6 Fluid Mechanics

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    FLUID MECHANICS

      It is the branch of science that deals with the behaviour of the fluids at rest as wellas motion. Fluid mechanics study is classified into the following types.

    Fluid statics - Study of Static Fluid• Fluid Kinematics - Study of Moving fluid with no pressure acting on it

    • Fluid dynamics - Study of moving fluid with pressure acting on it

    Viscosity :

      It is the property of a fluid with offers resistance to the movement of one layer of

    fluid over another adjacent layer of the fluid. Let there be two layers of fluid with a

    distance dy and velocities u and udu respectively. !he viscosity along with relativevelocity causes a shear stress between the fluid layers.

    " # du $ dy

    " % & du $ dy

      'here & % (oefficient of dynamic viscosity. Mathematically viscosity is the

    shear stress re)uired to produce unit rate of shear strain.

      For li)uids & decreases with increase in temperature due to cohesive forces predominates than molecular momentum transfer. *owever for gases & increase with

    increases with increasing temperature+ because molecular momentum predominates

    cohesive forces.

    Differences between solids and fluids:

    !he differences between the behaviors of solids and fluids under an applied force are as

    follows,

    i. For a solid+ the strain is a function of the applied stress+ providing that the elastic

    limit is not eceeded. For a fluid+ the rate of strain is proportional to the appliedstress.

    ii. !he strain in a solid is independent of the time over which the force is applied

    and+ if the elastic limit is not eceeded+ the deformation disappears when the force

    is removed. fluid continues to flow as long as the force is applied and will notrecover its original form when the force is removed.

    Differences between liuids and !ases:

      lthough li)uids and gases both share the common characteristics of fluids+ they

    have many distinctive characteristics of their own. li)uid is difficult to compress and+for many purposes+ may be regarded as incompressible. given mass of li)uid occupies a

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    fied volume+ irrespective of the si/e or shape of its container+ and a free surface is

    formed if the volume of the container is greater than that of the li)uid.

      gas is comparatively easy to compress. (hanges of volume with pressure arelarge+ cannot normally be neglected and are related to changes of temperature. given

    mass of gas has no fied volume and will epand continuously unless restrained by acontaining vessel. It will completely fill any vessel in which it is placed and+ therefore+

    does not form a free surface.

    Fluid Classifications :

      ll fluids can be classified as either 0ewtonian or non-0ewtonian. !he differencelies in the relationship between the fluid1s tangential stress 2friction force between the

    layers per unit surface3 and the shear rate or gradient 2difference in speed between the

    layers divided by the distance between them3. If the relationship is linear and the fluid has

    /ero stress at /ero velocity gradient then it is 0ewtonian. If not+ it is non-0ewtonian+ and

    is further classified into one of various subdivisions based on the curve of their stress vs.their velocity gradient.

      For non-0ewtonian fluids+ the velocity gradient is dependent on the viscosity4 that

    is+ the fluid has a higher or lower stress depending on its velocity. 5ased on these)ualities+ the fluid can be given its sub classification

    .

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    NE"#$NIAN

    Water Most salt solutions in water 

    Light suspensions of dyeKaolin (clay slurry)High-viscosity fuelsGasolineKeroseneMost motor oils(see below for motor oils with additives)Most mineral oils

    N$N%NE"#$NIAN

    6I7L8 9S7:8;9LS!I(+ 5I0

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    "ewage sludge$aper pulpGrease"oap$aint$rinter%s in&

    "tarchLate' solutionsMost emulsions

    DILA#AN#

    eldspar Micalayeach sand*uic&sand"tarch in water 

    #HI'$#($&IC % (HE$&EC#IC

    +n&sMost paintsarbo'ymethyl cellulose"ilica gelter  

    !hi'otropic - decreases viscosity over time,heopectic - increases viscosity over time

    Various non%Newtonian )e*a+iors:

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    Time-Independent behaviors:

    9roperties are independent of time under shear.

     Bingham-plastic, =esist a small shear stress but flow easily under larger shear stresses.

    e.g. tooth-paste+ jellies+ and some slurries.

     Pseudo-plastic, Most non-0ewtonian fluids fall into this group. >iscosity decreases withincreasing velocity gradient. e.g. polymer solutions+ blood. 9seudoplastic fluids are also

    called as Shear thinning fluids. t low shear rates2du$dy3 the shear thinning fluid is more

    viscous than the 0ewtonian fluid+ and at high shear rates it is less viscous.  

