Buoyancy
In
physics, buoyancy is an upward force on an object immersed in a fluid , enabling it to float or at least to appear lighter. Buoyancy is important for many
vehicles such as
boats,
ships,
balloons, and
airships.
Encyclopedia
In
physics,
buoyancy is an upward force on an object immersed in a fluid , enabling it to float or at least to appear lighter. Buoyancy is important for many
vehicles such as
boats,
ships,
balloons, and
airships.
Forces and equilibrium
The buoyancy provides an upward force on the object. The upward forces have to balance the downward forces weight. Otherwise, it will accelerate upwards or downwards.
If such an object's compressibility is less than that of the surrounding fluid, it is in stable equilibrium and will, indeed, remain at rest, but if its compressibility is greater, its equilibrium is
unstable, and it will rise and expand on the slightest upward perturbation, or fall and compress on the slightest downward perturbation. For an object to float, it must be able to displace enough water equal to its weight.
Archimedes's principle
It was the ancient Greek,
Archimedes of
Syracuse, who first discovered the law of buoyancy, sometimes called Archimedes's principle:
- The buoyant force is equal to the weight of the displaced fluid.
The story of Archimedes discovering buoyancy while sitting in his bathtub is described in Book 9 of
De architectura was a treatise on architecture [i] written by the Roman [i] architect [i] ...
by
Vitruvius.
The weight of the displaced fluid is directly proportional to the volume of the displaced fluid . Thus, among objects with equal masses, the one with greater volume has greater buoyancy.
Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum. Suppose that when the rock is lowered by the string into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs will be 10 newtons minus the 3 newtons of buoyant force: 10 − 3 = 7 newtons.
Density
If the weight of an object is less than the weight of the fluid the object would displace if it was fully submerged, then the object is less dense than the fluid and it floats at a level so it displaces the same weight of fluid as the weight of the object.
If the object has exactly the same
density as the liquid, then it will stay still, neither sinking nor floating upwards, just as the liquid nearby stays still.
An object made of a material of higher density than the fluid, for example a metal object in water, can still float if it has a suitable shape that keeps a large enough volume of air below the surface level of the fluid. In that case, for the average density mentioned above, the air is included also, which may reduce this density to less than that of the fluid.
Acceleration
Although Archimedes's principle gives the force on a buoyant object, this does not allow the direct determination of the
acceleration of the object in the usual way using Newton's second law. This is because as well as accelerating the object, the fluid also has to be dynamically displaced- resulting in drag.
While Archimedes's principle is hydrostatic force, it must be taken into account, even in hydrodynamic situations. A simple case would be that of a submerged sphere that is twice as dense as water starting at rest and as it first starts to fall through the water. Initially ignoring drag, a first approximation might be to include the force of gravity and subtract the force of buoyancy and then apply Newton's equation
F =
ma. The next step would be to attempt to take into account the drag forces due to viscosity, which is a form of dynamic friction. Next is the inertial forces of the water that has to get pushed out of the way as the sphere passes through the water: the inertial component of drag. One might use the drag equation. The velocity would increase and the force of drag will increase until the object reached terminal velocity, where
turbulence might also be a consideration. Still, the hydrostatic force of buoyancy operating on the submerged or floating object must be taken into account.
Applications
See also
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[i]
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External links
