Monroe L. Weber-Shirk S chool of Civil and Environmental Engineering Fluid Properties and Units CEE 331 June 15, 2015 CEE 331 June 15, 2015 

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 

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!

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

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

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! (  ) F = If this parameter increases, what does F do?

Shear Stress change in velocity with respect to distance dimension of Tangential force per unit area Rate of angular deformation rate of shear Our general equation relating shear and viscosity

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

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 20 cm high. The power required to turn the inner cylinder is 100x10 -6 watts. What is the dynamic viscosity of the fluid? Outer cylinder Thin layer of water Inner cylinder

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

Viscosity Measurement: Solution Outer cylinder Thin layer of water Inner cylinder r = 5 cm t = 2 mm h = 20 cm P = 100 x W 10 rpm rr 2  rh FrFr

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 Dynamics 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 Dynamics ä Fluid viscosity is very important when the fluid is moving zero

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

Density and Specific Weight  Density (mass/unit volume)  ä density of water: ä density of air at atmospheric pressure and 15  C:  Specific Weight of water (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 of water (weight per unit volume)  ä __________________ Temperature (C) Density (kg/m 3 ) Temperature (C) Density (kg/m 3 ) 1000 kg/m kg/m 3  =  g = 9806 N/m 3 Specific mass

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 kg/mole Why is this M gas for air reasonable? N 2 28 g/mol, O 2 32 g/mol

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 ______ __________ Temperature (C) Bulk Modulus of elasticity (GPa) sound water hammer Water How much does water compress?

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)

Speed of Sound (c) For gasses, if no heat exchanged (isentropic) then we have It can be shown that (homework) Connection to Mach number!. Solve for and E v is large for fluids that are difficult to compress

Vapor Pressure Temperature (C) Vapor pressure (Pa) liquid What is vapor pressure of water at 100°C? 101 kPa Cavitation! When absolute pressure drops below vapor pressure

 p  R 2 = 2  R  Surface Tension ä Pressure increase in a spherical droplet pR2pR2 2R2R Surface molecules Temperature (C) Surface tension (N/m) Fp=Fp= F=F=

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 m  = N/m What is the difference between pressure in a water droplet and in an air bubble?

Review: Fluid Properties ä Viscosity ä Density and Specific Weight ä Elasticity ä Vapor Pressure ä Surface Tension ä Viscosity ä Density and Specific Weight ä Elasticity ä Vapor Pressure ä Surface Tension