This is the boss. No calculator. Tonight $g = 10\ \mathrm{m/s^2}$, the bore area comes pre-rounded, the buoyancy flux lands on a perfect cube, the downwind distance is 1000 m so $x^{2/3}$ is exactly 100, the effective height comes out at exactly twice $\sigma_z$ so the exponent is $-2$, and $e^{-2}$ is handed to you as 0.135. The product $\pi \sigma_y \sigma_z u$ is pre-multiplied on the sheet. Everything is chosen to fit in your head.

One source, five lines, and every answer feeds the next: flow and bore to exit velocity, exit velocity and the temperature difference to buoyancy flux, flux and distance and wind to plume rise, rise plus steel to effective height, and effective height into the exponential that decides what reaches the ground. Write each line down as you go — a slip at the top rides all the way to the fence, and it rides in squared.

Note what the last line actually asks. It does not want another number; it wants a decision: does this source comply at the nearest residence, yes or no. The arithmetic exists only to earn you the right to make it. Watch for the trap the whole chapter has been building — the steel on its own is rarely enough, and it is the plume rise that decides which side of the limit the answer lands on.

Everything in the chapter rides in this one stack. 5★ under par here is the chapter crown. Clock in.