This relatively short chapter deals with the pressure under the surface of an
incompressible fluid, which in practice means a liquid, which, compared with a gas, is
nearly, if not quite, incompressible.
It also deals with Archimedes’ principle and the
equilibrium of floating bodies.
The chapter is perhaps a little less demanding than some
of the other chapters, though it will assume a familiarity with the concepts of centroids
and radius of gyration, which are dealt with in chapters 1 and 2.
There is little to be said about density other than to define it as mass per unit volume.
However, this expression does not literally mean the mass of a cubic metre, for after all a
cubic metre is a large volume, and the density may well vary from point to point
throughout the volume.
Density is an intensive quantity in the thermodynamical sense,
and is defined at every
A more exact definition of density, for which I shall
usually use the symbol
The awful term “specific gravity” was formerly used, and is still regrettably often heard,
as either a synonym for density, or the dimensionless ratio of the density of a substance to
the density of water.
It should be avoided.
The only concession I shall make is that I
shall use the symbol
to mean the ratio of the density of a body to the density of a fluid
in which is may be immersed on or which it may be floating,
The density of water varies with temperature, but is approximately 1 g cm
or 1000 kg
Pressure is force per unit area, or, more precisely,
There is no particular direction associated with pressure – it acts in all directions – and it
is a scalar quantity.
The SI unit is the
(Pa), which is a pressure of one newton per
square metre (N m
Blaise Pascal (1623-1662) was a French mathematician and
philosopher who contributed greatly to the theory of conic sections and to hydrostatics.