's lobby doors are hard to open in January.

GEP height: $H_{GEP} = h_b + 1.5\,L$, the US EPA's good-engineering-practice rule. $h_b$ is the height of the building causing the wake, and $L$ is its LESSER dimension — the smaller of that height and the width it presents to the wind. Reading the greater one is the standard error and it over-states the stack every time. Two things to know about it: GEP is a ceiling on credit, not a licence to build tall, and the rule takes the greater of this formula height and a floor of 65 m, so any source may claim 65 m regardless of what stands beside it.

The trade lore, in one line: raising exit velocity fights downwash where extra height is not available, and a tapered exit cone buys it without touching the fan.