     Dilatant fluids, >iscosity increases with increasing velocity gradient. !hey are

    uncommon+ but suspensions of starch and sand behave in this way. 8ilatant fluids are

    also called as shear thic?ening fluids.

    Time dependent behaviors,

    !hose which are dependent upon duration of shear.

    Thixotropic fluids, for which the dynamic viscosity decreases with the time for which

    shearing forces are applied. e.g. thiotropic jelly paints.

     Rheopectic fluids, 8ynamic viscosity increases with the time for which shearing forces

    are applied. e.g. gypsum suspension in water.

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    Visco-elastic fluids, Some fluids have elastic properties+ which allow them to spring bac?

    when a shear force is released. e.g. egg white.

    #y,es of Fluid :

    Ideal fluid , Incompressible and where & % @.

    =eal fluid , If & A @ then it is called as real fluid.

    Ideal plastic fluid , Shear stress is more than yield value and proportional to velocity

    gradient.

    Isot*er-al &rocess : 

    (hanges in density ta?es place at constant temperature. 9 $ B % constant.

    Adiabatic ,rocess : 

    (hanges in density occurs without any heat transfer to and from the gas in theabsence of friction.

    Surface #ension : 

    It is the tensile force acting on the surface of a li)uid in contact with a gas or on

    the surface between two immiscible li)uids+ such that the contact surface behaves li?e amembrane under tension. It is denoted by C. It is the magnitude of force per unit

    distance. SI unit % 0 $ m.

      Surface tension of li)uid droplet C % pd $ D

    Surface tension of hollow bubble C % pd $ E

    Surface tension of a li)uid jet C % pd $

    Ca,illarity :

      It is the phenomenon of rise or fall of a li)uid in a capillary tube relative to the

    adjacent general level of li)uid+ when the tube is held vertically in the li)uid. =ise in

    li)uid level is called as capillary rise and fall in li)uid level is called as capillarydepression. 2 First figure shows capillarity rise and second figure shows capillarity

    depression 3 Its value is epressed in (m or mm. Its value is dependent upon

    • Surface tension+

    • 8iameter of pipe and

    • 'eight density of li)uid.

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      (apillary rise % h% DC (osG $ wd.

      G for glass and water % @ and hence the above epression becomes h % DC $ wd.

    &ascal.s Law :

      9ressure at a point in static fluid is e)ual in all directions.

    Hydrostatic Law :

      !he rate of increase in pressure in vertically downward direction must be e)ual to

    specific weight at that point.

      w % 9 $ /

      'here+

      / % *eight of fluid element from the fluid surface 2 9ressure head 3

      p % 9ressure above the atmospheric pressure.

    &ressure -ana!e-ent syste-s :

      If measurement is made above complete vacuum then it is called as absolute

     pressure. If the pressure is measured above atmospheric pressure than it is called as

    gauge pressure. !he atmospheric pressure at sea level at Ho is [email protected] K0 $ m. !here aretwo types of pressure measuring devices. !hey are manometer and mechanical gauges.

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     Manometer :  !hese are devices that are used for the measure of pressure at a point in

    fluid by balancing a column of the fluid by same or another column of fluid. !here are

    two types of manometers. !hey are simple manometers and differential manometers.

    imple Manometer :  It is a glass tube where one end is connected to a point where

     pressure is to be measured and the other end remains open in the atmosphere. !here areJ types of simple manometers. !hey are

    H. 9ie/ometer+. : - !ube manometer and

    J. Single column manometer.

    ! - Tube manometer : It contains a u tube. ;ne end of which is connected to a point

    where pressure is to be measured and the other end open to atmosphere. !he : - !ube

    contains mercury. !here are two types of manometer. !hey are

    H. Single column manometer 2 In this+ there are further vertical single column

    manometer and inclined single column manometer 3

    . 8ifferential manometer , !hese are devised used to measure the pressuredifferent between two points in a pipe or between two different pipes. It

    contains a : tube with a heavier li)uid. 2 !here are types. !hey are

    differential : - tube manometer and inverted : - tube manometer. 3

     Mechanical gauges : 

    !hese are device that are useful for measuring the pressure by balancing the fluid

    column by spring or dead weight.

    )uoyancy : 

    'hen a body is immersed in a fluid a upward force is eerted by the fluid on the

     body. !his upward force is e)ual to the weight of fluid displaced by the body.

    "enter of buo#anc# :

      It is the point through which the force of buoyancy acts on the body. 5uoyant

    force is a vertical force and is e)ual to the weight of the fluid displaced. *ence center of

     buoyancy % center of gravity of fluid displaced.

