Bilge — Water lab

The laws in play

• Water is level; the ship is not. Each cabin's surface is a horizontal line at its own height. The hull rotates underneath it — a tilted room shows a level pool sitting in one corner, never a slanted one.
• Flow follows head. Through a door, water moves at a rate set by the height difference between the two surfaces at the doorway (Torricelli, sampled down the opening). Two cabins that share an open door equalise; a shut door only seeps. A door above both surfaces carries nothing, which is why a raised stern stays dry.
• Leaks gush by depth. A hole's inflow is proportional to the square root of how far it sits below the sea, minus the cabin's own head at the hole. A flooded cabin stops leaking once its surface reaches sea level; a hole lifted above the sea by a list stops entirely.
• Buoyancy is the hull below the sea line. The ship sinks until the submerged area matches the weight of hull, water and cargo, and trims until the centre of buoyancy (▲) sits under the centre of mass (▼). Water that is free to move shifts the mass toward the low end as she tilts — the free-surface effect — so half-full cabins list her harder than full ones.
• Sealed air holds. A full cabin behind a shut door takes no more; the pocket is what sealing buys you. The ladder holes on deck are never sealed.

Starting states

Readout

Tuning