Fundamental of Fluid Mechanics (2)

8/3/2019 Fundamental of Fluid Mechanics (2)

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Fundamentals of fluid

mechanics

M.Swapna



CONTENT



Definition

What is fluid

A fluid can be

defined as a

substance which

is capable of

flowing. It has no

definite shape of

its own but

confirms the to the

shape of the

containing vessel.Fluid further

classified as

liquids and

gaseous

liquid is a fluid, which posses adefinite volume, which varies

only slightly with temperature

and pressure. Liquids are

almost incompressible.

Gas is a fluid, which is

compressible and posses no

definite volume and expands until itvolume is equal to that of container.

Even a slight change in

temperature causes a significant

change in volume and pressure.



Characteristics of fluids

Fluids has no tensile strength.

Fluids can resist the compressive forces only when it kept in

container

When fluids subjected to a shearing force, a fluid deforms

continuously as long as this force is applied.

When the fluid at rest no shear force can exist.

As the fluid flows there exists shearing stresses between the

adjacent fluid layers.

The amount of shear stress depends on the rate of angular

deformation of the fluid element.

Gases can compress readily under the action of external force.



Basic Definitions



Mass density

Mass density of a fluid is the mass which it possesses per unit

volume.

= M / V ( Kg/m3).

With temperature Mass density

With Pressure Mass density



Specific Weight

Specific weight of a fluid is the weight it possesses per unit

volume.

= Mg / V

= g ( N/m3).

With temperature Specific weight

With Pressure Specific weight



Specific volume

Specific Volume of a fluid is the volume of fluid per unit weight.

v = V / mg (m3/ N) for liquids

= V / m (m3/ Kg) for gases

With temperature Specific Volume

With Pressure Specific volume



Specific gravity

Specific gravity is the ratio of specific weight of the fluid to the

specific weight of standard fluid

For liquids

specific gravity = specific weight of liquid

Specific weight of water

For gases

specific gravity = mass density of gas

mass density of air



Properties of fluids



Properties of fluids

ViscosityViscosity

The property of fluid by virtue of which it offers resistance to the

movement of one layer of fluid over an adjacent layer. This is primarly

due to cohesion and molecular momentum exchange between fluid

layers and as flow occurs these effects appear as shearing stresses

between the layers of the fluid.

Cohesion:

Cohesion means inter molecular attraction between the molecules of

same fluid.

Adhesion:

Adhesion means attraction between molecules of aliquid and the

molecules of solid boundary surface in contact with the liquid.



Viscosity of fluids

F ~ AV / Y

= F / A = µ dv /dy

V

Y

v

y

dy

dv

F

This equation called as Newton's equation of viscosity.

µ is called as coefficient of viscosity / dynamic viscosity /

viscosity



Viscosity of fluids

µ defined as the shear stress required to produce unit rate of angular

deformation.

µ = / (dv/dy) N.s/m2

With pressure: Viscosity of liquid / gas independent of the pressure.

With temperature:

In liquids

Viscosity temperature

In gases

Viscosity temperature.



Classification of fluids

(dv / dy)

Ideal Fluid Newtonian fluid Non Newtonian fluid

Plastics Thixotropic Elastic Solid



Kinematic Viscosity

Kinematic viscosity (Nu) defined as ratio of dynamic viscosity andmass density.

(nu) = µ / m2/s



Vapour Pressure

When the liquid is confirmed in a closed vessel, the ejected

vapour molecules gets accumulated in the space between the free

surface and top of the vessel.



Compressibility and Elasticity

All the fluids may be compressed by the application of external

force and when the external force is removed the compressed

volumes of fluids expand to their original volumes. Fluids can also

exerts characteristics like elastic fluid.

Compressibility of fluids quantitatively expressed as

inverse of bulk modulus of elasticity

Bulk modulus of elasticity k is a measure of the incremental

change in pressure (dp) which takes place when a volume of V of

the fluid is changed by an incremental amount of (dv)



Bulk modulus of elasticity

Bulk modulus K = - dp / (dv/V)

Example: A cylinder containing a fluid of volume V which is being

compressed by a piston, A piston moved so that volume V

decreased by V then the pressure will increase by (dp).

The magnitude of (dp) depends on the bulk modulus of

elasticity of the fluid.

Effect of Pressure and temperature

Pressure Bulk modulus

For liquids

For gasesTemperature



Surface tension

B

A

L The attractive forces causes the liquidsurface to contract toward the interior

until repulsive collisional forces from

the other molecules halt the

contraction at the point where the

surface area minimum

The amount of energy required

to create a surface per unit area

is called as surface tension and

denoted by

Surface tension can be defined as either energy per unit area or

force per unit length.

=F/A (N/m)



Properties of fluidsFactors effecting surface tension:

Directly depend on the molecular cohesive forces .

Temperature Surface tension

The property of the liquid surface film to exert tension is called

the surface tension. Denoted by .

= force required to main unit length of the film in equilibrium .

Units N/m



EXAMPLE 1 Floating a Needle on the Surface of Water

Surface tension

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Fundamental of Fluid Mechanics (2)