This is the boss. No calculator — and today the constants are the ones a balancer carries up a ladder: standard air at 1.2 W per litre per second per kelvin, water at 4.2 kW per litre per second per kelvin, and the 800 mm round main's face taken as 0.50 m², which is within half a per cent of $\pi d^{2}/4$ and is exactly how the number gets used on site.

One air handler, one long problem, and every answer feeds the next: the traverse gives a velocity, the velocity gives an airflow, the airflow and the coil's temperature rise give a load, the load and the design drop give a water flow, and the efficiency turns that load into fuel. Write each line down as you go — one early slip rolls all the way to the boiler.

And note what the last line actually asks for. Not another number: a decision, which is what a balancing report is for. The arithmetic is only there to earn you the right to sign it. Mind the comparison too — a boiler is rated on the fuel it can fire, so hold it against the fuel this coil demands, not against the coil load itself.

Then one bonus mark from the last page of the report. It is either the fill valve, with a metre of water rounded to 10 kPa, or an old manometer sheet in the trade's own units, with the pitot constant rounded to 4000 so that $V = 4000\sqrt{\mathrm{VP}}$ and every root is one you know.

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