    Meta centre : It is the point about which a body starts oscillating when the body is tilted by a small angle.

    /ine-atics of flow :

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      !here are two methods to describe the fluid motion. !hey are lagrangian method

    and 7uler method. In lagrangian method a fluid particle is followed during its motion

    and its velocity+ acceleration and density are described.

      5ut in 7ulerian method the velocity+ acceleration and density are described at a

     point in flow field. !his is most commonly used.

    #y,es of fluid flows :

    tead# $lo% : is defined as the type of flow in which the fluid characteristics li?e

    velocity+ pressure and density at any point does not change with time.

    !nstead# flo% : is defined as the type of flow in which the fluid characteristics li?e

    velocity+ pressure and density at any point changes with time.

    !niform motion : is defined as the type of flow in which the velocity at any given time

    does not change with respect to space.

     &on-!niform motion : is defined as the type of flow in which the velocity changes withrespect to space.

     'aminar flo% : is the one in which the fluid particles move in well defined paths+ with

    one layer of fluid moving over another layer of fluid smoothly. Streamlines are straight

    and parallel. !his is also called as viscous flow.

    Turbulent $lo% : is the one in which the fluid move in ig/ag manner randomly. 7ddy

    formation ta?es place and thus there is a loss of energy.

    "ompressible $lo% : *ere the density of fluid changes from point to point.

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     Incompressible $lo% :!he density is constant. !hus gas is compressible fluid+ but li)uids

    are incompressible fluids.

     Rotational $lo% : In this the fluid particles when traveling in a stream line+ rotate abouttheir ais.

    Disc*ar!e :

      It is defined as the )uantity of fluid flowing per second through a section of pipe

    or channel.

    For incompressible fluids discharge % >olume $ second % Lit $ sec.

      For compressible fluid discharge % 'eight $ second % 0 $ s.

    Continuity Euation :

      It is based on the principle of conservation of mass. For a fluid flowing through a

     pipe+ at any cross section+ the )uantity of fluid flowing per second is constant.

    BH H>H % B>

    Venturimeter : It is a device used to measure the rate of flow of fluid in a pipe

    (rifice meter : It is a device used for the measurement of rate of flow of a fluid through a pipe. (heaper than the >enturimeter.

     Pitot)s Tube : is a device used to measure the velocity of flow at any point in a pipe orchannel. 'hen a velocity of a fluid is made /ero by bringing it to rest+ the ?inetic energy

    is converted to pressure energy and hence pressure is increased.

    Di-ensional Analysis :

      It is a mathematical techni)ue used in research wor?s and for conducting model

    test. It deals with the dimension of various physical )uantities involved in the

     phenomenon.

    )oundary Layer Flow :

      'hen a real fluid passes through the boundary+ it adheres to it. *ence the velocity

    of fluid near the boundary will be same as that of the boundary. If the boundary is

    stationery then the velocity of fluid near the boundary is /ero. 5ut for away from the

     boundary there is a high velocity and hence a velocity gradient eists.

      !he increase in velocity from /ero to free stream velocity is normal to the

     boundary. !his variation ta?es place in a very small region near the boundary. !his is

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    called as boundary layer. In the boundary layer region+ the fluid eerts a shear stress on

    the wall e)ual to

    " % & du $ dy

      5ut however outside the boundary layer velocity > % : and du $ dy % @ and henceshear stress % @.

    Forces actin! on a body:

      force eerted by the fluid on the body. !he total force Fr 2 resultant force 3 acts

    in a direction normal to the surface of the body.

     Drag : !his is the component of resultant force+ in the direction of motion. !his force iseerted by the fluid in the direction of motion.

     'ift : !his is the component of resultant force which is eerted by the fluid on the bodynormal to the direction of motion. Lift occurs only when the body is inclined at an angle

    to the direction of fluid flow.

    Hydraulic Mac*ines :

       *re those %hich convert fluid energ# into mechanical energ# or vice versa+

    Turbines :

      !urbines convert *ydraulic energy to mechanical energy. turbine is a device

    which converts the enthalpy and ?inetic energy of a moving fluid into some form ofmechanical wor?. basic turbine consists of a rotor or series of rotors. !hese rotors are

    mainly composed of fins connected to a shaft. 'hen a fluid flows through the fins+ the

    angle of the fins causes the rotor or rotors spin+ which causes the shaft to rotate. !hetor)ue in the shaft is then able to do some form of mechanical wor?+ such as rotate a

    compressor or turn a generator which produces current. n important application is the

    steam power plant which utili/es steam pressure to rotate a generator and produce

    electricity. s the fluid passes through the turbine+ it loses some of its velocity+ pressure+and temperature.

