CHAPTER 16
HYDROSTATICS
1.
Introduction
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.
2.
Density
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
point
.
A more exact definition of density, for which I shall
usually use the symbol
ρ,
is
.
0
V
m
Lim
V
δ
δ
=
ρ
→
δ
16.2.1
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
s
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
−
3
or 1000 kg
m
−
3
.
3.
Pressure
Pressure is force per unit area, or, more precisely,
.
0
A
F
Lim
P
A
δ
δ
=
→
δ
16.3.1
There is no particular direction associated with pressure – it acts in all directions – and it
is a scalar quantity.
The SI unit is the
pascal
(Pa), which is a pressure of one newton per
square metre (N m
−
2
).
Blaise Pascal (16231662) was a French mathematician and
philosopher who contributed greatly to the theory of conic sections and to hydrostatics.
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He showed that the barometric pressure decreases with height – hence the famous
examination question: “Explain how you would use a barometer to measure the height of
a tall building” – to which the most accurate answer is said to be: “I would drop it out of
the window and time how long it took to reach the ground.”
The CGS unit of pressure is dyne cm
−
2
, and 1 Pa = 10 dyne cm
−
2
.
Some other silly units for pressure are often seen, such as psi, bar, Torr or mm Hg, and
atm.
A psi or “pound per square inch” is all right for those who define a “pound” as a unit of
force (US usage) but is less so for those who define a pound as a unit of mass (UK
usage).
A psi is about 6894.76 Pa.
[The “British Engineering System”, as far as I know, is used exclusively in the U.S. and is not and never
has been used in Britain, where it would probably be unrecognized.
In the “British” Engineering System,
the pound is defined as a unit of force, whereas in Britain a pound is a unit of mass.]
A bar is 10
5
Pa or 100 kPa.
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 Fall '10
 monfered
 Buoyancy, Archimedes

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