Archimedes' Principle - Formula

Formula

The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (if the surrounding fluid is of uniform density)the weight of the object in water is less than the weight of object in air, Because of the force acting on it which is called as upthrust. In simple terms, the principle states that the buoyant force on an object is equal to the weight of the fluid displaced by the object, or the density of the fluid multiplied by the submerged volume times the gravitational constant, g. Thus, among completely submerged objects with equal masses, objects with greater volume have greater buoyancy.

Suppose a rock's weight is measured as 10 newtons when suspended by a string in a vacuum with gravity acting upon it. Suppose that when the rock is lowered into water, it displaces water of weight 3 newtons. The force it then exerts on the string from which it hangs would be 10 newtons minus the 3 newtons of buoyant force: 10 − 3 = 7 newtons. Buoyancy reduces the apparent weight of objects that have sunk completely to the sea floor. It is generally easier to lift an object up through the water than it is to pull it out of the water.

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. The density of the immersed object relative to the density of the fluid can easily be calculated without measuring any volumes:

(This formula is used for example in describing the measuring principle of a dasymeter and of hydrostatic weighing.)

Example: If you drop wood into water, buoyancy will keep it afloat.

Example: A helium balloon in a moving car. In increasing speed or driving a curve, the air moves in the opposite direction of the car's acceleration. The balloon however, is pushed due to buoyancy "out of the way" by the air, and will actually drift in the same direction as the car's acceleration. When an object is immersed in a liquid the liquid exerts an upward force which is known as buoyant force and it is proportional to the weight of displaced liquid. The sum force acting on the object, then, is proportional to the difference between the weight of the object ('down' force) and the weight of displaced liquid ('up' force), hence equilibrium buoyancy is achieved when these two weights (and thus forces) are equal.