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Wednesday,2019 31, July BASIC FLUIDMECHANICS DEPARTMENTOF MECHANICAL NIT JAMSHEDPUR DR.SATISH KUMAR 1

Copyright 2013-2014 • • Basically a study of the: study of a Basically &gasses) the of – – and behavior Action pattern the and Physically science behavior fluid of laws at . of . the rest which behavior systems of governing resulting and is that deals motion on , of branch and ( fluids fluid with flow this . of

Copyright 2013-2014 Fluid shear tangential includes continuously is defined any stress, liquid is as as . applied starts a one or result . FLUID which deforming In of other under shearing continuously words, continuously action it as can . applied long flow This as 3

Copyright 2013-2014 constant deforming approachesand a neverwhereasangle, fluid a deforming at some fixed strain applied When aconstantforceshear is proportional strain In stresssolids, is proportional to matter how stress shear a of influence the A stressby deforming . A gas phase Fluid What fluid cansolid resist shear an applied : , but in fluids, stress is fluids, in , but A substanceA or liquid in the deforms continuouslyunder , a eventually solid a , s a Fluid?is a rate . small. small. to to of strain. . stops stops stops stops , no acts on an stressthatrubbershownthe is on .shear influencea shear of The between two parallel plates under the Deformationrubber blockplaceda of equal oppositebut the upper plate.the — 4

Copyright 2013-2014 establishhorizontala freesurface. develops liquid container istilted,a shear Whenwalls the are removed or a a stateof zero stress.shear Stress Z at rest. stressNormal surface componentforce a of on a acting Shear stress surfaceunit areaper componentforce a of on a acting erostress shear : F per unit areaunit per orce per unit area. : as the liquid moves liquid the as to re The normal stressThe normal i : T : he tangential The : A fluidat restisat normal . . n a fluid n a - and pressure is the only normal stress. normal only pressureand the is fluids at rest,the shear stressis zero the surfaceelement.of afluidFor The normal stress and shear stress at 5

Copyright 2013-2014 A forms it and is in, free a surface a in larger container a gravitationalin field. betweenmolecules. the volume remainsrelatively constant becauseof the strong cohesive forces a In containercannot form freea surface. cohesive forcesbetween them are very small.Unlike available space. This is because the gas are gas liquid expands until it encountersthe walls of the container , groups, of canmolecules move relativeto eachother, but the As a As result,a liquidtakes theof shape the container it entire availablespace. the expandsto fill ,and it doesnot form a gasa Unlike liquid, a , a gasa liquids, inan open widely spaced, and the the and widely spaced, andthe fills entire 6

Copyright 2013-2014 phase, and positions The arrangement atomsof indifferent ( phases: orderingnonexistent. is Gas: Liquid: throughout. Solid: Intermolecular bonds are strongest andweakest in in . In In are gasthe molecules farthe phase, from apart other, each molecular and The molecules cules canmoleculesrotate liquidsIn and translatefreely. in a solid, ( solid, a in (c ) individual molecules move molecules individualabout at ) random in gas the phase. b in a solid are solidin a arrangedin a pattern thatrepeated is ) groups) of movemolecules about eachother in the liquid a ) molecules aremolecules) at relativelyfixed 7

Copyright 2013-2014 M of individual moleculesof individual average the on behavior M engineering problems. direct easyand way to analyze moleculesand of individual not requirea knowledge of thebehavior Gas Gas condensation. Vapor abovetemperature.critical the Gas: acroscopic or icroscopic or individual gas molecules. individual On On a microscopic scale, pressure is wethe measure can macroscopic scale with a pressure a macroscopicwith scale and and The vapor a of The phase determinedbyinteraction the of : U vapor sually impliesthat the current phase is not far from a stateof statistical classical are often usedas synonymous words. . approach of largeof groups approach provides a pressure a on substance is customarily called a H : owever, : D B oes oes gage. ased ased gas gas when it is it when 8

Copyright 2013-2014 • • • fluid The The relative to one another. particles continuously change their positions Flowthat means the constituent fluid flow act tendency . is called of continuous fluidity Fluid Flow of continuous . deformation is called of

Copyright 2013-2014 ApplicationMechanics Areas Fluid of Artificial Heart. Artificial here isthe Penn State ElectricTotal Shown hearts. artificial of designthe extensively isused in 10

