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Unformatted text preview: EGN 3353C Fluid Mechanics Chapter 2: Properties of Fluids
Lecture 2 (Read Chapter 2 of C&C) ! Properties of a system !
! Extensive properties " those whose values depends on the extent (size) of the system Intensive properties " those whose values are independent of the size of the system ! Simple Check " divide the system into two equal parts with an imaginary partition. Each part will have the same value of intensive properties as the original system but half the value of the extensive properties. ! Recall from Thermodynamics, the state of a system (single phase) is determined by 2 independent, intensive properties. Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
! Continuum o A fluid consists of molecules that can move w.r.t. each other but cannot sustain a shear stress w/o motion # Liquid has closely spaced molecules due to cohesive forces # Gas has much greater spacing between molecules than in a liquid o We assume that the fluid is continuously distributed throughout the region of interest, and the fluid properties are continuous functions of space # We are only concerned with bulk or macroscopic properties (not individual molecules as in molecular dynamics) Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
# Continuum assumption breaks down when the smallest dimension of interest is O ( mean free path ) " average distance between molecular collisions # We will restrict our attention in this course to continuum cases EXAMPLE ! Air at STP " ~ 66 nm # Continuum ok for looking at flows in devices that are at least ~10x larger than this or O ( m ) . # Continuum assumption invalid when looking at nanoscale! ! Air at 300,000 ft has ~ 1 ft! Continuum assumption probably not valid since this is rarefied flow, which is encountered in hypersonic and space flight. Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
! Some key fluid properties " SI units denoted by [ ] o Density =
m 3 kg m (reciprocal is specific volume) o Specific gravity SG = H O
2 [ ] (dimensionless). # Note H 2O = 1000 kg m3 at 4 C, so SG is easy to remember. # What happens if a substance has a SG < 1? o Specific weight s = g N m 3 " weight per unit volume NOTE: Review the ideal gas law! You are expected to know this. ! Vapor Pressure and Cavitation o At a given pressure, the temperature at which a pure substance changes phase is called the saturation temperature Tsat " Tsat = 100 C for water at 1 atm (101.325 kPa) o Likewise, at a given temperature, the pressure at which a pure substance changes phase is called the saturation pressure Psat " Psat = 1 atm for water at 100 C o The vapor pressure Pv of a pure substance is the pressure exerted by a vapor in phase equilibrium with its liquid at a given temperature " Pv = Psat # see Table 2-2 for water: Tsat as Psat Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics Brain Teaser: How does a pressure cooker work? ! What happens if the local pressure in a liquid system drops below the vapor pressure? Cavitation o The vapor bubbles (called cavitation bubbles since the bubbles form "cavities") collapse and generate high pressure destructive waves in the fluid " leads to serious erosion problems Surface erosion due to cavitation. ! NOTE: You are responsible for Section 2-5 on internal energy, enthalpy, and flow energy. This is a review from Thermodynamics. Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
! Coefficient of Compressibility Fluids, like solids, compress when the applied pressure is increased from P1 to P2. By analogy with Young's modulus of elasticity for solids, we define a coefficient of P P = compressibility = - T = const T = const Alternative way is to approximate the derivative - P P = T =const T = const [ Pa ] o change in pressure due to a fractional change in volume or density for a incompressible fluid
o EX. the pressure of water at normal atmospheric conditions must be raised to 210 atm to compress it 1 percent, corresponding to = 21,000 atm.
o Are you familiar with "water hammer" in pipes when a valve is suddenly closed? Isothermal compressibility =
1 =- 1 1 = P T = const P T = const Can you show that d = - d in general and that ideal gas = P ?
Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
! Coefficient of Volume Expansion In general, for a pure substance, = (T , P ) . Using a Taylor Series (truncated at first order)
d = dT + dP = ( dT - dP ) T P = const P T =const ! #" " $ ! #" " $ - K -1 represents the variation in fluid density (or volume) vs. temperature with constant pressure =- @ const P T T As shown, is important in natural convection that produces a buoyancy force. Can you show that ideal gas = 1 T ? Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
! Viscosity " fluid property that quantifies the internal resistance of a fluid to motion Consider a fluid between 2 large || plates with area A. The upper plate moves with a velocity V due to a shear stress = F A . The lower plate
du V y = . is fixed. The fluid velocity profile is linear: u ( y ) = V or dy % % During time interval dt , fluid line moves from MN to MN through
du dt d du Vdt du dy small angle d " tan d d = = = = dt " dt dy % % dy % States that rate of deformation = velocity gradient. Also, we find that du du for a Newtonian fluid (e.g., water, air, oil) " = where dy dy [ kg m s ] is the constant of proportionality. Non-Newtonian fluids
have nonlinear relationships (e.g., blood, plastics, toothpaste, quicksand). Do you know how to measure viscosity of a fluid? viscometer Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
! Surface tension Attractive forces applied on the interior molecule by the surrounding molecules balance each other because of symmetry, but the attractive forces acting on the surface molecule are not. Result is a net attractive force acting on the molecule at the surface of the liquid, which tends to pull the molecules on the surface toward the interior of the liquid " surface tension s [ N m] Stretching a liquid film with a U-shaped wire, and the forces acting on the movable wire of length b. Force balance gives F = 2 s b &
2 sides of film Work is Fdx = 2 s bdx = s A " ratio of work to surface area is surface energy s = W A [ N/m ] See text for other examples of a droplet and bubble Lou Cattafesta MAE Dept. University of Florida EGN 3353C Fluid Mechanics
! Capillary effect o Another example of surface tension " rise or fall of a liquid in a small diameter tube (important in manometers used to measure pressure) " leads to a meniscus Force balance on the region in lower left figure. Pressure is atmospheric at all faces, so no pressure force Fluid Weight = Surface Tension Force g = s cos circumference g R 2 h = 2 R s cos h = 2 s cos gR Note that (1) h as R (important effect is small R tubes), (2) h s (which is a function of the fluid-gas interface (see Table 2-4), (3)
cos > 0 for < 90o (air water) " h > 0 (4) What happens when > 90o (e.g., Mercury)? Impurities (e.g., surfactants) greatly influence surface tension (e.g., wax on a car, Rain-X). Why does mercury form a spherical drop that rolls on a surface? Lou Cattafesta MAE Dept. University of Florida ...
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This note was uploaded on 08/01/2008 for the course EGM 3353 taught by Professor Brucecarrol during the Spring '08 term at University of Florida.
- Spring '08
- Fluid Mechanics