Chapter 2: Fluid Properties

Byy

Dr Ali JawarnehDr Ali Jawarneh

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OutlineIn this chapter we willIn this chapter we will • Discuss the following properties of a fluid:

– Density specific weight specific gravity– Density, specific weight, specific gravity.– Specific heat, Internal energy and enthalpy.

• Present the equation of state• Present the equation of state.• Discuss in detail the physical meaning of

viscosity, its definitions, variation, andviscosity, its definitions, variation, and applications.

• Present newtonian versus Non-Newtonian Fluids

• Discuss the properties of elasticity and surface t i

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tension.• Discuss the considerations of vapour pressure.

2.1: Basic Units• SI (International system):Length (m), time (s), temperature (K), work & energy (J) or (N.m), Power (W) or (J/s).

• English system:• English system:Mass: 1slug=14.59 kg, or Ibm=0.4536 kg, or 1

slug=32.2 Ibmslug 32.2 IbmLength: foot (ft)=30.48 cmForce: pound force {Ibf}=4.448 Np { }Temperature: Rankine{oR}=460+oFT(oF)=1.8 T(oC)+32

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( ) ( )

2.2: System; Extensive & Intensive Properties

• A system is defined as a given quantity ofA system is defined as a given quantity of matter.

• The total mass of a given system is constant,The total mass of a given system is constant, since it always consists of the same matter.

• Extensive properties are properties related to p p p pthe total mass of the system,example: M, W.

• Intensive properties are properties p p p pindependent of the amount of fluid, example: p, T, ρ.

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2.3: properties Involving the Mass or Weight of the Fluidthe Fluid

- Mass Density, ρ• The mass density (or simply density) is the

mass per unit volume.• It is represented by the symbol (ρ) and has a

unit of kg/m3.3• Density of water at 4°C = 1000 kg/m3.

• Density of air at 20°C and standard pressure = 1 2 kg/m3= 1.2 kg/m3.

• Values densities of common fluids are given in tables A.2 – A.5 in the textbook.

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in tables A.2 A.5 in the textbook.

- Specific Weight

• The specific weight is simply the weight per nit ol meunit volume.

• It is represented by the symbol (γ) and has a unit of N/m3unit of N/m .

The specific weight of water at 20°C = 9 79

gργ =• The specific weight of water at 20°C = 9.79

kN/m3.• The specific weight of air at 20°C andThe specific weight of air at 20 C and

standard pressure = 11.8 N/m3. • See tables A-3 to A-5

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- Specific GravitySpecific Gravity• Specific gravity is the ratio of the specific

weight of a given fluid to the specific weight g g p gof water at a standard reference temperature.

• Specific gravity is represented by the symbol p g y p y y(S) or sp.gr. or SG and is dimensionless.

fluidfluidSργ

==

• At standard reference temp of 4 oC, waterwater

Sργ

==

p ,γwater=9810 N/m3

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- The Equation of State

• The equation of state for an ideal gas b dcan be expressed as:

TRp ρ=

• The value of (R) is the gas constant which is characteristic of the gas itself.

• Values of (R) are given in Table A.2.• Although no gas is ideal, most gases g g g

that we deal with behave like ideal gases.

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Variation of Densityy

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Density {at standard atm press and 15 oC Table A 2}15 oC, Table A-2}

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Density (Air) {Table A.3}y ( ) { }

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Density (Water, Table A.5)y ( , )

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2.4: Properties Involving the Flow of Heat

• The specific heat (c) is the amount of thermal energ that m st be transferred to a nit

- Specific Heat

energy that must be transferred to a unit mass of a substance to raise its temperature by one degree.y g

• It is a measure of the capacity of a substance to store thermal energy.

• It is given in units of J/kg.K.• Specific heat can be given at constant

( ) t t t l ( )pressure (cp)or at constant volume (cv).• The ratio cp/cv.is given by the symbol (k) and

is always constant for a given gas14

is always constant for a given gas.

Specific Internal Energy- Specific Internal Energy• The specific internal energy (u) is the energy

that a substance possesses per unit mass because of the state of the molecular activity in the substancein the substance.

- Specific EnthalpyS ifi th l (h) i i h + /• Specific enthalpy (h) is given as h= u + p/ρ

• Both of u and h are given in J/kg.F id l d h f ti f• For an ideal gas u and h are function of temperature alone.

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2.5: ViscosityA fl id i b t th t d f• A fluid is a substance that deforms continuously when subjected to a shear stressshear stress.

• Shear stress in a viscous fluid is proportional to the time rate of the ofproportional to the time rate of the of strain as follows:

dV

h t d i i itdy

μτ =

• τ: shear stress, μ: dynamic viscosity, dV/dy: velocity gradient, or time rate of strain or shear strain

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strain, or shear strain

Viscosityy

• μ is the viscosity of the fluid, referred to at times as dynamic viscosity or absolute viscosity.

• It is basically defined as the ratio of the shear stress to the velocity gradient.y g

• Thus, the unit used for viscosity is: N.s/m2

• Another unit used for the viscosity is the• Another unit used for the viscosity is the poise, which is 0.1 N.s/m2.

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Viscosityy

• Viscosity and density are inter-related in many equations used in fluid mechanics.

• The quantity μ/ρ is commonly used and termed the kinematic viscosity (ν).y ( )

ν= μ/ρThe units of the kinematic viscosity are• The units of the kinematic viscosity are m2/s.

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Viscosityy

• The velocity distribution in a fluid near a boundary can be given as follows:

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Viscosityy

• The previous distribution implies the following:– The velocity of the fluid is zero at the y

boundary (no-slip condition).– The velocity gradient at the boundary is

finite.– The velocity gradient becomes less steep

with distance from the boundary; the maximum shear stress is at the boundary.