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Copyright 2013-2014 Fluids Fluids

Copyright 2013-2014 High speed rail-speed Aircraft Vehicles Surface ships Submarines

Copyright 2013-2014 Air pollution Air Environment River

Copyright 2013-2014 Blood pump Blood PhysiologyMedicine and Ventricular device assist

Copyright 2013-2014 Water sports Auto racing SportsRecreation & Cycling Surfing Offshore racing

Copyright 2013-2014 FacesMechanicsFluid of (C. 287-212BC) (1785-1836) Navier (1819-1903) (1642-1727) Stokes Newton (1646-1716) History (1842-1912) Reynolds Leibniz (1875-1953) (1667-1748) Bernoulli Prandtl (1886-1975) (1707-1783) Taylor Euler

Copyright 2013-2014 Wednesday,2019 31, July PROPERTIESOF FLUID 19

Copyright 2013-2014 The specific gravity (or relative ) can be defined in two ways: two defined in be relative can gravity density) (orThe specific Definition 2 Definition Definition 1 Definition Unit: dimensionless.Unit: SG : A ratio of the weight specific to of aliquid the : A ratio of the to density of aliquid the density of and pressure(20° (STP) standard at water weight ofspecific (20 (STP) pressure temperature standard and at water = SPECIFIC GRAVITY ° ρ C, 1 1 C, water ρ liquid atm @ STP ), or = γ water γ liquid C, 1 1 C, @ STP atm ),

Copyright 2013-2014 Solution: m of 0.917 A reservoir of oilhas aof mass 825kg. The reservoir has a volume gravity of the oil. the gravityof SG ρ γ 3 . Compute the the density,Compute . specific and weight, specific oil oil oil = = = = = volume volume weight mass ρ STP w ρ @ oil = = Example m ∀ mg ∀ = 1000 = 0 900 825 ρ . 917 g = 900 = 900 0.9 x 9 kg . 81 / = m 8829 3 N / m 3

Copyright 2013-2014 • • is also known as dynamic viscosity. asdynamic also known is viscosity water. such as viscosity than low a fluid with The highsyrupmoreslowlysuchdeforms viscosity as viscosity.its of indication an pours is a with Fluid shear stress. the fluid a same which with ease The under rates different at deform Different fluids energy loss. which then can to lead motion tofluid internal as seen be can viscosity other words, flow as aresult of intermolecular In cohesion. Viscosity, . . Water1.14x10 = Typical values: kg/m/s Units: µ , N.s/m is a measure of resistance resistance fluid to measure of a is 2 or kg/m/s - 3 kg/m/s; kg/m/s; Air= 1.78x10 Viscosity - 5

Copyright 2013-2014 Newtonian and Non Newtonian and • • The magnitude of velocitygradient the (du/dy) haseffect no magnitudethe on of µ temperature. viscosity The Newton’s’viscosityoflaw is given by; du/dy µ τ τ Fluid = , rate of strainvelocitygradientor = viscosity of fluid of viscosity= stress shear = = µ µ du dy is a functionis only of condition the of fluid, the particularly its obey of viscosity Newton’s law - refer Newtonian fluids fluids Newtonian Glycerine Benzene Kerosene Alcohol Gasoline Oil Water Air Example: .

Copyright 2013-2014 Wednesday,2019 31, July VISCOSITY 24

Copyright 2013-2014 Wednesday,2019 31, July VISCOSITY 25

Copyright 2013-2014 . non . . . NewtonianFluids • the viscosity is constant is viscosity the velocitygradient The viscosity of non the slope of the curves for non for curves slope ofthe constant slope is the of shear), (rate the stressand shear relationship between linear a Newtonian and Non Newtonian and - Fluid Newtonian fluids Newtonian Do not obey Do of viscosity Newton’s law as well as the as the as well Newtonian fluids varies -Newtonian - Newtonian fluidis dependent onthe condition . fluid condition the of -Newtonian Fluid fluids Non - Newtonian

