Chapter 1 - Chapter 1 - A PowerPoint Presentation byA PowerPoint Presentation by

NOOR ASSIKIN BINTI ABD WAHABNOOR ASSIKIN BINTI ABD WAHAB

© 2011

IntroductionIntroduction This chapter will begin with several concepts, This chapter will begin with several concepts,

definition, terminologies and approaches definition, terminologies and approaches which should be understood by the students which should be understood by the students before continuing reading the rest of this before continuing reading the rest of this module. module.

Then, it introduces the student with typical Then, it introduces the student with typical properties of fluid and their dimensions which properties of fluid and their dimensions which are then being used extensively in the next are then being used extensively in the next chapters and units like pressure, velocity, chapters and units like pressure, velocity, density and viscosity. density and viscosity.

Some of these can be used to classify type Some of these can be used to classify type and characteristic of fluid, such as whether a and characteristic of fluid, such as whether a fluid is incompressible or not or whether the fluid is incompressible or not or whether the fluid is Newtonian or non-Newtonianfluid is Newtonian or non-Newtonian..

Fluid ConceptFluid Concept•Fluid mechanics is a division in Fluid mechanics is a division in applied applied

mechanics related to the behaviour of mechanics related to the behaviour of liquid or gas which is either in rest or in liquid or gas which is either in rest or in motion.motion.

•The study related to a fluid in rest or The study related to a fluid in rest or stationary is referred to stationary is referred to fluid staticfluid static, , otherwise it is referred to as otherwise it is referred to as fluid dynamicfluid dynamic..

•Fluid can be defined as a substance which Fluid can be defined as a substance which can deform continuously when being can deform continuously when being subjected to shear stress at any subjected to shear stress at any magnitudemagnitude. In other words, it can flow . In other words, it can flow continuously as a result of shearing action. continuously as a result of shearing action. This includes any liquid or gas. This includes any liquid or gas.

DEFINE FLUIDSDEFINE FLUIDS

(a) Solid (b) Liquid (c) Gas

k

k k

k

Free surface

For solid, imagine that the molecules can be For solid, imagine that the molecules can be fictitiously linked to each other with springs.fictitiously linked to each other with springs.

• In fluid, the molecules can move freely but are In fluid, the molecules can move freely but are constrained through a traction force called constrained through a traction force called cohesioncohesion.. This force is interchangeable from one This force is interchangeable from one molecule to anothermolecule to another..

• For gases, it is very weak which enables the gas to For gases, it is very weak which enables the gas to disintegrate and move away from its container.disintegrate and move away from its container.

For liquids, it is stronger which is sufficient enough For liquids, it is stronger which is sufficient enough to hold the molecule together and can withstand to hold the molecule together and can withstand high compression, which is suitable for application high compression, which is suitable for application as hydraulic fluid such as oil. On the surface, the as hydraulic fluid such as oil. On the surface, the cohesion forms a resultant force directed into the cohesion forms a resultant force directed into the liquid region and the combination of cohesion liquid region and the combination of cohesion forces between adjacent molecules from a forces between adjacent molecules from a tensioned membrane known as tensioned membrane known as free surfacefree surface..

Definition of a FluidDefinition of a Fluid

A fluid is a substance that flows under the action of shearing forces. If a fluid is at rest, we know that the

forces on it are in balance.

A gas is a fluid that is easily compressed. It fills any vessel in which it is contained.

A liquid is a fluid which is hard to compress. A given mass of liquid will occupy a fixed volume,

irrespective of the size of the container.

A free surface is formed as a boundary between a liquid and a gas above it.

Fluid PropertiesFluid Properties

• Define “characteristics” of a specific Define “characteristics” of a specific fluidfluid

•Properties expressed by basic Properties expressed by basic “dimensions”“dimensions”

– length, mass (or force), time, length, mass (or force), time, temperaturetemperature

• Dimensions quantified by basic Dimensions quantified by basic “units”“units”

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

System International (SI)System International (SI)

• Length = meters (m)Length = meters (m)

• Mass = kilograms (kg)Mass = kilograms (kg)

• Time = second (s)Time = second (s)

• Force = Newton (N)Force = Newton (N)– Force required to accelerate 1 kg @ 1 m/sForce required to accelerate 1 kg @ 1 m/s22

– Acceleration due to gravity (g) = 9.81 m/sAcceleration due to gravity (g) = 9.81 m/s22

– Weight of 1 kg at earth’s surface = W = mg = 1 kg Weight of 1 kg at earth’s surface = W = mg = 1 kg (9.81 m/s(9.81 m/s22) = 9.81 kg-m/s) = 9.81 kg-m/s22 = 9.81 N = 9.81 N

• Temperature = Kelvin (Temperature = Kelvin (ooK)K)– 273.15 273.15 ooK = freezing point of water K = freezing point of water

– ooK = 273.15 + K = 273.15 + ooC C

System International (SI)System International (SI)

• Work and energy = Joule (J)Work and energy = Joule (J)

J = N*m = kg-m/sJ = N*m = kg-m/s22 * m = kg-m * m = kg-m22/s/s22

• Power = watt (W) = J/sPower = watt (W) = J/s

• SI prefixes:SI prefixes:

G = giga = 10G = giga = 1099 c = centi = c = centi = 1010-2-2

M = mega = 10M = mega = 1066 m = milli = m = milli = 1010-3-3

k = kilo = 10k = kilo = 1033 = micro = = micro = 1010-6-6

DensityDensity

• Mass per unit volume (e.g., @ 20 Mass per unit volume (e.g., @ 20 ooC, 1 atm)C, 1 atm)

– WaterWater waterwater = 1,000 kg/m= 1,000 kg/m3 3 (62.4 (62.4 lbm/ftlbm/ft33))

– MercuryMercury HgHg = 13,500 kg/m= 13,500 kg/m33

– AirAir airair = 1.205 kg/m= 1.205 kg/m33

• Densities of gases = strong f (T,p) Densities of gases = strong f (T,p) =compressible=compressible

• Densities of liquids are nearly constant Densities of liquids are nearly constant (incompressible) for constant temperature(incompressible) for constant temperature

• Specific volume = 1/density = Specific volume = 1/density = volume/massvolume/mass

DensityDensityThe density of a fluid is defined as its mass per unit volume. It is denoted by the Greek symbol, .