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Viscosityy

• The viscosity of a gas increases with temperature as given by the Sutherland’s equation:

STST

TT

++

⎟⎟⎠

⎞⎜⎜⎝

⎛= o

oo

2/3

μμ

• The value of (S) is characteristic of the gas itself Values of (S) are given for

⎠⎝

gas itself. Values of (S) are given for different gases in table A.2

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Viscosityy• In contrast, the viscosity of a liquid

decreases with temperature, according to the equation: TbCe /=μ Ceμ

• Where C and b are empirical constants determined from at least two data points.Th i ti f i it (d i d• The variation of viscosity (dynamic and kinematic) for different fluids are given in figures A 2 and A 3

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figures A.2 and A.3.

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Dynamic or absolute Viscosity {Fig A 2}{Fig.A.2}

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Kinematic Viscosity {Fig. A.3}y { g }

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Example: Two plates are separated by 1/4 inch space The lo er plate is stationar the pperspace. The lower plate is stationary, the upper plate moves at a velocity of 10 ft/s. Oil (SAE 10W-30 150 oF) which fills the space The10W 30, 150 F) which fills the space. The variation in velocity of the oil is linear. What is the shear stress in the oil?

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Solution:From Figure A.2: 241025 Ib.s/ftx.μ −=

48010===

VdV Δ 4801241

===/)/(ydy Δ

24 25004801025 Ib/ft.xx.dVμτ === −

Another way to find dV/dy since the relation is linear:

5008005 b/ft.xx.dy

μτ

V=a y+b@y=0, V=0 0=0+b b=0@y@y=(1/4)/12, V=10 10=a [(1/4)/12]+0 a=480V=480 y dV/dy=480y y

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Example: A block weighing 1 kN and having dimensions 200 mm on an edge is allo able todimensions 200 mm on an edge is allowable to slide down an incline on a film of oil having a thickness of 0 005 mm If we use a linearthickness of 0.005 mm. If we use a linear velocity profile in the oil. What is the terminal speed of the block. The viscosity of the oil is p y7x10-3 N.s/m2

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Solution: 23107 N.s/mxμ −=

shearFsinW =o20

dVμτdy

μτ =

T VVdV 000200 TT V

)/.(dy000200

10000050==

TV1400=τ

TTshear V)x)(VAF 561000200

10002001400 === τ

shearFsinW =o20

29TVsinxx 562010001 =o m/s.VT 116=

Viscosityy

• Not in all fluids, the relationship between the - Newtonian versus Non-Newtonian Fluids

, pshear stress and the rate of strain is directly proportional, as discussed earlier.

• In some fluids, these relationship is not directly proportional. These are called “non-N i ” fl idNewtonian” fluids.

• Examples of non-Newtonian fluids are shear-thi i [ i t i k] h thi k ithinning[ paints, ink], shear thickening[mixture of glass particles in water, and Bingham plastic [toothpaste]

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Bingham plastic [toothpaste].

Viscosityytoothpaste

paintsp

mixture of glass particles in water

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2.6: Elasticity

• Elasticity (also often called compressibility) of the fl id is related to the amo nt ofof the fluid is related to the amount of deformation (expansion or contraction) for a given pressure change, quantitatively g p g , q ydescribed by the bulk modulus of elasticity Eν :

dp dp

Th b lk d l f t i d 2 2

dp dpEd dV Vν = = −ρ ρ

• The bulk modulus of water is around 2.2GN/m2, corresponding to a change of 0.05% in volume for a change of 1 MPa.

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g

Elasticityy

• The elasticity of an ideal gas is proportional to pressure.

• For an isothermal process:p

pTRE == ρν

• For and adiabatic process:

pcc

Ev

p=ν

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2.7- Surface Tension, σ• Theory of molecular attraction: molecules of

liquid below the surface act on each other by f th t l i ll di tiforces that are equal in all direction. However, molecules near the surface have a greater attraction for each other than they do g yfor molecules below the surface.

• This produces in effect a surface on theThis produces in effect a surface on the liquid where each portion exerts tension on adjacent portions.S f t i ( ) i ll f d t i• Surface tension (σ) is usually referred to in units of N/m.

• At room temperature, surface tension for a 34

p ,water-air surface is 0.073 N/m.

Capillary Action:Th h f ill ff t b• The phenomenon of capillary effect can beexplained microscopically by considering cohesiveforces (forces between like molecules, such as( ,water & water) and adhesive forces (forcesbetween unlike molecules such as water & glass).The liq id molec les at solid liq id interface areThe liquid molecules at solid-liquid interface aresubjected to both cohesive & adhesive forces. Therelative magnitude determine whether a liquidg qwets a solid surface or not. Obviously, the watermolecules are more strongly attracted to the glassmolecules than they are to other water moleculesmolecules than they are to other water molecules,and thus water tends to rise along the glasssurface. The opposite occurs for mercury, which

35causes the liquid surface near the glass wall tosuppressed.

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2.8: Vapour Pressure

• Vapour pressure is the pressure at which a liq id ill boilliquid will boil.

• The vapour pressure increases with temperaturetemperature.

• When the temperature of a liquid increases, its vapour pressure increases to the point atits vapour pressure increases to the point at which it is equal to atmospheric pressure, and thus boiling occurs.

• Similarly, boiling can occur at low temperatures if the pressure in the liquid is decreased to its vapour pressure

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decreased to its vapour pressure.

Vapour Pressurep• The effect of vapour pressure can be noticed

in flowing liquids when vapour bubbles start growing in local regions of very low pressure and collapse in regions of high pressure. This phenomenon is known as cavitation.

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Cavitation• As these bubbles

move to the higher pressure region they collapsecollapse.

• This can cause excessive intermittentexcessive intermittent pressures that can cause severe damage gto moving parts.

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