Answer :
Answer: write this
Explanation:
The most fundamental approach for analysing the mechanical behaviour of a fluidic
system may be a ‘deterministic’ molecular approach in which the dynamics of individual molecules is investigated by writing their respective equations of motion.
While this is fundamentally appealing and may be suitable for certain cases, several
practical constraints also seem to be inevitable. In order to appreciate the underlying
consequences, consider the molar volume of a gas at normal temperature and pressure, which, by Avogadro’s hypothesis, contains 6.023 ¥ 1023 number of molecules.
To describe motion of each of these molecules, three translational velocity components (along three mutually perpendicular coordinate directions) and three rotational
components (along the same coordinate directions as above) need to be specified.
Therefore, one has to deal with 6 ¥ 6.023 ¥ 1023 number of equations of motion, even
for an elementary molar volume, which is an extremely demanding computational task
even today, in spite of the advent of high-speed supercomputers. Hence, from a
practical point of view, there must be certain approaches that can reduce the number
of variables to a figure that can be handled conveniently for practical computations.
In particular, there are two specific approaches that can be introduced in this
context. In one approach, we deal with ‘statistically averaged’ behaviour of many
molecules constituting the matter under investigation. This is exactly the approach
followed in kinetic theories of matter and statistical mechanics, which in general is
termed as the ‘microscopic’ point of view, since the primary focus of attention is on
the averaged behaviour of individual microscopic constituents of matter.
The second approach reduces the number of variables even further, by considering the gross effect of many molecules that can be captured by direct measuring
instruments and can be perceived by our senses. Such an approach is the so-called
‘macroscopic’ approach. For a clearer distinction between macroscopic and microscopic approaches, we can refer to a very simple example as follows: When we conceive the term ‘pressure’ of a gas (we will deal with this term more formally later) in the
microscopic point of view, it originates out of the rate of change of momentum of
molecules as a consequence of a collision. On the other hand, from a macroscopic
point of view, we describe the same quantity in terms of time-averaged force over a
given area, which can be measured by a pressure gauge.
Though the macroscopic approach provides us with a more practical method of
analysis, one should not presume that it can give the correct solution in all situations.
In order to assess the underlying implications, let us consider certain aggregations of
molecules, such as a set of widely spaced molecules for a gas and a set of closely
spaced molecules for a liquid. If we consider a very small elementary volume within
the medium, then numerous molecules may come into it or move out of it during some