    !here are three types of turbines. !hey are 9elton+ Francis and Kaplan turbines.

    !urbines are classified as

    • Impulse turbine , *ere the water at the inlet of turbine contains only ?inetic

    energy.

    • =eaction turbine ,If the water at the inlet posses both ?inetic energy and

     pressure energy then it is called as reaction turbine.

    • !angential flow. !he water flows tangential to the runner.

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    • =adial flow , If the water flows in the radial direction through runner then it is

    called as radial flow. Further they are classified into Inward radial and outward

    radial.

    • ial flow , !he water flows in a direction parallel to the ais of rotation of

    runner.

    • Mied flow , If the water enters racially+ but leaves in a direction parallel to the

    ais of rotation of runner+ then it is called as mied flow turbine.

    Draft #ube :

      !he pressure at eit in the reaction turbine is less than atmospheric pressure.*ence a pipe of gradually increasing area is used to carry the discharge from turbine

    outlet to tail race.

    Unit 0uantities in turbines:

      In order to compare the performance of different turbines which operate withdifferent speeds+ blade angles the results are obtained in terms of )uantities which is

    obtained when the head of the turbine is made unity. :nit speed and unit discharge are

    two such )uantities. :nit speed is the speed of the turbine at unit head. and :nitdischarge is the discharge is the discharge of turbine at unit head.

    &u-,s :

      (onvert mechanical energy to *ydraulic energy. pump is a device used to raise+

    transfer+ or compress li)uids and gases. 'ater is a typical fluid used by pumps inapplications such as irrigation and cooling+ among others. nother very typical use of a pump is to force gas into a combustion chamber such as in a jet engine+ where it is termed

    a compressor. Multitudes of uses have been discovered for pumps involving li)uids

    varying from blood to sludge. lthough a pump can be used with almost any li)uid+certain attributes of the wor?ing fluid must be considered when designing a pump. For

    eample+ if the pump must displace an acidic fluid+ the pump must be composed of

    materials which will not react with the acid.

      In a pump system+ there must be some form of wor? done on the pump to ma?e it

    operate. In most cases+ this would be a motor which would drive either a piston or a type

    of rotor. !he pump then does wor? on the fluid passing through it+ and this wor? istranslated into total energy within the fluid. Following are the different types of pumps.

    Centrifu!al &u-,s :

      !he hydraulic energy is in the form of pressure energy. If the mechanical energy is

    converted to pressure energy by means of centrifugal force then that hydraulic machine iscalled as centrifugal pump.

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     Principle :

      !he centrifugal pump wor?s in the principle of forced vorte flow. ccording to

    which when a li)uid is rotated by a eternal tongue+ there is arise in pressure head. !hisrise in pressure head at any point in the rotating li)uid is proportional to the s)uare of

    tangential velocity of the li)uid at that point. t the outlet of the impeller+ the pressure ismore and hence the rise in pressure head is also more. !he li)uid will be discharged at

    the outlet at a high pressure. !his high pressure will be sufficient to lift the li)uid to avery great heights.

     Multistage "entrifugal Pumps :

      If the centrifugal pump contains two or more impellers then it is multistage pump.

    !hey may be mounted on same shafts or different shafts. !his arrangement is done toobtain

    *igh head or

    • 8ischarge huge )uantity of water.

      !o obtain huge )uantity of water impellers are connect in series 2 In same shaft3.

    If the discharge is re)uired is high the impellers are connected in parallel 2 different shafts3

    (eci,rocatin! &u-, :

      If the mechanical energy is converted into hydraulic energy by suc?ing a li)uid

    into a cylinder in which a piston reciprocates and eerts a thrust on the li)uid andincrease the hydraulic energy is called the reciprocating pump. Following are parts inreciprocating pumps.

    • Suction 9ipe+

    • >alve

    • 8elivery pipe and valve+

    •  piston+ connecting rod and cran?.

      !he piston moves bac? with the cran? and connecting rod attachment. !he cran?rotates by electric motor.  Both the valves are one %a# valves or &on return valves,allo%ing the %ater to flo% onl# in one direction+

      'hen the piston moves from left to right vacuum is created in cylinder. 5ut the

    li)uid is at atmospheric pressure. *ence because of this pressure drop+ the li)uid isforced through the suction valve into cylinder. 'hen it moves from right to left the

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     pressure in cylinder is above atmospheric suction valve closes and delivery valve opens

    and li)uid is forced into delivery pipe.

    Lastly updated on +