PROPERTIES OF FLUIDS

1. PROPERTIES OF FLUIDS WHAT ARE PROPERTIES? DENSITY & SPECIFIC GRAVITY VAPOUR PRESSURE COMPRESSIBILITY EXPANSION VISCOSITY SURFACE TENSION SOME APPLICATIONS KK's FLM 221 - WK2: FLUID PROPERTIES

2. PROPERTIES OF FLUIDS • Characteristics of a system e.g. Mass ‘m’, internal energy ‘U’, pressure ‘P’, Temperature ‘T’, viscosity ‘µ’ etc • Intensive properties – do not vary with mass in the system e.g. density ‘ρ’, viscosity ‘µ’, temperature ‘T’, pressure ‘P’ etc • Extensive properties – depend on total mass in system e.g. Mass ‘m’, Kinetic energy ‘E’, Volume ‘V’ etc • Specific property – refers to the extensive property per unit mass: (2.1) Where is an extensive property and is the intensive property for a mass • Continuum – the fluid is treated as a homogeneous continuous system with no spaces between its individual particles KK's FLM 221 - WK2: FLUID PROPERTIES

3. DENSITY & SPECIFIC GRAVITY • Mass m is an extensive property of matter measuring its inertia • Matter occupies space measured by the volume V • Density ‘ρ’ is an intensive property showing the uniform distribution of mass in the space or volume V ie: (2.2) From equation 2.2, show that the dimensions of density are: 1 in M and -3 in L • Units of density are: kg/m3; kg/l; g/cc where 1 kg/l = 1 g/cc = 1000 kg/m3 = density of water at 4oC • Relative density is the density of a substance compared with that of an other at specified conditions. If the substance of comparison is WATER AT 4oC, the relative density becomes the SPECIFIC GRAVITY (2.3) • For gases, it is preferable to compare their densities with that of AIR AT 1 atmosphere pressure and 15oC. (1.23 kg/m3) KK's FLM 221 - WK2: FLUID PROPERTIES

4. COMPRESSIBILITY • Fluids resist normal compressive stresses by building up an additional pressure ‘δP’ within themselves • The additional pressure causes a negative volumetric strain -δV/V • The ratio of Pressure (or normal stress) to volumetric strain gives the coefficient of compressibility , ‘κ’ • For liquids, this κ is sometimes called the BULK MODULUS OF ELASTICITY (2.4) • Density ‘ρ’ increases with additional pressure and the above equation becomes: (2.5) • For gases, Pressure depends on both temperature and density. At constant temperature (isothermal process), ‘κ’ equals the pressure P of an ideal gas: (2.6) KK's FLM 221 - WK2: FLUID PROPERTIES

5. EXPANSION OF FLUIDS • Fluids can not stand tensile stresses because these are always accompanied by shear ones – which cause shear strains • Most of matter expands when heated but fluids do so more than solids (why? - and - which material do you know that does not always behave this way?) • Density therefore reduces with temperature. Fractional change in density per unit change in temperature gives the COEFFICIENT OF VOLUME EXPANSION ‘β’ (2.7) • For ideal gases at constant pressure (isobaric process), high ‘T’ means low ‘β’ – and we get: (2.8) KK's FLM 221 - WK2: FLUID PROPERTIES

6. VISCOSITY I • The frictional force opposing relative motion between different parts of a fluid • Primarily originates from adhesion to supporting solid surfaces • Molecules at the surface ‘stick’ there but continue to attract those off the surface thus ‘retarding’ the latter . These also affect their neighbours farther away in like manner • The farther away from the surface, the smaller the influence – and hence the higher are the velocities • Overall effect is a fluid being sheared backward (when viewed from far point off the surface) – ie the surface initiates backward shear forces in the fluid. • Newton’s 3rd law requires that the fluid ‘reacts’ by exerting an opposite force on the surface. Hence the latter gets a FORWARD force called DRAG in the direction of fluid motion • SEE FIGURE 2.1 BELOW KK's FLM 221 - WK2: FLUID PROPERTIES

7. VELOCITY VARIATION IN FLUID ABOVE SURFACE γ FLUID NOW DEFORMED BY ADHESION TO SOLID SURFACE FLUID INITIALLY MOVING AT VEL. ‘V’ REL. TO SURFACE y FREE BODY DIAGRAM OF DEFORMED FLUID SOLID SURFACE FREE BODY DIAGRAM OF SOLID SURFACE SURFACE DRAG FORCE = - FLUID SHEAR FORCE FIGURE 2.1; HOW VISCOSITY (FLUID SHEAR) COMES ABOUT KK's FLM 221 - WK2: FLUID PROPERTIES

8. VISCOSITY II – NEWTON’S LAW • For many common fluids, the shear stress caused by the shear force increases directly with the rate of change of the angle ‘γ’ in figure 2.1. ie Big force on small surface means Big change in ‘γ’ during a given time (2.9) • This is Newton’s law of viscosity: ie “The viscous shear stress ‘τ’ in a fluid is directly proportional to the velocity gradient, ‘V/y’ ” • The constant of proportionality ‘µ’ is called the coefficient of viscosity or simply the DYNAMIC VISCOSITY of the fluid. It is an intensive property of the fluid. • WHAT ARE THE DIMENSIONS & UNITS OF DYNAMIC VISCOSITY? KK's FLM 221 - WK2: FLUID PROPERTIES

