advertisement

II. Properties of Fluids Contents 1. Definition of Fluids 2. Continuum Hypothesis 3. Density and Compressibility 4. Viscosity 5. Surface Tension 6. Vaporization 7. Forces Acting on Fluids 1. Definition of Fluids Definition of Fluids Flows A fluid is a substance that deforms continuously when subjected to a shear stress, no matter how small that the shear stress may be Solid Fluid F Fluid Fixed Plate U Definition of Fluids A fluid is a substance that cannot support any shear stress in static state Classification of Fluids Liquids (water) Fluids Gases (air) Liquids and Gases Liquid has definite volume; gas has no definite volume. 2. Continuum Hypothesis The Sensitive Volume The minimal volume in which the number of fluid molecule is big enough so that the average of any physical quantity over this volume is essentially independent of the volume itself Physical quantity B Micro effect Macro effect Sensitive volume V0 V The Sensitive Volume FACT: There are 2.71016 molecules in 1 mm3 air of 0 C at 1 atm The sensitive volume is usually very small (infinitesimally small) from a macroscopic view Fluid Particle A mass of fluid that has a spatial dimension equivalent to the sensitive volume Mathematical point of view: Fluid particle = Moving point with no size with no orientation Continuum Hypothesis At any point in a fluid we can find a fluid particle which occupies that point The fluid is a continuum formed by fluid particles 3. Density and Compressibility Density V m Dm r = lim DV ® 0 D V Density Density is the mass per unit volume Unit: kg / m3 Specific Weight W = mg (g = 9.8 m s2 ) g = rg Unit: N / m3 Specific Volume Specific Volume is the volume occupied by a unit mass of fluid 1 v = r Compressibility of Fluid Dv Dp = - K v Dp K = Dv v (Bulk modulus) Compressibility of Water ´ 109 3 2.5 2 K 1.5 1 0.5 0 0 10 20 30 40 50 T 60 70 80 90 100 Incompressible Fluid Dp K = ® ¥ Dv v Incompressible Fluid The bulk modulus of liquid is usually very large, or the compressibility of liquid is usually very small Water can be assumed as incompressible fluid in hydraulics Incompressible Fluid A fluid can be assumed to be incompressible if the variation of density within the flow is not large Air can be assumed as incompressible fluid when velocity is much smaller than the speed of sound 4. Viscosity Viscosity A measurement on stickiness of fluids EXPERIMENT Viscosity A measurement on the ability of a fluid to resist shearing y F U Moving Plate u Fixed Plate x y F Measured Results U u The flow is nearly parallel The fluid near the lower plate does not move The fluid near the upper plate moves with the plate The velocity distribution in y direction is linear Fd U µ A x Viscosity F U du t = µ = A d dy Shear stress du t = m dy Viscosity Rate of strain Udt d Udt t m= du dy Viscosity Coefficient of Viscosity Absolute Viscosity Dynamic Viscosity Unit of m : N s / m2 Dynamic Viscosity of Fluids Viscosity is a function of temperature Li qu id s m G as es T Id ea lP la st ic Newtonian and Non-Newtonian Fluid N n o N ew n o t i an F i lu d lu F ian n o wt e N id Ideal Fluid Inviscid Fluid ( m = 0 ) The viscosity of water is very small and may be omitted depends on the problem of interest Water can be assumed as inviscid fluid in many situations Kinematic Viscosity m n = r Unit of n : m2 / s Kinematic Viscosity of Fluids Problem A journal bearing consists of a shaft and a sleeve as shown in the following figure. The clearance space is filled with oil. The sleeve is fixed. The shaft turns at a known speed. Calculate the rate of heat generation at the bearing. Oil Diameter of shaft: d (m) Diameter of sleeve: d + (m) Sleeve Length of sleeve: l (m) Viscosity of oil: m (N s/m2) Speed of shaft: n (rpm) Shaft Solution Angular velocity of the shaft: v = 2pn 60 Shear stress on the surface of the shaft: U v d 1 n pmd t = m = m = d 2 d 60d ( ) Torque to keep rotation of the shaft: T = t A = n ml p 2d 2 60d Heat generation rate (= Power): Q = T v = n 2 ml p 3d 2 1800d (J s ) 5. Surface Tension Capillary Rise h Surface Tension = Surface tension per unit length Unit of : N / m 6. Vaporization ICE WATER VAPOR F u s io n n io at po r iz Liq u i d S o l id Va Pre s s u re CP Ga s TP S u b lim a tio n Te m p e ra t u re Vapor Pressure Vapor Water p h Vapor Pressure kg m 2 10000 8000 6000 4000 2000 0 0 20 40 60 80 100 o C 6. Forces Acting on Fluids Two Types of Forces • Body force • Forces acting on fluid mass, e.g. gravity force Surface force Contact force acting on fluid surface Description of Body Force r r DF f = lim DV ® 0 D m V m (Force per unit mass) r DF In case of gravity, r r f = - gk Description of Surface Force r r D Pn pn = lim DA ® 0 D A (Force per unit area = Stress) r DA F r n r D Pn • Normal stress • Shear Stress END OF CHAPTER II