Fluid Mechanics

The branch of physics that deals with the behavior of fluids, both in motion and at rest, is known as fluid mechanics. Fluids refer to both the gases and the liquids.

Buoyancy is the upward force experienced by an object that is partially or completely submerged in a stationary liquid or gas, resulting from the pressure exerted by the fluid.

Archimedes' principle states that When an object is partially or completely immersed in a stationary fluid (liquid or gas), it experiences an upward buoyant force that is equal to the weight of the fluid displaced by the object. Archimedes' principle is also referred to as the hydrostatic principle.

Example: If a piece of wood is floating in water, what percentage of it will be submerged? (Density of wood ρ = 0.5 × ${10}^3\mathrm{kg}{m}^{-3}$, Density of water ${\rho }_w={10}^3\mathrm{kg}{m}^{-3}$)

Solution: For a floating object,

            Weight of the object = Weight of the displaced water 

                        $V\rho g=V_{\mathrm{dw}}{\rho }_{w}g$

            ∴ The fraction of the volume of the wood that is submerged in water, 
                        $\frac{V}{V_{\mathrm{dw}}}=\frac{{\rho }_w}{\rho }$
        

When an object is immersed in a fluid, it experiences two main forces. One is its weight (W) that pulls it downward. Another is the buoyant force (F_b) that pushes it upward. Whether the object sinks or floats - is determined by the relative magnitudes of these forces. Three types of phenomenon can be observed:

• If Weight is less than Buoyant Force (W < F_b) than the object floats. It means that the density of the fluid is more than the density of the object.
• If Weight is equal to Buoyant Force (W = F_b) than the object neither floats nor sinks. It remains suspended in the liquid. That is because the density of the fluid is equal to the density of the object.
• If Weight is greater than Buoyant Force (W > F_b) than the object sinks. It means that the density of the fluid is less than the density of the object.