This is the boss. No calculator. Tonight $g = 10\ \mathrm{m/s^2}$, the bore area comes pre-rounded, and $\rho/\mu$ for water is handed to you as $10^{6}\ \mathrm{s/m^2}$ so the Reynolds number is a shift of the decimal point. Everything is chosen to fit in your head.

One line, six steps, and every answer feeds the next: flow to velocity, velocity to Reynolds number, Reynolds number to the right friction relation and its $f$, $f$ to the friction head, the same velocity head to the fittings, and the two of them together to the verdict. Write each line down as you go — one slip at the top rolls all the way to the pump.

And note what the last line actually asks. It does not want another number; it wants a decision: will this circulator carry this line, 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 straight pipe alone can sit comfortably inside the pump's head while the fittings quietly sink it.

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