Density and PressureDensity and Pressure

The density of an object is defined as its mass per unit volume.

Mass is measured directly using a digital balance. Volume is measured either using measurements taken with a ruler, digital calliper of micrometer (for regular solids), or by displacement (for irregular solids).

Pressure is defined as the normal force exerted per unit cross-sectional area.

Pressure exists in all fluids due to constant bombardment by molecules. The pressure exerted by a vertical column of liquid can be calculated by:

In this equation, h is the height of the liquid column, ρ is the density of the liquid, and g is the acceleration of free fall. The pressure in any fluid at any particular depth is the same in all directions.

Upthrust is the upward buoyancy force acting on an object when it is in a fluid. It is derived as follows:

force at top surface = hpga

force at bottom surface = (h + x) pga

resultant force upwards(upthrust) = (h + x)pga  – hpga = xpgA

Archimedes’ principle states that the Upthrust exerted on a body immersed in fluid (fully or partially) is equal to the weight of fluid displaced. An object will sink if its upthrust is less than its weight, and will float if its upthrust is greater than its weight.