Copyright 2013-2014 For For e.g. Water, kerosene, air deformation. Newtonian fluids Newtonian stress stress is totoadeformation. be causecontinuous exceeded Plastic fluids Non of flow. are generally complexmixtures and are studied under a science of deformation For e.g. mud polymersolutions, Solutions flows, bloodfluids orsuspensions, etc.these shear termed-Newtonianareas Non and fluids.stress rateofdeformation For suchfluidsdoesnotFor viscositychangewith rateof Wednesday,2019 31, July Newtonian fluids -Newtonian : caseplasticwhichanyieldIn thesubstance isnon-Newtonianinitial ofa TYPES OFTYPES FLUIDS : fluidsthese follow Newton’s viscosity. : Fluids which do not follow the linear relationship betweenfollowlinearFluids whichtherelationship donot etc 27

Copyright 2013-2014 (iv) (ii) (iii) • (i) Newtonian and Non Newtonian and generalizedA Power milk When sludge When printing When = When n , paper n , n n drilling = ink TYPES OFFLUIDS < > 1, 1, 1 1, . , pulp B = B the the ≠ muds,etc. 0, , 0, fluid etc fluid it isNewtonian fluid. the τ . Newtonian fluid as following: as -Newtonianfluid law model can describe both both describe can -law model + = is fluid AB is    pseudo du dy dilatants is n Bingham plastic, , i .e . , plastic, i .e quicksand, ., gelatin i .e ., sewage , butter, blood ,

Copyright 2013-2014 Wednesday,2019 31, July TYPES OFTYPES FLUIDS 29

Copyright 2013-2014 • • them, and so theso them, and separatefrom other, each decreasingattractionthe between In the case ofa that somixing the molecular movement more vigorousincreases and molecular In the case ofgases, increasedtemperature Variationtemperature viscosityof with liquid, asits liquid, temperatureincreases viscosity decreases viscosity increases . . makes the molecules

Copyright 2013-2014 Viscosity moleculer This of The changes increase Wednesday,2019 31, July gases EFFECT OFTEMPERATUREEFFECT PRESSURE AND viscosity is due increases with in is cohesion pressure effected to increase under the with which . reason by However in ordinary the temperature pressure decreases increase that ON VISCOSITY ON the conditions in . viscosity in liquids . with The temperature increase viscosity is the of not shear some . of appreciably of temperature oils stress liquids has is decreases been due affected . found to the but by to inter that the be 31

Copyright 2013-2014 – increased to Consider a cylinderfitted with a piston let and pressureis stressto volumetric strain. , K which is definedas ratiothe of compressive reciprocalthe is of modulus bulk of dV COMPRESSIBILITYAND BILKMODULUS Compressibility= Bulk modulus, K = Volumetric strain= - , the volumethe gasp+dp, of decreasesfrom V K 1 nraeo rsuedp Increase pressure of Volumetric strain dV V - decreases with increase of pressure ve sign means thevolume = - dV V to to = V − dV dp V

Copyright 2013-2014 (i) (i) Where is Bulk Modulusand K Relationshipp betweenand K For Isothermal Process.( For Adiabatic Process. ( K= p K= K= p K= pV γ pV=constant) γ γ =constant) is Ratio of Specificheats.

Copyright 2013-2014 the surfacebalanceof thebelowforce it. tothe molecules and is in equilibrium. At the free surface of the liquid there are no liquid moleculesabove in liquidmass issurrounded byotherallaroundinteriorliquidof the theof molecules Capillary actiontoboth isdue cohesion and adhesion. liquid to stickanotherbody. molecules of a solid boundary surface in contact with liquid. This property enables a Adhesion: Surface tocohesionbetweenparticlesatfree isdue tension surface. of the liquid to remain as one assemblage of particles. liquid. stresses. is aliquidto tendency ItresistCohesion enablesasmallamountoftensile Cohesion Surface Tension Wednesday,2019 31, July : of theattractionbetweenmolecules sameCohesionintermolecular means Adhesion means attraction between the molecules of a liquidandmolecules theattractionbetweentheAdhesion means SURFACE TENSION : is caused by theatsurface.is causedofcohesionfree force the A liquidmolecule 34

Copyright 2013-2014 . . the cut. cut. the Thus, 2πR Fig. R radius of shape spherical of a diagram body free a using calculated be can fluid of drop a inside pressure The pressure pressure internal the between difference with the balance be must force This σ 1.7, and the force developed around the edge of the cut sphere is sphere cut the of edge the around developed force the and 1.7, . 2πR ∆p p = = σ i p and the external pressure pressure external the and = = i – ∆p p e πR = Surface Tension 2 p e acting on the circular area of area circular the on acting ∆p= cut cut in in as shown half, 2 R σ -

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