Buoyancy. Archimedes' principle

A (partly) submerged object feels an upward force equal to the weight of the displaced fluid. $F_B = \rho_{fluid}\, g\, V_{sub}$ It comes from the pressure difference: the water pushes harder on the bottom than on the top → Hydrostatic pressure $p = \rho g X$ at depth $X$, times the bottom area.

Floating ship (box shape, $L \times W$): $F_B = Mg$ $X L W \rho_{water}\, g = Mg \quad\Rightarrow\quad X = \frac{M}{L W \rho_{water}}$ $X$ = draught (depth under the waterline), $M$ = ship + load.

Why it matters for transport: $X$ sets the submerged frontal area $A = XW$ for Drag. A heavier ship sinks deeper → more area → more drag.

Combined with Drag: $P_{water} = \frac12 c_{drag} (XW) \rho_{water} v^3 = \frac12 c_{drag} \frac{M}{L} v^3$ $W$, $\rho_{water}$ (and $g$) cancel: denser water → ship sinks less, but each m³ pushed is heavier; wider ship → wider front, but sinks less. Drag depends only on mass per length $M/L$ → long, slim ships are efficient (in this model; in reality $c_{drag}$ depends on size and shape).

Related: Hydrostatic pressure, Drag