Floating: density and buoyancy
Density tells how much mass sits in each cubic metre. Sea water is about 1025 kg/m³. An object floats if its density is less than the water's. The part under water is
fraction under water = object density ÷ water density
Wood of 600 kg/m³ sinks in 600 ÷ 1025 = 59% of its height. An object of 1025 or more sinks (at exactly 1025 it just hangs fully under water). Fresh water has density 1000, so the same wood sits a little lower in a river.
A steel ship floats because its hollow hull holds air, so the average density of ship plus air is below water.
Water pressure at depth
Water has weight. The deeper you go, the more water is above you, so the pressure is bigger.
P = P0 + ρ × g × h
P0 is the air pressure at the surface (101.3 kPa). ρ is density (1025 kg/m³), g is 9.81 m/s², h is depth. ρg ≈ 10.05 kPa per metre, so every 10 m adds about 100 kPa, about one more atmosphere.
At 30 m: P = 101.3 + 10.05 × 30 ≈ 403 kPa, four times the air pressure. Underwater cameras, ROVs and diving suits must be built for this.
Mooring and anchoring
An anchor holds a boat by digging into the seabed. It holds best when the pull is flat along the seabed. A long rope or chain makes the pull flat.
Scope = rope length ÷ water depth
A common rule is a scope of at least 3 in calm weather, and 5 or more in wind or rough water. In 10 m of water that means 30 m of rope or more. Add a length of heavy chain at the anchor end. Too short a rope lifts the anchor and the boat drags.
Rust and sacrificial anodes
Salt water makes steel rust (corrode) faster, because salt helps electricity flow. Paint slows it down. Another trick is a sacrificial anode: a block of zinc or aluminium bolted to the steel. Zinc is more eager to corrode, so it is eaten first and the steel stays safe. When the zinc is mostly gone, it is replaced.
Try it
Fill a bucket with water. Float a piece of wood, a candle and a stone one by one and see which sit high or sink. Then measure a rope: tie a stone to a string, find the depth of a bucket, and use the 3D slider to choose a rope 3 times the depth.
Key formulas and definitions
- Fraction under water = object density ÷ water density (sea water ≈ 1025 kg/m³)
- Pressure P = P0 + ρ × g × h
- P0 ≈ 101.3 kPa; ρg for sea water ≈ 10.05 kPa per metre
- Scope = rope length ÷ depth (at least 3, more in rough weather)
- Zinc anode corrodes first and protects steel
Worked examples
1. A wooden block has density 600 kg/m³. How much of it is under sea water (1025 kg/m³)?
Fraction = 600 ÷ 1025 = 0.585, so about 59% is under water and 41% sticks out.
2. Find the total pressure at 30 m depth in the sea. Use P0 = 101.3 kPa and ρg = 10.05 kPa per m.
P = 101.3 + 10.05 × 30 = 101.3 + 301.5 = 402.8 kPa, about 403 kPa.
3. A boat anchors in 8 m of water. The skipper wants a scope of 5 because of wind. How much rope?
Rope = scope × depth = 5 × 8 = 40 m.
Common mistakes
- Thinking heavy things always sink. A steel ship floats because of its hollow shape.
- Forgetting the air pressure P0. Total pressure at 10 m is about 200 kPa, not 100.
- Using a rope as long as the depth. It pulls the anchor up. Use at least 3 times the depth.
- Painting over zinc blocks. The zinc must touch the water to protect the steel.