BUOYANCY AND ARCHIMEDES PRINCIPLE - An object submerged in a fluid, experiences greater pressure at the bottom of the fluid than at the top. This difference in pressure results in a net force that tends to accelerate an object upwards. The magnitude of that force is proportional to the difference in the pressure between the top and the bottom of the column, and is also equivalent to the weight of the fluid that would otherwise occupy the column, i.e. the displaced fluid. It is for that reason that an object whose density is greater than that of the fluid that it is submerged in will sink. Archimedes' principle allows for the experimental determination of density by providing an easy and accurate method for determining the volume of an irregularly shaped object.

.....................................................................

Buoyancy and Archimedes Principle

 

WHAT IS BUOYANCY?

Buoyancy is a force exerted by a liquid or gas that opposes an object's weight.

Buoyancy can also be stated as the weight of displaced fluid. Pressure in a fluid increases with depth as a result of the weight of the overlying fluid.

Thus an object submerged in a fluid, experiences greater pressure at the bottom of the fluid than at the top.

This difference in pressure results in a net force that tends to accelerate an object upwards.

The magnitude of that force is proportional to the difference in the pressure between the top and the bottom of the column, and is also equivalent to the weight of the fluid that would otherwise occupy the column, i.e. the displaced fluid.

It is for that reason that an object whose density is greater than that of the fluid that it is submerged in will sink.

Archimedes' principle allows for the experimental determination of density by providing an easy and accurate method for determining the volume of an irregularly shaped object.

Archimedes' principle is named after Archimedes of Syracuse, who first discovered this law in 212 B.C.

Archimedes' principle may be stated thus in terms of forces:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

For objects, floating and sunken, and in gases as well as liquids, Archimedes' principle may be stated in terms of forces:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object, with the clarifications that for a sunken object the volume of displaced fluid is the volume of the object, and for a floating object on a liquid, the weight of the displaced liquid is the weight of the object.

Archimedes' principle indicates that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.

Notice that the acting forces increase with the depth of the fluid.

The resultant of all forces upward is called buoyancy and is equal to the weight of the displaced fluid.

Archimedes principle allows the buoyancy of an object partially or wholly immersed in a liquid to be calculated.

The downward force on the object is simply its weight. The upward, or buoyant, force on the object is that stated by Archimedes' principle, above.

Thus the net upward force on the object is the difference between the buoyant force and its weight.

If this net force is positive, the object floats; if negative, the object sinks; and if zero, the object is neutrally buoyant - that is, it remains in place without either rising or sinking.

In simple words Archimedes principle states that when a body is partially or completely immersed in a fluid, it experiences an apparent loss in weight which is equal to the weight of the fluid displaced by the immersed part of the body.

Note: Archimedes' principle does not consider the surface tension (capillarity) acting on the body but this additional force modifies only the amount of fluid displaced, so the principle that Buoyancy = weight of displaced fluid remains valid.

Consider a cube immersed in a fluid, with its sides parallel to the direction of gravity. Only the forces on the top and bottom faces of the cube will contribute to buoyancy.

The pressure difference between the bottom and the top face is directly proportional to the height (difference in depth).

Multiplying the pressure difference by the area of a face gives the net force on the cube - the buoyancy, or the weight of the fluid displaced.

FORMULAS

For a fully submerged object, Archimedes' principle can be formulated as follows:

apparent immersed weight = weight of object - weight of displaced fluid

density of object/density of fluid = weight/(weight of displaced fluid)

density of object/density of fluid =weight/(weight - apparent immersed weight)

The "buoyancy force" on a submerged body is directed in the opposite direction to gravity and is equal in magnitude to: 

(density of fluid)(Volume of displace fluid)(acceleration)

When will an object float or balloon rise?

A object will float in a fluid if the density of that object is less than the density of the fluid.

Example: If you drop wood into water, buoyancy will keep it afloat. Wood is less dense than water.

Hot air balloons rise into the air because the density of the air (warmer air) inside the balloon is less dense than the air outside the balloon (cooler air).

The balloon and the basket displaces a fluid that is heavier than the balloon and the basket, so it has a buoyant force acting on the system. Balloons tend to fly better in the morning, when the surrounding air is cool.

SAMPLE PROBLEM

A steel block with a density of 7800 kg/m3 is suspended from a string in a beaker of
water so that the block is completely submerged but not resting on the bottom. The block is a
cube with sides of 3 cm (0.03 m).

Buoyant force = weight of displaced water
= mass of water * acceleration due to gravity
= density of water * volume of cube * g
= 1x10³ kg/m ³ * 27*10-6 m3 9.8 m/s2 = 2.65 *10-1 N = 0.265 N

weight of block = mass g
W= mg = 2.106 x 10-1 kg x 9.8 m/s2 = 2.106x9.8 x 10-1 kg*m/s2 = 20.64 x 10-1 N
= 2.064 N kg*m/s2 = N (Newton)

Archimedes of Syracuse

ABOUT ARCHIMEDES --Archimedes was the son of an astronomer. He had traveled to Alexandria, Egypt, a place of great learning, where he studied the works of some other mathematicians, like Euclid and Conon.

Archimedes helped his friend King Hiero II by creating machines for the king's army. The pulley was one of these inventions, but Archimedes thought the study of mathematics was the most important thing he could do.

Archimedes wrote some books about Mathematics, including On Floating Bodies. 

Archimedes died during the Siege of Syracuse when he was killed by a Roman soldier despite orders that he should not be harmed.

https://www.edinformatics.com/math_science/archimedes_principle.htm