9. VISCOSITY VARIATION WITH TEMPERATURE • Liquids – ‘µ’drops dramatically with temperature rise due to reduction in attraction between molecules and to increased mobility – see Table 2 • Gases – ‘µ’INCREASES gently with temperature due to increased transfer of slower molecules from near surface into the bulk of the gas KK's FLM 221 - WK2: FLUID PROPERTIES

10. VISCOSITY III – TYPES OF VISCOUS FLUIDS Viscosity µ is not constant for all materials but we will consider only Newtonian fluids PLASTIC PSEUDO PLASTIC eg colloids, milk, lotions BINGHAM PLASTIC eg sewage Shear stress ‘τ’ NEWTONIAN eg water, oil, etc FIGURE 2.2 DIFFERENT TYPES OF VISCOUS MATERIALS DILATANT eg Quick sand Strain rate V/y KK's FLM 221 - WK2: FLUID PROPERTIES

11. KK's FLM 221 - WK2: FLUID PROPERTIES

12. VISCOSITY IV – KINEMATIC VISCOSITY • A useful ratio in Thermo-fluids: the ratio of Dynamic viscosity to density is called KINEMATIC VISCOSITY ‘ν’ (2.10) • ‘ν’ has dimensions of 2 in ‘L’ and -1 in ‘t’. It is measured in m2/s. For water at 20oC, µw = 1 mPas and νw≈1µm2/s For air at 20oC and 1 atm, µa = 18.3µPas and νa≈15.2 µm2/s KK's FLM 221 - WK2: FLUID PROPERTIES

13. SURFACE TENSION I • Molecules on a liquid surface have more neighbours below or adjacent than from above. • Where the surface contacts a solid or other supporting medium, unbalanced forces parallel to the surface of the liquid result. • Thus an unsupported liquid will form spherical droplets to balance out the forces • On contact with a solid, adhesive forces compete with cohesive ones and a meniscus forms: • If adhesion is stronger than cohesion, a concave meniscus results and the liquid contacts the solid at an acute angle, thereby WETTING the solid • If cohesion is stronger, a convex meniscus results and an oblique angle of contact results – with the liquid tending to form rolling globules • Whether to wet or to agglutinate depends on the nature of liquid and surface KK's FLM 221 - WK2: FLUID PROPERTIES

14. θ< 90O SURFACE IN TENSION SURFACE IN TENSION θ > 90O SPHERICAL SHAPE: NO RESULTANT FORCE FOR UNSUPPORTED LIQUID BALANCED FORCES INSIDE BALANCED FORCES INSIDE ADHESION > COHESION; CONCAVE MENISCUS & WETTING ADHESION < COHESION; CONVEX MENISCUS & AGGLUTINATING FIG. 2.3: SURFACE TENSION PHENOMENA KK's FLM 221 - WK2: FLUID PROPERTIES

15. SURFACE TENSION II • Surface tension is the energy on the strained interface per unit surface area • This works out as a force along any line on the surface per unit line length ie: (2.11) • Show that the dimensions of ‘σ’ are: 1 in ‘M’ and -2 in ‘t’ and that the units are the N/m or kg/s2 KK's FLM 221 - WK2: FLUID PROPERTIES

16. VAPOUR PRESSURE • The pressure exerted by the vapour when in equilibrium with its parent liquid • It arises out of high energy molecules that would have left the liquid surface earlier returning into the liquid • Vapour pressure increases with temperature • Partial pressure – the pressure of a particular gas within the mixture • In flow pipelines, if the pressure falls to saturation, the liquid boils causing a phenomenon called CAVITATION • Partial pressure can not exceed saturation pressure at the temperature in question KK's FLM 221 - WK2: FLUID PROPERTIES

17. SOME APPLICATIONS I VAPOUR PRESSURE & CAVITATION: • Usually dangerous in liquid distribution pipelines due to formation of gas/vapour bubbles and subsequent shock waves at low pressures. For the given liquid distribution temperature, the saturation pressure and the behaviour of dissolved gases at higher pressures are noted to avoid this phenomenon • Useful in the following applications (among many others): • Ultrasonic cleaning and etching to produce the cleanest possible surfaces of precision parts • NASA’s hydro sonic pump to generate heat for processing some organic salts. Cavitation shockwaves generate much more heat than the work input to the pump! • In the medical world, breakup and removal of kidney stones using cavitation bubbles reinforcing ultrasonics (Lithotripsy) KK's FLM 221 - WK2: FLUID PROPERTIES

18. SOME APPLICATIONS II • VISCOSITY: Perhaps one of the most important fluid properties • Digestion, absorption and assimilation of drugs, foods etc in animals depends partly on the viscosity of the solutions of these substances • Lubrication of industrial machinery is fully dependent on viscosity • Atomisation of diesel in compression ignition engines is dependent on viscosity – and present research on bio diesel has viscosity as one of its focus areas • Principal determinant of power requirements in all fluid pumping power requirements ranging from water distribution to concrete pumping in mega engineering projects to heart-lung machines in hospitals etc KK's FLM 221 - WK2: FLUID PROPERTIES

19. SOME APPLICATIONS III SURFACE TENSION • Natural design of some insects (low weight, large leg contact perimeter) enables them walk on water • Capillary action in plants enables water and mineral intake by plants • Surfactants (lower water surface tension) used in manufacture of cosmetics, tooth pastes, detergents, disinfectants etc • Gas exchange in alveoli of the lungs depends on surface tension of the fluid coating them KK's FLM 221 - WK2: FLUID PROPERTIES