# 1 FLUID PROPERTIES Chapter 2 CE319F: Elementary Mechanics of Fluids.

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FLUID PROPERTIESChapter 2CE319F: Elementary Mechanics of Fluids

Fluid Properties Define characteristics of a specific fluidProperties expressed by basic dimensionslength, mass (or force), time, temperature Dimensions quantified by basic units

We will consider systems of units, important fluid properties (not all), and the dimensions associated with those properties.

Systeme International (SI)Length = meters (m)Mass = kilograms (kg)Time = second (s)Force = Newton (N)Force required to accelerate 1 kg @ 1 m/s2Acceleration due to gravity (g) = 9.81 m/s2Weight of 1 kg at earths surface = W = mg = 1 kg (9.81 m/s2) = 9.81 kg-m/s2 = 9.81 N Temperature = Kelvin (oK)273.15 oK = freezing point of water oK = 273.15 + oC

Systme International (SI)Work and energy = Joule (J)J = N*m = kg-m/s2 * m = kg-m2/s2

Power = watt (W) = J/s

SI prefixes:G = giga = 109c = centi = 10-2 M = mega = 106m = milli = 10-3k = kilo = 103m = micro = 10-6

English (American) SystemLength = foot (ft) = 0.3048 mMass = slug or lbm (1 slug = 32.2 lbm = 14.59 kg)Time = second (s)Force = pound-force (lbf)Force required to accelerate 1 slug @ 1 ft/s2 Temperature = (oF or oR)oRankine = oR = 460 + oFWork or energy = ft-lbfPower = ft-lbf/s1 horsepower = 1 hp = 550 ft-lbf/s = 746 W

Banana SlugMascot of UC Santa Cruz

DensityMass per unit volume (e.g., @ 20 oC, 1 atm)Waterrwater= 1,000 kg/m3 (62.4 lbm/ft3)Mercury rHg= 13,500 kg/m3Air rair= 1.205 kg/m3

Densities of gases = strong f (T,p) = compressibleDensities of liquids are nearly constant (incompressible) for constant temperatureSpecific volume = 1/density = volume/mass

Example: Textbook Problem 2.8Estimate the mass of 1 mi3 of air in slugs and kgs. Assume rair = 0.00237 slugs/ft3, the value at sea level for standard conditions

ExampleA 5-L bottle of carbon tetrachloride is accidentally spilled onto a laboratory floor. What is the mass of carbon tetrachloride that was spilled in lbm?

Specific WeightWeight per unit volume (e.g., @ 20 oC, 1 atm)

gwater= (998 kg/m3)(9.807 m2/s)= 9,790 N/m3[= 62.4 lbf/ft3]gair= (1.205 kg/m3)(9.807 m2/s)= 11.8 N/m3[= 0.0752 lbf/ft3]

Specific GravityRatio of fluid density to density of water @ 4oC WaterSGwater = 1 MercurySGHg = 13.55

Note: SG is dimensionless and independent of system of units

ExampleThe specific gravity of a fresh gasoline is 0.80. If the gasoline fills an 8 m3 tank on a transport truck, what is the weight of the gasoline in the tank?

Ideal Gas Law (equation of state)P = absolute (actual) pressure (Pa = N/m2)V = volume (m3)n = # molesRu = universal gas constant = 8.31 J/oK-molT = temperature (oK)

R = gas-specific constant R(air) = 287 J/kg-oK (show)

ExampleCalculate the volume occupied by 1 mol of any ideal gas at a pressure of 1 atm (101,000 Pa) and temperature of 20 oC.

ExampleThe molecular weight of air is approximately 29 g/mol. Use this information to calculate the density of air near the earths surface (pressure = 1 atm = 101,000 Pa) at 20 oC.

Example: Textbook Problem 2.4Given: Natural gas stored in a spherical tankTime 1: T1=10oC, p1=100 kPaTime 2: T2=10oC, p2=200 kPaFind: Ratio of mass at time 2 to that at time 1Note: Ideal gas law (p is absolute pressure)

Viscosity

Some Simple FlowsFlow between a fixed and a moving plateFluid in contact with plate has same velocity as plate (no slip condition)u = x-direction component of velocity

Some Simple FlowsFlow through a long, straight pipeFluid in contact with pipe wall has same velocity as wall (no slip condition)u = x-direction component of velocity

Fluid DeformationFlow between a fixed and a moving plateForce causes plate to move with velocity V and the fluid deforms continuously.

Fluid DeformationFor viscous fluid, shear stress is proportional to deformation rate of the fluid (rate of strain)

ViscosityProportionality constant = dynamic (absolute) viscosity

Newtons Law of Viscosity

Viscosity

Units

Water (@ 20oC): m = 1x10-3 N-s/m2

Air (@ 20oC): m = 1.8x10-5 N-s/m2

Kinematic viscosity

Kinematic viscosity: m2/s

1 poise = 0.1 N-s/m2

1 centipoise = 10-2 poise = 10-3 N-s/m2

Shear in Different FluidsShear-stress relations for different fluidsNewtonian fluids: linear relationshipSlope of line = coefficient of proportionality) = viscosityShear thinning fluids (ex): toothpaste, architectural coatings; Shear thickening fluids = water w/ a lot of particles, e.g., sewage sludge; Bingham fluid = like solid at small shear, then liquid at greater shear, e.g., flexible plastics

Effect of TemperatureGases: greater T = greater interaction between molecules = greater viscosity.

