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West Bengal University of technology
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B.Tech
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NOTES OF LESSON
MECHANICS OF FLUIDS
1

Introduction to Fluid Mechanics
Definition of a fluid
A fluid is defined as a substance that deforms continuously under the action of a shear stress,
however small magnitude present. It means that a fluid deforms under very small shear stress,
but a solid may not deform under that magnitude of the shear stress.
Fig.L-1.1a: Deformation of solid under a constant shear force
Fig.L-1.1b: Deformation of fluid under a constant shear force
By contrast a solid deforms when a constant shear stress is applied, but its deformation does not
continue with increasing time. In Fig.L1.1, deformation pattern of a solid and a fluid under the
action of constant shear force is illustrated. We explain in detail here deformation behaviour of a
solid and a fluid under the action of a shear force.
In Fig.L1.1, a shear force F is applied to the upper plate to which the solid has been bonded, a
shear stress resulted by the force equals to,
Where A is the contact area of the upper plate. We know that in the case of the solid block the
deformation is proportional to the shear stress t provided the elastic limit of the solid material is
not exceeded.
When a fluid is placed between the plates, the deformation of the fluid element is illustrated in
Fig.L1.3. We can observe the fact that the deformation of the fluid element continues to increase
as long as the force is applied. The fluid particles in direct contact with the plates move with the
same speed of the plates. This can be interpreted that there is no slip at the boundary. This fluid
behavior has been verified in numerous experiments with various kinds
of fluid and boundary material.
In short, a fluid continues in motion under the application of a shear stress and can not sustain
any shear stress when at rest.
2

Fluid as a continuum
In the definition of the fluid the molecular structure of the fluid was not mentioned. As we now the
fluids are composed of molecules in constant motions. For a liquid, molecules are closely spaced
compared with that of a gas. In most engineering applications the average or macroscopic effects
of a large number of molecules is considered. We thus do not concern about the behavior of
individual molecules. The fluid is treated as an infinitely divisible substance, a continuum at which
the properties of the fluid are considered as a continuous (smooth) function of the space
variables and time.
To illustrate the concept of fluid as a continuum consider fluid density as a fluid property at a
small region.(Fig.L1.2 (a)). Density is defined as mass of the fluid molecules per unit volume.
Thus the mean density within the small region C could be equal to mass of fluid molecules per
unit volume. When the small region C occupies space which is larger than the cube of molecular
spacing, the number of the molecules will remain constant. This is the limiting volume above
which th
fect of molecular variations on fluid properties is negligible. A plot of the mean density
versus the size of unit volume is illustrated in Fig.L1.2 (b).
for all liquids and for gases at atmospheric
Note that the limiting volume
is about
temperature. Within the given limiting value, air at the standard condition has approximately
molecules. It justifies in defining a nearly constant density in a region which is larger than
the limiting volume.
In conclusion, since most of the engineering problems deal with fluids at a dimension which is
larger than the limiting volume, the assumption of fluid as a continuum is valid. For example the
fluid density is defined as a function of space (for Cartesian coordinate system, x, y, and z) and
. This simplification helps to use the differential calculus for solving fluid
time (t ) by
problems
3

Properties of fluid
Some of the basic properties of fluids are discussed belowDensity : As we stated earlier the density of a substance is its mass per unit volume. In fluid
mechanic it is expressed in three different ways1. Mass density ρ is the mass of the fluid per unit volume (given by Eq.L1.1)
2. Specific weight, w: - As we express a mass M has a weight W=Mg . The specific weight
of the fluid can be defined similarly as its weight per unit volume.
3. Relative density (Specific gravity), S :Specific gravity is the ratio of fluid density (specific weight) to the fluid density (specific
weight) of a standard reference fluid. For liquids water a
is considered as standard
fluid.
Similarly for gases air at specific temperature and pressure is considered as a standard
reference fluid.
Units: pure number having no units
Dimensio
Typical vales : - Mercury- 13.6
Water-1
4

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