=V m3kgm-3

If the density is constant (most liquids), the flow is incompressible.If the density varies significantly (eg some gas flows), the flow is compressible.(Although gases are easy to compress, the flow may be treated as incompressible if there are no large pressure fluctuations)

water= 998 kgm-3

air =1.2kgm-3

kgm

Mass DensityMass Density

2 kg, 4000 cm3

Wood

177 cm3

45.2 kg

; mass m

Densityvolume V

Lead: 11,300 kg/mLead: 11,300 kg/m33

Wood: 500 kg/mWood: 500 kg/m33

4000 cm3

Lead

Same volume

2 kgLead

Same mass

Example 1:Example 1: The density of steel is The density of steel is 7800 7800 kg/mkg/m33. What is the volume of a . What is the volume of a 4-kg4-kg block block of steel?of steel?

4 kg3

4 kg;

7800 kg/m

m mV

V

V = 5.13 x 10-4 m3V = 5.13 x 10-4 m3

What is the mass if the volume is 0.046 m3?3 3(7800 kg/m )(0.046 m );m V

m = 359 kgm = 359 kg

Specific WeightSpecific Weight

]/[]/[ 33 ftlbformNg

• Weight per unit volume (e.g., @ 20 Weight per unit volume (e.g., @ 20 ooC, 1 C, 1 atm)atm)

waterwater = (998 kg/m= (998 kg/m33)(9.807 m)(9.807 m22/s)/s)

= 9,790 N/m= 9,790 N/m33

[= 62.4 lbf/ft[= 62.4 lbf/ft33]]

airair = (1.205 kg/m= (1.205 kg/m33)(9.807 m)(9.807 m22/s)/s)

= 11.8 N/m= 11.8 N/m33

[= 0.0752 lbf/ft[= 0.0752 lbf/ft33]]

Specific GravitySpecific Gravity

Ratio of fluid density to density of water @ 4oC

3/1000 mkgSG liquid

water

liquidliquid

Water SGwater = 1

Mercury SGHg = 13.55

Note: SG is dimensionless and independent of system of units

Specific GravitySpecific GravityThe specific gravity (or relative density) of a

material is the ratio of its density to the density of water (1000 kg/m3).

Steel (7800 kg/m3) r = 7.80

Brass (8700 kg/m3) r = 8.70

Wood (500 kg/m3) r = 0.500

Steel (7800 kg/m3) r = 7.80

Brass (8700 kg/m3) r = 8.70

Wood (500 kg/m3) r = 0.500

Examples:Examples:

31000 kg/mx

r

viscosity in fluid flowsviscosity in fluid flows

ViscosityViscosity• Viscosity, Viscosity, ,, is a measure of resistance to fluid flow as is a measure of resistance to fluid flow as

a result of intermolecular cohesion. In other words, a result of intermolecular cohesion. In other words, viscosity can be seen as internal friction to fluid viscosity can be seen as internal friction to fluid motion which can then lead to energy loss. motion which can then lead to energy loss.

• Different fluids deform at different rates under the Different fluids deform at different rates under the same shear stress. The ease with which a fluid pours is same shear stress. The ease with which a fluid pours is an indication of its viscosity. Fluid with a high viscosity an indication of its viscosity. Fluid with a high viscosity such as syrup deforms more slowly than fluid with a such as syrup deforms more slowly than fluid with a low viscosity such as water. The viscosity is also low viscosity such as water. The viscosity is also known as dynamic viscosity. known as dynamic viscosity.

Units:Units: N.s/m2 or kg/m/s N.s/m2 or kg/m/s

Typical values:Typical values: Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/skg/m/s

ViscosityViscosity

• Proportionality constant = dynamic Proportionality constant = dynamic (absolute) viscosity(absolute) viscosity

• Newton’s Law of ViscosityNewton’s Law of Viscosity

• ViscosityViscosity

• UnitsUnits

• Water (@ 20Water (@ 20ooC): C): = 1 = 1xx1010-3-3 N-s/mN-s/m22

• Air (@ 20Air (@ 20ooC): C): = 1.8 = 1.8xx1010-5-5 N-s/mN-s/m22

• Kinematic viscosityKinematic viscosity

V

V+dv

dy

dV

dydV /

2

2

//

/

m

sN

msm

mN

Kinematic viscosity: m2/s

1 poise = 0.1 N-s/m2

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

Newtonian and Non-Newtonian Newtonian and Non-Newtonian FluidFluid

Example:Air

WaterOil

GasolineAlcohol

KeroseneBenzeneGlycerine

Newton’s’ law of viscosity is given by;

dy

du

(1.1)

= shear stress

= viscosity of fluid

du/dy = shear rate, rate of strain or velocity gradient

• The viscosity is a function only of the condition of the fluid, particularly its temperature.

• The magnitude of the velocity gradient (du/dy) has no effect on the magnitude of .