chest a large, light but strong wooden plank is
placed first, is saved from this accident. Such
everyday experiences convince us that both the
force and its coverage area are important. Smaller
the area on which the force acts, greater is the
impact. This impact is known as pressure.
When an object is submerged in a fluid at
rest, the fluid exerts a force on its surface. This
force is always normal to the object’s surface.
This is so because if there were a component of
for
ce parallel to the surface, the object will also
exert a force on the fluid parallel to it; as a
consequence of Newton’s third law. This force
will cause the fluid to flow parallel to the surface.
Since the fluid is at rest, this cannot happen.
Hence, the force exerted by the fluid at rest has
to be perpendicular to the surface in contact
with it. This is shown in Fig.10.1(a).
The normal force exerted by the fluid at a point
may be measured. An idealised form of one such
pressure-measuring device is shown in Fig.
10.1(b). It consists of an evacuated chamber with
a spring that is calibrated to measure the force
acting on the piston. This device is placed at a
point inside the fluid. The inward force exerted
by the fluid on the piston is balanced by the
outward spring force and is thereby measured.
If F is the magnitude of this normal force on the
piston of area A then the average pressure P
av
is defined as the normal force acting per unit
area.
(10.1)
In principle, the piston area can be made
arbitrarily small. The pressure is then defined
in a limiting sense as
P =
(10.2)
Pressure is a scalar quantity. We remind the
reader that it is the component of the force
normal to the area under consideration and not
the (vector) force that appears in the numerator
in Eqs. (10.1) and (10.2). Its dimensions are
[ML
–1
T
–2
]. The SI unit of pressure is N m
–2
. It has
been named as pascal (Pa) in honour of the
French scientist Blaise Pascal (1623-1662) 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 (1 atm = 1.013 × 10
5
Pa).
Another quantity, that is indispensable in
describing fluids, is the density
ρ
. For a fluid of
mass m occupying volume V,
(10.3)
The dimensions of density are [ML
–3
]. Its SI
unit is kg m
–3
. 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 4
o
C (277 K) is
1.0 × 10
3
kg m
–3
. The relative density of a
substance is the ratio of its density to the
density of water at 4
o
C. It is a dimensionless
positive scalar quantity. For example the relative
density of aluminium is 2.7. Its density is
2.7 × 10
3
kg m
–3
.
The densities of some common
fluids are displayed in Table 10.1.
Table 10.1 Densities of some common fluids
at STP*
(a) (b)
Fig. 10.1 (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 (0
0
C) and 1 atm pressure.
MECHANICAL PROPERTIES OF FLUIDS 251