Principle of Floatation and Its Applications

Vocabulary flashcards generated from lecture notes covering the principle of floatation, mathematical ratios, specific fluid and body densities, and real-world applications including ships, submarines, human floating, icebergs, swim bladders, and balloons.

Principle of floatation

States that the weight of a floating body is equal to the weight of the liquid displaced by its submerged part.

Apparent weight of a floating body

Equal to zero ($0$), because the weight of the body is balanced by an equal upthrust due to its submerged part.

Submerged volume ratio formula

The relationship given by $\frac{v}{V} = \frac{\rho_S}{\rho_L}$, where $v$ is the volume of the immersed part, $V$ is the total volume, $\rho_S$ is the density of the body, and $\rho_L$ is the density of the liquid.

Plimsoll line

A white line painted on the side of a ship that indicates the safe limit for loading the ship in water of density $10^3\,\text{kg\,m}^{-3}$.

Ballast

Sand or stones filled at the bottom of an unloaded ship to lower its centre of gravity and make its equilibrium stable.

Average density of human body with empty lungs

$1.07\,\text{g\,cm}^{-3}$.

Average density of human body with lungs filled with air

$1.00\,\text{g\,cm}^{-3}$.

Density of sea water

$1.026\,\text{g\,cm}^{-3}$.

Density of fresh (river) water

$1.0\,\text{g\,cm}^{-3}$.

Density of Dead Sea water

$1.16\,\text{g\,cm}^{-3}$.

Floatation mechanism of a submarine

Uses ballast tanks filled with water to increase average density and dive, or forced out with compressed air to decrease average density and rise.

Density of ice

$0.917\,\text{g\,cm}^{-3}$.

Volume percentage of an iceberg submerged in fresh water

$91.7\%$ of its total volume is submerged below the water surface ($v = 0.917\,V$), leaving $8.3\%$ above.

Volume percentage of an iceberg submerged in sea water

$89.3\%$ of its total volume is submerged inside sea water ($v = 0.893\,V$), leaving $10.7\%$ above.

Swim bladder

An organ in many fish species that acts like a submarine's ballast tank by diffusing oxygen gas from blood into the bladder to increase volume and lower average density to rise, or emptying it to sink.

Water level behavior when floating ice melts

The water level does not change when floating ice melts because the melting ice contracts by a volume equal to its portion that was above the water surface.

Rising limit of a light gas balloon

A balloon stops rising when upthrust becomes equal to its weight, which occurs because the density of atmospheric air decreases with increasing altitude.