S K Mondal’s
Properties of Fluids
Theory at a Glance (for IES, GATE, PSU)
Definition of Fluid
A fluid is a substance which deforms continuously when subjected to external
Characteristics of Fluid
It has no definite shape of its own, but conforms to the shape of the containing
Even a small amount of shear force exerted on a fluid will cause it to undergo
a deformation which continues as long as the force continues to be applied.
It is interesting to note that a solid suffers strain when subjected to shear
forces whereas a fluid suffers Rate of Strain i.e. it flows under similar
Concept of Continuum
The concept of continuum is a kind of idealization of the continuous description of
matter where the properties of the matter are considered as continuous functions
of space variables. Although any matter is composed of several molecules, the
concept of continuum assumes a continuous distribution of mass within the matter
or system with no empty space, instead of the actual conglomeration of separate
Describing a fluid flow quantitatively makes it necessary to assume that flow
variables (pressure, velocity etc.) and fluid properties vary continuously from one
point to another. Mathematical descriptions of flow on this basis have proved to be reliable
and treatment of fluid medium as a continuum has firmly become established.
For example density at a point is normally defined as
Here Δ is the volume of the fluid element and m is the mass
If Δ is very large ρ is affected by the inhomogeneities in the fluid medium.
Considering another extreme if Δ is very small, random movement of atoms (or
molecules) would change their number at different times. In the continuum
approximation point density is defined at the smallest magnitude of Δ , before
statistical fluctuations become significant. This is called continuum limit and is
denoted by Δ c.
One of the factors considered important in determining the validity of continuum
model is molecular density. It is the distance between the molecules which is
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