Liquids: greater T = lower cohesive forces between molecules = viscosity down.

Typical Viscosity EquationsLiquid:Gas:T = KelvinS = Sutherlands constantAir = 111 oK+/- 2% for T = 170 1900 oKC and b = empirical constants

Flow between 2 plates

Thus, slope of velocity profile is constant and velocity profile is a st. lineForce is same on top and bottom

Flow between 2 plates

u=VMoving plateFixed plateyxVu=0BShear stress anywhere between platest t

Flow between 2 plates2 different coordinate systemsBV

Example: Textbook Problem 2.33Suppose that glycerin is flowing (T = 20 oC) and that the pressure gradient dp/dx = -1.6 kN/m3. What are the velocity and shear stress at a distance of 12 mm from the wall if the space B between the walls is 5.0 cm? What are the shear stress and velocity at the wall? The velocity distribution for viscous flow between stationary plates is

Example: Textbook Problem 2.34A laminar flow occurs between two horizontal parallel plates under a pressure gradient dp/ds (p decreases in the positive s direction). The upper plate moves left (negative) at velocity ut. The expression for local velocity is shown below. Is the magnitude of the shear stress greater at the moving plate (y = H) of at the stationary plate (y = 0)?

Elasticity (Compressibility) If pressure acting on mass of fluid increases: fluid contracts If pressure acting on mass of fluid decreases: fluid expands Elasticity relates to amount of deformation for a given change in pressureEv = bulk modulus of elasticitySmall dV/V = large modulus of elasticityHow does second part of equation come about?

Example: Textbook Problem 2.45Given: Pressure of 2 MPa is applied to a mass of water that initially filled 1000-cm3 (1 liter) volume. Find: Volume after the pressure is applied.

Ev = 2.2x109 Pa (Table A.5)

ExampleBased on the definition of Ev and the equation of state, derive an equation for the modulus of elasticity of an ideal gas.

Surface TensionBelow surface, forces act equal in all directions

At surface, some forces are missing, pulls molecules down and together, like membrane exerting tension on the surface

Pressure increase is balanced by surface tension, s

surface tension = magnitude of tension/length

s = 0.073 N/m (water @ 20oC)

Surface TensionLiquids have cohesion and adhesion, both involving molecular interactionsCohesion: enables liquid to resist tensile stressAdhesion: enables liquid to adhere to other bodies

Capillarity = property of exerting forces on fluids by fine tubes or porous mediadue to cohesion and adhesionIf adhesion > cohesion, liquid wets solid surfaces at risesIf adhesion < cohesion, liquid surface depresses at pt of contactwater rises in glass tube (angle = 0o)mercury depresses in glass tube (angle = 130-140o)

See attached information

Example: Capillary RiseGiven: Water @ 20oC, d = 1.6 mmFind: Height of waterW

Example: Textbook Problem 2.51Find: Maximum capillary rise between two vertical glass plates 1 mm apart.

Examples of Surface Tension

Example: Textbook Problem 2.48Given: Spherical soap bubble, inside radius r, film thickness t, and surface tension s.Find: Formula for pressure in the bubble relative to that outside. Pressure for a bubble with a 4-mm radius?Should be soap bubble

Vapor Pressure (Pvp)Vapor pressure of a pure liquid = equilibrium partial pressure of the gas molecules of that species above a flat surface of the pure liquidConcept on boardVery strong function of temperature (Pvp up as T up)Very important parameter of liquids (highly variable see attached page)When vapor pressure exceeds total air pressure applied at surface, the liquid will boil.Pressure at which a liquid will boil for a given temperatureAt 10 oC, vapor pressure of water = 0.012 atm = 1200 PaIf reduce pressure to this value can get boiling of water (can lead to cavitation)If Pvp > 1 atm compound = gasIf Pvp < 1 atm compound = liquid or solid

ExampleThe vapor pressure of naphthalene at 25 oC is 10.6 Pa. What is the corresponding mass concentration of naphthalene in mg/m3? (Hint: you can treat naphthalene vapor as an ideal gas).

Vapor Pressure (Pvp) - continuedVapor pressure of water (and other liquids) is a strong function of temperature.

Vapor Pressure (Pvp) - continuedPvp,H2O = Pexp(13.3185a 1.9760a2 0.6445a3 0.1299a4)P = 101,325 Pa a = 1 (373.15/T) T = oKvalid to +/- 0.1% accuracy for T in range of -50 to 140 oCEquation for relative humidity of air = percentage to which air is saturated with water vapor.What is affect of RH on drying of building materials, and why? Implications?

Example: Relative HumidityThe relative humidity of air in a room is 80% at 25 oC. What is the concentration of water vapor in air on a volume percent basis?If the air contacts a cold surface, water may condense (see effects on attached page). What temperature is required to cause water condensation?

Saturation Vapor Pressure