appears in the numerator in Eqs. ( . ) and ( . ).
Its dimensions are [ML – T – ]. The SI unit of pressure is N m – . It has been named as pascal (Pa) in honour of the French scientist Blaise Pascal ( - ) who carried out pioneering studies on fluid pressure. A common unit of pressure is the atmosphere (atm), i.e.
the pressure exerted by the atmosphere at sea level ( atm = . × Pa). Another quantity, that is indispensable in describing fluids, is the density ρ . For a fluid of mass m occupying volume V , ρ = m V ( .
) The dimensions of density are [ML – ]. Its SI unit is kg m – . It is a positive scalar quantity. A liquid is largely incompressible and its density is therefore, nearly constant at all pressures.
Gases, on the other hand exhibit a large variation in densities with pressure. The density of water at o C ( K) is . × kg m – . The relative density of a substance is the ratio of its density to the density of water at o C.
It is a dimensionless positive scalar quantity. For example the relative density of aluminium is . . Its density is .
× kg m – . The densities of some common fluids are displayed in Table . . Table .
Densities of some common fluids at STP* Fig. . (a) The force exerted by the liquid in the beaker on the submerged object or on the walls is normal (perpendicular) to the surface at all points. (b) An idealised device for measuring pressure.
* STP means standard temperature ( C) and atm pressure. Example . The two thigh bones (femurs), each of cross-sectional area10 cm support the upper part of a human body of mass kg. Estimate the average pressure sustained by the femurs.
Answer Total cross-sectional area of the femurs is A = × cm = × – m . The