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Module1, 2, 3

Week 1

Books to follow

1. F. M. White, Fluid Mechanics2. Fm by kodandaraman3. Fm by rk bansal4. Fm by Robert w fox

Fluid mechanics

Introduction: Dimensions and units:

o Basic units M, L, t, To Unit systems ( SI, metric

systems etc)

Fluid propertieso Density or mass densityo Specific weight or weight

density

o Specific gravity Viscosity

Newtons law of viscosityo Type of fluids

Compressibility and bulk modulus Surface tension Capillarity Concept of continuum

Note: All the data taken from the above text books with

some additional explanation.

The given data is only for initiation and it acts as a guide

it is better to go through the text books.

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Dimensions and

Units:

Properties of fluid:

Density: ()

A dimension is the measure by which a physical variable isexpressed quantitatively.Dimension is a powerful concept about which a splendid toolcalled dimensional analysis has been developed

In general there are only four basic dimensions from which the

other dimensions are derived. They are

Length {L}

Mass {M}

Time {t}

Temperature {T}

Every other dimension such as velocity acceleration, density etc,

are represented with these four basic dimensions

For example units of velocity = meter/second

= Length/time=L/T=>LT

-1

Acceleration = m/s2=L/T

2=LT

-2

Fluid property is defined as a characteristic of the material

structure of the fluid. All the fluid properties are variables rather

than constants and assumed to be functions of space and time.

The ration of mass of the fluid to its volume is called density

OrThe concentration of mass in particular volume

Density = mass of fluid/volume of fluidDensities of different fluids which are useful in our daily life

Fluid Density

kg/m3

Air 1.204

Petrol 737

Kerosene 817

Diesel 820-950

Coconut oil 924

Castor oil 956Water 1000

Milk 1020-1050

Mercury 13600

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Weight density or

specific weight: ()

Specific gravity or

relative density:SG

The specific weight of a fluid is the ratio of weight of the fluid tothe volume of the fluid

= weight/volume= mg/v

= g since (m/v= )

Specific gravity, denoted by SG, is the ratio of the density of thefluid to the density of standard fluid.

For liquids water is the standard fluid andFor gases air is the standard fluid.

For example:Specific gravity of mercury = density of mercury/density of water

= 13600/1000=13.6

Specific gravity of milk = density of milk/density of water

=1020/1000=1.2

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Viscosity (or)

Dynamic viscosity: Viscosity is a property of the fluid which resists the fluid to flow

Or

The resistance offered to the flow of a fluid is called viscosity

Or

The viscosity of a fluid is a measure of its resistance to flow.

Viscosity is a measure of the importance of friction in fluid flow.

The higher the value of the viscosity then the greater is theresistance. So, a substance with a low viscosity will flow morefreely than another substance with a higher viscosity.

Velocity

profile

Fig:1

Let us assume a fluid is flowing over a fixed plate with a velocityu. The surface of the fluid is present at a distance of y4 from the

fixed plate. The velocity of the fluid particles flowing near theplate that is at yo is zero and the velocity of the fluid particles

flowing at the surface that is at y4 is umax as shown in figure 1.

The fluid particles at the free surface will move with a velocity offree stream velocity and the fluid particles at the plate moves withzero velocity. The velocity variation of the fluid particles from the

plate to the surface is shown in the figure.The top row that is row 4 molecules exert a shear stress on row 3molcules and creates velocity gradient du/dy.The viscosity of the fluid in this case can be expressed as

Viscosity = shear stress/velocity gradient

that is =/(du/dy)In general the word viscosity means dynamic viscosity otherwise

it will mention as kinematic viscosity if nothing is specified thenwe have to assume it as dynamic viscosityThe SI unit for dynamic viscosity is pascal second [Pa s]

1 Pa s = 1 newton second/square metre

Another unit often used is the 'poise' where10 poise = 1 Pa s

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Kinematic Viscosity:

Newtons law of

viscosity:

Types of fluids:

Fluidity:

Compressibility and bulk

modulus:

Kinematic viscosity of a substance is a measure of its dynamicviscosity per unity density of that substance.The SI unit is sq.metre/second but, as that is such a large unit,many prefer the 'stoke' where

10,000 stokes = 1 sq.metre/secondor 1stoke=1cm2/s

Newtons law of viscosity states that the shear stress is directlyproportional to the rate of shear strain.

= (du/dy)Fluids which obey Newtons law are called Newtonian fluids and

which does not obey are called non-Newtonian fluids

Newtonian fluidsNon-Newtonian fluidsIdeal fluids

Real fluidsBinghamPseudoplastics

The measure of the fluidity of a substance is given by the

reciprocal of its dynamic viscosity.

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Surface Tension: The tension exerted between two fluid surfaces when they are incontact is called surface tension.

Air

water

picture a. Picture b.

In the above picture a. water is present in the beaker and air ispresent above the water surface a tensile membrane (thin layer) of

water forms between the two fluids as shown in the figure b.

Many of us would have seen the demonstration of a needle beingsupported on water surface without it being wetted. This is due tothe surface tension of water.

All liquids exhibit a free surface known as meniscus when incontact with vapour or gas. Liquid molecules exhibit cohesive

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Capillarity:

Continuum:

forces binding them with each other. The molecules below thesurface are generally free to move within the liquid and they moveat random. When they reach the surface they reach a dead end inthe sense that no molecules are present in great numbers above thesurface to attract or pull them out of the surface. So they stop andreturn back into the liquid. A thin layer of few atomic thicknessesat the surface formed by the cohesive bond between atoms slowsdown and sends back the molecules reaching the surface. Thiscohesive bond exhibits a tensile strength for the surface layer andthis is known as surface tension. Force is found necessary tostretch the surface.

Surface tension may also be defined as the work in Nm/m2 orN/m required to create unit surface of the liquid. The work isactually required for pulling up the molecules with lower energyfrom below, to form the surface.

Another definition for surface tension is the force required to keepunit length of the surface film in equilibrium (N/m). The

formation of bubbles, droplets and free jets are due to the surfacetension of the liquid.

The rise or fall of liquid surface when the fluid come into contact

with any other solid bodies.(refer the book rk bansal )

As gas molecules are far apart from each other and as there is

empty space between molecules doubt arises as to whether a gasvolume can be considered as a continuous matter like a solid forsituations similar to application of forces.Under normal pressure and temperature levels, gases are

considered as a continuum (i.e., as if no empty spaces existbetween atoms). The test for continuum is to measure propertieslike density by sampling at different locations and also reducingthe sampling volume to lowlevels. If the property is constant irrespective of the location andsize of sample volume, then the gas body can be considered as acontinuum for purposes of mechanics (application of force,consideration of acceleration, velocity etc.) and for the gas volumeto be considered as a single body or entity. This is a veryimportant test for the application of all laws of mechanics to a gasvolume as a whole. When the pressure is extremely low, and whenthere are only few molecules in a cubic metre of volume, then thelaws of mechanics should be applied to the molecules as entitiesand not to the gas body as a whole. In this text, only systemssatisfying continuum requirements are discussed. (from text bookkodandaraman)