| A boat stays afloat because its weight | | | | the slightest downward perturbation. |
| is equal to that of the water it | | | | The depth of a submarine tends to be |
| displaces. The material of the boat | | | | unstable. A submarine is more |
| itself may be heavier than water (per | | | | compressible than the surrounding water. |
| volume!), but it forms only the outer | | | | As depth increases, the resulting |
| layer. Inside it is air, which is | | | | pressure causes the submarine's volume |
| negligible in weight. But it does add to | | | | to decrease more than the volume of the |
| the volume. The central term here is | | | | surrounding water decreases. Buoyancy |
| density, which is mass ('weight') per | | | | depends upon the object's volume and the |
| volume. One has to divide the mass of | | | | weight of the displaced fluid. Volume |
| the boat (plus contents) as a whole by | | | | has decreased so the the weight |
| the volume below the waterline. If the | | | | displaced has decreased which means a |
| boat floats than that is equal to the | | | | decrease in buoyancy and the submarine |
| density of water (1 kg/l). One could say | | | | tends to sink further. A rising |
| that to the water it is as if there is | | | | submarine expands more than the |
| water there because the average density | | | | surrounding water, the submarine tends |
| is the same. If one adds weight to the | | | | to rise further. |
| boat, the volume below the waterline | | | | The height of a balloon tends to be |
| will have to increase too, to keep the | | | | stable. As a balloon rises it will tend |
| mass/weight balance equal, so the boat | | | | to increase in volume with reducing |
| sinks a little to compensate. | | | | atmospheric pressure. But the balloon's |
| In physics, buoyancy is the upward force | | | | cargo will not expand. The average |
| on an object arising from the | | | | density of the balloon decreases less, |
| displacement of the fluid (i.e., a | | | | therefore, than that of the surrounding |
| liquid or a gas) in which it is fully or | | | | air. The balloon's buoyancy reduces |
| partially immersed. This force enables | | | | because the weight of the displaced air |
| the object to float or to at least to | | | | is reduced. A rising balloon tends to |
| appear lighter. Buoyancy is important | | | | stop rising. Similarly a sinking balloon |
| for many vehicles such as boats, ships, | | | | tends to stop sinking. |
| balloons, and airships. | | | | Archimedes' principle |
| Explanation | | | | It was the ancient Greek, Archimedes of |
| The downward force on the top surface of | | | | Syracuse, who first discovered the law |
| an immersed object in a fluid is smaller | | | | of buoyancy, sometimes called |
| than the butt upward force on the bottom | | | | Archimedes's principle: |
| surface, because pressure increases with | | | | The buoyant force is equal to the weight |
| depth. The vector sum of the forces is | | | | of the displaced fluid. |
| thus vertically upward. The buoyancy | | | | The story of Archimedes discovering |
| force disappears if the fluid is not | | | | buoyancy while sitting in his bathtub is |
| allowed to flow under the bottom of the | | | | described in Book 9 of De architectura |
| object, for example if the object's | | | | by Vitruvius. |
| bottom is fully in contact with the | | | | The weight of the displaced fluid is |
| bottom of the container. | | | | directly proportional to the volume of |
| Forces and equilibrium | | | | the displaced fluid (specifically if the |
| Buoyancy provides an upward force on the | | | | surrounding fluid is of uniform |
| object. The magnitude of this force is | | | | density). Thus, among objects with equal |
| equal to the weight of the displaced | | | | masses, the one with greater volume has |
| fluid. (Displacement is the term used | | | | greater buoyancy. |
| for the weight of the displaced fluid | | | | Suppose a rock's weight is measured as |
| and, thus, is an equivalent term to | | | | 10 newtons when suspended by a string in |
| buoyancy.) The buoyancy of an object | | | | a vacuum. Suppose that when the rock is |
| depends, therefore, only upon two | | | | lowered by the string into water, it |
| factors: the object's volume, and the | | | | displaces water of weight 3 newtons. The |
| density of the surrounding fluid. The | | | | force it then exerts on the string from |
| greater the object's volume and | | | | which it hangs will be 10 newtons minus |
| surrounding density, the higher the | | | | the 3 newtons of buoyant force: 10 - 3 = |
| buoyancy. | | | | 7 newtons. |
| If the buoyancy of an (unrestrained and | | | | The density of the immersed object |
| unpowered) object exceeds its weight, it | | | | relative to the density of the fluid is |
| will tend to rise. And an object whose | | | | easily calculated without measuring any |
| weight exceeds its buoyancy will tend to | | | | volumes: |
| sink. | | | | Density |
| The atmosphere's density depends upon | | | | If the weight of an object is less than |
| altitude. As an airship rises in the | | | | the weight of the fluid the object would |
| atmosphere, therefore, its buoyancy | | | | displace if it was fully submerged, then |
| reduces as the density of the | | | | the object has an average density less |
| surrounding air reduces. The density of | | | | than the fluid and has a buoyancy |
| water is essentially constant: As a | | | | greater than its weight. If the fluid |
| submarine expels water from its buoyancy | | | | has a surface, such as water in a lake |
| tanks (by pumping them full of air) it | | | | or the sea, the object will float at a |
| rises because its buoyancy stays the | | | | level so it displaces the same weight of |
| same (because volume of water it | | | | fluid as the weight of the object. If |
| displaces stays the same) while its | | | | the object is immersed in the fluid, |
| weight is decreased. | | | | such as a submerged submarine or a |
| As a floating object rises or falls the | | | | balloon in the air, it will tend to |
| forces external to it change and, as all | | | | rise. |
| objects are compressible to some extent | | | | If the object has exactly the same |
| or another, so will the object's volume. | | | | density as the liquid, then it's |
| Buoyancy depends on volume and so an | | | | buoyancy equals its weight. It will tend |
| object's buoyancy reduces if it is | | | | neither to sink nor float. |
| compressed and increases if it expands. | | | | An object with a higher average density |
| If an object's compressibility is less | | | | than the fluid has less buoyancy than |
| than that of the surrounding fluid, it | | | | weight and it will sink. |
| is in stable equilibrium and will, | | | | A ship floats because although it is |
| indeed, remain at rest, but if its | | | | made of steel which is more dense than |
| compressibility is greater, its | | | | water, it encloses a volume of air and |
| equilibrium is unstable, and it will | | | | the resulting shape has an average |
| rise and expand on the slightest upward | | | | density less than that of water. |
| perturbation, or fall and compress on | | | | |