Fluid Properties and UnitsDimensions and UnitsSlide 3Slide 4Definition of a FluidFluid Deformation between Parallel PlatesShear StressFluid ViscosityExample: Measure the viscosity of waterSolution SchemeViscosity Measurement: SolutionRole of ViscosityDynamic and Kinematic ViscosityDensity and Specific WeightPerfect Gas LawBulk Modulus of ElasticityCompression and Expansion of Gases: What is Ev?Speed of Sound (c)Vapor PressureSurface TensionExample: Surface TensionReview: Fluid PropertiesMonroe L. Weber-Shirk School of Civil and Environmental EngineeringFluid Properties and UnitsFluid Properties and UnitsCEE 331January 13, 2019Dimensions and UnitsThe dimensions have to be the same for each term in an equationDimensions of mechanics arelengthtimemassforcetemperatureaF mLTMMLT-2Dimensions and UnitsQuantity Symbol DimensionsVelocity V LT-1Acceleration a LT-2Area A L2Volume  L3Discharge Q L3T-1Pressure p ML-1T-2Gravity g LT-2Temperature T’ Mass concentration C ML-3Show this!Dimensions and UnitsQuantity Symbol DimensionsDensity  ML-3Specific Weight  ML-2T-2Dynamic viscosity  ML-1T-1Kinematic viscosity  L2T-1Surface tension  MT-2Bulk mod of elasticity E ML-1T-2These are _______ properties!fluidHow many independent properties? _____4mnr=gg r=Definition of a Fluid“a fluid, such as water or air, deforms continuously when acted on by shearing stresses of any magnitude.” - Young, Munson, OkiishiWhy isn’t steel a fluid?Fluid Deformation between Parallel PlatesSide viewForce F causes the top plate to have velocity U.What other parameters control how much force is required to get a desired velocity?Distance between plates (t)Area of plates (A)FtUViscosity! ()F=AUtmIf this parameter increases, what does F do?Shear Stresschange in velocity with respect to distanceAF2mNtUtUdydutAUFAUFt2msNdimension ofs1Tangential force per unit areaRate of angular deformationrate of shearOur general equation relating shear and viscositydudyFluid ViscosityExamples of highly viscous fluids______________________________Fundamental mechanismsGases - transfer of molecular momentumViscosity __________ as temperature increases.Viscosity __________ as pressure increases.Liquids - cohesion and momentum transferViscosity decreases as temperature increases.Relatively independent of pressure (incompressible)molasses, tar, 20w-50 oil, glycerinincreases_______increasesExample: Measure the viscosity of waterThe inner cylinder is 10 cm in diameter and rotates at 10 rpm. The fluid layer is 2 mm thick and 20 cm high. The power required to turn the inner cylinder is 100x10-6 watts. What is the dynamic viscosity of the fluid?Outer cylinderThin layer of waterInner cylinderdydutAUFSolution SchemeRestate the goalIdentify the given parameters and represent the parameters using symbolsOutline your solution including the equations describing the physical constraints and any simplifying assumptionsSolve for the unknown symbolicallySubstitute numerical values with units and do the arithmeticCheck your units!Check the reasonableness of your answerViscosity Measurement: SolutionhrPt322-6-3 22 3(100 10 W) (0.002 m)1.16x10 N s/m2 (1.047/s) (0.05 m) (0.2 m)xmp= = �tAUFUAthrF22PthrP322Outer cylinderThin layer of waterInner cylinderr = 5 cmt = 2 mmh = 20 cmP = 100 x 10-6 W10 rpmr2rhFr10 2 min1.047 /min 60rev radrad srev spw = =Role of ViscosityStaticsFluids at rest have no relative motion between layers of fluid and thus du/dy = 0Therefore the shear stress is _____ and is independent of the fluid viscosityDynamicsFluid viscosity is very important when the fluid is moving zeroDynamic and Kinematic ViscosityKinematic viscosity (__) is a fluid property obtained by dividing the dynamic viscosity (__) by the fluid density3mkgsmkgm�[ ]N =[m2/s]Connection to Reynolds number!mnReVD VDrm n= =nu2mN s�� �� �� �2skg m�� �� �� �Density and Specific WeightDensity (mass/unit volume) density of water:density of air at atmospheric pressure and 15 C:Specific Weight of water (weight per unit volume) __________________95096097098099010000 50 100Temperature (C)Density (kg/m3)99799899910000 10 20Temperature (C)Density (kg/m3)1000 kg/m31.22 kg/m3 = g = 9806 N/m3Specific massPerfect Gas LawPV = nRTR is the universal gas constantT is in KelvinNote deviation from the text!R 8 314.N mmol KRRMtextgasMgas is molecular massMgas for air is 0.029 kg/moleWhy is this Mgas for air reasonable?N2 28 g/mol, O2 32 g/molBulk Modulus of ElasticityRelates the change in volume to a change in pressurechanges in density at high pressurepressure waves_______________ __________2.002.052.102.152.202.252.302.350 20 40 60 80 100Temperature (C)Bulk Modulus of elasticity (GPa)soundwater hammerEdpdv //vdpEdV V=-WatervdV dpV E=-How much does water compress?vEdpdr r=Compression and Expansion of Gases: What is Ev?Isothermal (constant temperature)Isentropic (no heat exchanged)p constantCkpr=kccpvwhere(specific heat ratio)pVn constantdpd r=Edpdv /vE p=RTE kpv1kdpCkdrr-=1kkdp pkdrr r-=dp pkd r r=1r�Speed of Sound (c)cEvcdpdEdpdv /E dpdv E kpvFor gasses, if no heat exchanged (isentropic) then we haveIt can be shown that (homework)ckRTMgasConnection to Mach number!VMac=. Solve for dpd randc is large for difficult to compress fluidsVapor Pressure0100020003000400050006000700080000 10 20 30 40Temperature (C)Vapor pressure (Pa)liquidWhat is vapor pressure of water at 100°C?101 kPaCavitation!When absolute pressure returns to exceed vapor pressurewaterpR2 = 2RSurface TensionPressure increase in a spherical dropletRp2pR22RSurface molecules0.0500.0550.0600.0650.0700.0750.0800 20 40 60 80 100Temperature (C)Surface tension (N/m)Fp=F=Example: Surface TensionEstimate the difference in pressure (in Pa) between the inside and outside of a bubble of air in 20ºC water. The air bubble is 0.3 mm in diameter.2pRsD =R =