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Fluid Properties and Units CEE 331 April 26, 2015 CEE 331 April 26, 2015

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Dimensions and Units ä The dimensions have to be the same for each term in an equation ä Dimensions of mechanics are ä length ä time ä mass ä force ä temperature ä The dimensions have to be the same for each term in an equation ä Dimensions of mechanics are ä length ä time ä mass ä force ä temperature L T M MLT -2

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Dimensions and Units QuantitySymbolDimensions VelocityV LT -1 AccelerationaLT -2 AreaA L 2 Volume L 3 DischargeQ L 3 T -1 Pressurep ML -1 T -2 Gravityg LT -2 TemperatureT’ Mass concentrationC ML -3 QuantitySymbolDimensions VelocityV LT -1 AccelerationaLT -2 AreaA L 2 Volume L 3 DischargeQ L 3 T -1 Pressurep ML -1 T -2 Gravityg LT -2 TemperatureT’ Mass concentrationC ML -3 Show this!

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Dimensions and Units QuantitySymbolDimensions Density ML -3 Specific Weight ML -2 T -2 Dynamic viscosity ML -1 T -1 Kinematic viscosity L 2 T -1 Surface tension MT -2 Bulk mod of elasticityE ML -1 T -2 QuantitySymbolDimensions Density ML -3 Specific Weight ML -2 T -2 Dynamic viscosity ML -1 T -1 Kinematic viscosity L 2 T -1 Surface tension MT -2 Bulk mod of elasticityE ML -1 T -2 These are _______ properties! fluid How many independent properties? _____ 4

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Definition of a Fluid ä “a fluid, such as water or air, deforms continuously when acted on by shearing stresses of any magnitude.” - Munson, Young, Okiishi Why isn’t steel a fluid?

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Fluid Deformation between Parallel Plates Side view Force 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) F t U Viscosity!

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Shear Stress change in velocity with respect to distance dimension of Tangential force per unit area Rate of angular deformation rate of shear

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Fluid classification by response to shear stress ä Newtonian ä Ideal Fluid ä Ideal plastic ä Newtonian ä Ideal Fluid ä Ideal plastic Newtonian Ideal Fluid Ideal plastic Shear stress Rate of deformation dy du

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Fluid Viscosity ä Examples of highly viscous fluids ä ______________________________ ä Fundamental mechanisms ä Gases - transfer of molecular momentum ä Viscosity __________ as temperature increases. ä Viscosity __________ as pressure increases. ä Liquids - cohesion and momentum transfer ä Viscosity decreases as temperature increases. ä Relatively independent of pressure (incompressible) ä Examples of highly viscous fluids ä ______________________________ ä Fundamental mechanisms ä Gases - transfer of molecular momentum ä Viscosity __________ as temperature increases. ä Viscosity __________ as pressure increases. ä Liquids - cohesion and momentum transfer ä Viscosity decreases as temperature increases. ä Relatively independent of pressure (incompressible) molasses, tar, 20w-50 oil, glycerin increases _______ increases

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Example: Measure the viscosity of water 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 cylinder Thin layer of water Inner cylinder

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Solution Scheme ä Restate the goal ä Identify the given parameters and represent the parameters using symbols ä Outline your solution including the equations describing the physical constraints and any simplifying assumptions ä Solve for the unknown symbolically ä Substitute numerical values with units and do the arithmetic ä Check your units! ä Check the reasonableness of your answer ä Restate the goal ä Identify the given parameters and represent the parameters using symbols ä Outline your solution including the equations describing the physical constraints and any simplifying assumptions ä Solve for the unknown symbolically ä Substitute numerical values with units and do the arithmetic ä Check your units! ä Check the reasonableness of your answer Team Work

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Role of Viscosity ä Statics ä Fluids at rest have no relative motion between layers of fluid and thus du/dy = 0 ä Therefore the shear stress is _____ and is independent of the fluid viscosity ä Flows ä Fluid viscosity is very important when the fluid is moving ä Statics ä Fluids at rest have no relative motion between layers of fluid and thus du/dy = 0 ä Therefore the shear stress is _____ and is independent of the fluid viscosity ä Flows ä Fluid viscosity is very important when the fluid is moving zero

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Dynamic and Kinematic Viscosity ä Kinematic viscosity (__) is a fluid property obtained by dividing the dynamic viscosity (__) by the fluid density [m 2 /s] Connection to Reynolds number! nu

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Density and Specific Weight Density (mass/unit volume) ä density of water: ä density of air at atmospheric pressure and 15 C: Specific Weight (weight per unit volume) ä __________________ Density (mass/unit volume) ä density of water: ä density of air at atmospheric pressure and 15 C: Specific Weight (weight per unit volume) ä __________________ 950 960 970 980 990 1000 050100 Temperature (C) Density (kg/m 3 ) 997 998 999 1000 01020 Temperature (C) Density (kg/m 3 ) 1000 kg/m 3 1.22 kg/m 3 = g = 9806 N/m 3 Specific mass

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Perfect Gas Law ä PV = nRT ä R is the universal gas constant ä T is in Kelvin ä PV = nRT ä R is the universal gas constant ä T is in Kelvin Note deviation from the text! M gas is molecular mass M gas for air is 0.029 kg/mole Why is this M gas for air reasonable?

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Bulk Modulus of Elasticity ä Relates the change in volume to a change in pressure ä changes in density at high pressure ä pressure waves ä _________ ä ______ __________ ä Relates the change in volume to a change in pressure ä changes in density at high pressure ä pressure waves ä _________ ä ______ __________ 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 020406080100 Temperature (C) Bulk Modulus of elasticity (GPa) sound water hammer Water

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Compression and Expansion of Gases ä Isothermal (constant temperature) ä Isentropic (no heat exchanged) ä Isothermal (constant temperature) ä Isentropic (no heat exchanged) where (specific heat ratio)

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Speed of Sound (c) For gasses, if no heat exchanged (isentropic) then we have It can be shown that (homework) Connection to Mach number! See ch. 11!

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Vapor Pressure 0 1000 2000 3000 4000 5000 6000 7000 8000 010203040 Temperature (C) Vapor pressure (Pa) liquid What is vapor pressure of water at 100°C? 101 kPa Cavitation!

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p R 2 = 2 R Surface Tension ä Pressure increase in a spherical droplet pR2pR2 2R2R Surface molecules 0.050 0.055 0.060 0.065 0.070 0.075 0.080 020406080100 Temperature (C) Surface tension (N/m)

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Example: Surface Tension ä 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. R = 0.15 x 10 -3 m = 0.073 N/m What is the difference between pressure in a water droplet and in an air bubble? Statics!

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Viscosity Measurement: Solution Outer cylinder Thin layer of water Inner cylinder r = 5 cm t = 2 mm h = 10 cm P = 50 x 10 -6 W 10 rpm rr 2 rh FrFr

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