Buoyancy

Buoyancy (/ˈbɔɪənsi, ˈbuːjənsi/),[1][2] or upthrust is a net upward force exerted by a fluid that opposes the weight of a partially or fully immersed object.

For this reason, an object whose average density is greater than that of the fluid in which it is submerged tends to sink.

This can occur only in a non-inertial reference frame, which either has a gravitational field or is accelerating due to a force other than gravity defining a "downward" direction.

Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it.

Assuming Archimedes' principle to be reformulated as follows, then inserted into the quotient of weights, which has been expanded by the mutual volume yields the formula below.

However, because the balloon is buoyant relative to the air, it ends up being pushed "out of the way", and will actually drift in the same direction as the car's acceleration (i.e., forward).

Using this the above equation becomes: Assuming the outer force field is conservative, that is it can be written as the negative gradient of some scalar valued function: Then: Therefore, the shape of the open surface of a fluid equals the equipotential plane of the applied outer conservative force field.

In this case the field is gravity, so Φ = −ρfgz where g is the gravitational acceleration, ρf is the mass density of the fluid.

In other words, the "buoyancy force" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to Though the above derivation of Archimedes principle is correct, a recent paper by the Brazilian physicist Fabio M. S. Lima brings a more general approach for the evaluation of the buoyant force exerted by any fluid (even non-homogeneous) on a body with arbitrary shape.

[7] Interestingly, this method leads to the prediction that the buoyant force exerted on a rectangular block touching the bottom of a container points downward!

Once it fully sinks to the floor of the fluid or rises to the surface and settles, Archimedes principle can be applied alone.

For a sunken object, the entire volume displaces water, and there will be an additional force of reaction from the solid floor.

An object which tends to float requires a tension restraint force T in order to remain fully submerged.

An object which tends to sink will eventually have a normal force of constraint N exerted upon it by the solid floor.

To find the force of buoyancy acting on the object when in air, using this particular information, this formula applies: The final result would be measured in Newtons.

A simplified explanation for the integration of the pressure over the contact area may be stated as follows: Consider a cube immersed in a fluid with the upper surface horizontal.

The upward force on the cube is the pressure on the bottom surface integrated over its area.

Similarly, the downward force on the cube is the pressure on the top surface integrated over its area.

Angled surfaces do not nullify the analogy as the resultant force can be split into orthogonal components and each dealt with in the same way.

This situation is typically valid for a range of heel angles, beyond which the center of buoyancy does not move enough to provide a positive righting moment, and the object becomes unstable.

Once the weight has been balanced so the overall density of the submarine is equal to the water around it, it has neutral buoyancy and will remain at that depth.

Most military submarines operate with a slightly negative buoyancy and maintain depth by using the "lift" of the stabilizers with forward motion.

Underwater divers are a common example of the problem of unstable buoyancy due to compressibility.

The desired condition is usually neutral buoyancy when the diver is swimming in mid-water, and this condition is unstable, so the diver is constantly making fine adjustments by control of lung volume, and has to adjust the contents of the buoyancy compensator if the depth varies.

It will remain submerged in the fluid, but it will neither sink nor float, although a disturbance in either direction will cause it to drift away from its position.