Gravity Water Autonomy in an Apartment Block During a Blackout: A Header-Tank Sizing Rule Bounded by Head Pressure and Roof Load, with a Ground-Level Fallback

When power fails in an apartment block, booster pumps stop and upper floors lose water first. This paper derives a gravity header-tank design from stated physical inputs, bounded by head pressure and roof load. Demand tiers are survival 7.5, hygiene 20, and rationed full use 50 litres per person per day, with a 10% leakage allowance and a 3,000-litre firefighting reserve (100 L/min for 30 minutes). The sizing rule V = 1.10 q T N + 3000 litres gives, for a 100-resident block at 72 hours, 54.75 litres per resident at survival, 96.0 at hygiene, and 195 at full tier. A reference design for a 10-floor, 100-resident block (9,600 litres gross, 6,600 litres domestic) delivers 72.0 hours at hygiene, 192.0 hours at survival, and 28.8 hours at full tier; a staged rationing schedule (24 hours hygiene, then survival) extends it to 152.0 hours, and a 5,000-litre tanker refill at hour 48 to 297.45 hours. Head fails from the top: the top floor has 5.5 m head (0.54 bar) at full tank, keeps a shower for only 26.18 hours, and never has an effective fire jet, which is available for the full duration only on floors one to four. Structure requires a frame: water on a slab alone may be only 0.102 m deep on a weak roof (1.0 kPa spare), and the reference tank presses on its own footprint at 21.19 kPa, needing 50.9 m2 of spread on a typical roof. An older 6-floor, 72-resident slab-only block can hold at most 3,058 litres, 1,724 litres short of its 72-hour survival requirement including the fire reserve, and short even at 24 hours (3,594 litres required); for such buildings a ground-level bladder is sized in full (7,752 litres for 72 hours at hygiene on 6.46 m2, ground pressure 11.77 kPa against a stated allowable 50 kPa) with standpipe distribution and container carriage costs computed by floor. All results are simulated, not measured; nothing was built, installed, or hardware-tested. Computations are reproducible from the deposited compute.py and results.json.