2.3 Buoyancy force (upthrust due to pressure difference)

photo courtesy:www.zastavki.com

Have you been on a boat? Have you seen an objects floating on the water? Have you floated on the water? If yes, then you know what a buoyant force is. Buoyancy force is basically an upward force exerted by a liquid due to the difference in pressure. The buoyancy force exerted on a body can be calculated easily, since the internal pressure of the fluid is known.

This section is only to make you understand a concepts on bouyant force and its origination. To begin watch this easy to understand video first,

 

The expression for the static fluid is given by the following expression,
 $$P=\rho g h$$ 
where, $\rho$=density of the fluid, $g=$gravitational acceleration, $h=$ height of the coloumn
           
From the expression we know that pressure increases with depth as a result of the weight of the overlying fluid. The pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. This pressure difference results in a net upwards force on the object.

Archimedes principle: "A law states that a body totally or partially immersed in a fluid is subject to an upward force equal in magnitude to the weight of fluid it displaces." The magnitude of that force exerted is proportional to that pressure difference, and is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. the displaced fluid.

This figure gives a perfect illustration of the idea above.

Can we derive an archimedes principle? Yes, we can. Here's a short easy to understand video of the derivation.

  Thus, Bouyancy force is an upthrust of the liquid due to pressure difference and to understand the magnitude of this upthrust we must understand the 'Archimedes principle'.