Fluid Properties and UnitsContinuumSlide 3Dimensions and UnitsSlide 5Slide 6Definition of a FluidFluid Deformation between Parallel PlatesShear StressFluid classification by response to shear stressFluid ViscosityExample: Measure the viscosity of waterSolution SchemeRole of ViscosityDynamic and Kinematic ViscosityDensity and Specific WeightPerfect Gas LawBulk Modulus of ElasticityVapor PressureCavitationCavitation DamageSurface TensionExample: Surface TensionOutline the solutionViscosity Measurement: SolutionFluid Properties and UnitsFluid Properties and UnitsCVEN 311CVEN 311ContinuumContinuumAll materials, solid or fluid, are composed of molecules discretely spread and in continuous motion. However, in dealing with fluid-flow relations on a mathematical basis, it is necessary to replace the actual molecular structure by a hypothetical continuous medium, called the cont inuum.All materials, solid or fluid, are composed of molecules discretely spread and in continuous motion. However, in dealing with fluid-flow relations on a mathematical basis, it is necessary to replace the actual molecular structure by a hypothetical continuous medium, called the continuum .ContinuumContinuumIn a continuum, the physical variable at a point in space is the averaged value of the variable in a small sphere.How good is the assumption?In a continuum, the physical variable at a point in space is the averaged value of the variable in a small sphere.How good is the assumption?10-3cm3x1010 molecules of airDimensions and UnitsDimensions and UnitsThe dimensions have to be the same for each term in an equationDimensions of mechanics arelengthtimemassforcetemperatureThe dimensions have to be the same for each term in an equationDimensions of mechanics arelengthtimemassforcetemperatureaF maF mLTMMLT-2Dimensions and UnitsDimensions 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-3Quantity 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-3Dimensions and UnitsDimensions 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? _____4Definition of a FluidDefinition of a Fluid“a fluid, such as water or air, deforms continuously when acted on by shearing stresses of any magnitude.” - Munson, Young, Okiishi“a fluid, such as water or air, deforms continuously when acted on by shearing stresses of any magnitude.” - Munson, Young, OkiishiWaterOilAirWhy isn’t steel a fluid?WaterOilAirWhy isn’t steel a fluid?Fluid Deformation between Parallel PlatesFluid Deformation between Parallel PlatesSide viewSide viewForce F causes the top plate to have velocity U.Force F causes the top plate to have velocity U.What other parameters control how much force is What other parameters control how much force is required to get a desired velocity?required to get a desired velocity?Distance between plates (b)Distance between plates (b)Area of plates (A)Area of plates (A)FbUViscosity!Viscosity!Shear StressShear Stresschange in velocity with respect to distancechange in velocity with respect to distanceAFAF2mN2mNbUbUbUbUdydudydubAUFbAUFAUFtAUFt2msN2msNdimension ofs1s1Tangential force per unit areaRate of angular deformationrate of shearFluid classification by response to shear stressFluid classification by response to shear stressNewtonianIdeal FluidIdeal plasticNewtonianIdeal FluidIdeal plasticNewtonianIdeal FluidIdeal plasticShear stress Shear stress Rate of deformationRate of deformationdydudydudydu1Fluid ViscosityFluid 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)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 oilincreases_______increasesExample: Measure the viscosity of waterExample: 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 10 cm high. The power required to turn the inner cylinder is 50x10-6 watts. What is the dynamic viscosity of the fluid?The inner cylinder is 10 cm in diameter and rotates at 10 rpm. The fluid layer is 2 mm thick and 10 cm high. The power required to turn the inner cylinder is 50x10-6 watts. What is the dynamic viscosity of the fluid?Outer Outer cylindercylinderThin layer of waterThin layer of waterInner Inner cylindercylinderSolution SchemeSolution 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 answer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 answerSolutionRole of ViscosityRole of ViscosityStaticsFluids at rest have no relative motion between layers of