topic 1- latest sem dec-mac 2014

8/13/2019 Topic 1- Latest Sem Dec-mac 2014

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BASIC FLUID MECHANICS

(ECW 211)

NURAKMAL HAMZAHBKBA 2.15

O13-5925330

EXT: 2637


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CONTENT

PROGRAM OUTCOMES

COURSE SYLLABUS

COURSE OUTCOMES

LESSON PLAN

COURSE ASSESSMENT


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PROGRAME OUTCOMESPO1 - Ability to acquire and apply basic knowledge of science,

mathematics and engineering.

PO2 - Ability to communicate effectively with technical personal

and the public.

PO3 - Ability to identify, formulate and solve engineering

problems.

PO4 - Ability to function on multi-disciplinary teams.

PO5 - Ability to function effectively as an individual and in a

group with leadership, managerial and entrepreneurial

capabilities.

PO6 - Understanding of the social, cultural, global andenvironmental responsibilities and ethics for sustainable

development.

PO7 - Recognising the need to undertake lifelong learning and

possessing/acquiring the capacity to do so.


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COURSE OUTCOMES

CO1 - Acquire and apply basic knowledge on various fluidproperties and problems related to fluid mechanics.

CO2 - Apply concept of hydrostatic pressure in determining forces

exerted by fluids on plane surfaces under static condition.

CO3 - Analyse concept of up thrust, buoyancy of objects immersedin fluids in determining the stability of floating bodies.

CO4 - Formulate and solve problems regards to the concepts of the

continuity, energy and momentum equations and flow

measurement in fluid mechanics.


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COURSE ASSESMENT

GRADING %

TEST 1 30%

SOFT SKILLS 10%

FINAL EXAMINATION 60%

TOTAL 100%


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COURSE ASSESMENT

QUESTION CHAPTER5 Questions

Question 1

Question 2

Question 3 Question 4

Question 5

Chapter 1Chapter 2Chapter 3Chapter 4Chapter 5

REMARKSDONTWRITE USING PENCIL, PLEASE WRITE USING PEN

PLEASE WRITE USING BALL POINT PEN RATHER THAN GEL PEN

BRINGS YOUR CALCULATOR DURING FINAL EXAMINATION SESSION

STANDARD MARKING ( BEWARE)

WRITE ALL UNITS/FORMULA.


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CH PTER ONE1.1 FLUID AS CONTINUUM

1.2 UNITS AND DIMENSION USED IN

ENGINEERING FLUIDS

At the end of this topic student should:

Be able to explainthe continuum concept of fluid. (CO1-PO1)

Be able to identifythe units and dimensionused in engineering

fluids.(CO1-PO3)


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WHAT IS

HYDRAULICS

WHAT IS

FLUIDMECHANICS

?

Mechanics of flui sIts that branch of engineering

science which deals with the

behaviour of fluid under the

conditions of rest & motion

Greek word HUDAR, means

WATER

Its that branch of engineeringscience deals with water ( at rest

or in motion)

Or its that branch of engineering

science which is based on

experimental observation of

water flow.

INTRODUCTION


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FLUID MECHANICS

FLUID MECHANICS is a study of the behavior

of liquids and gases either at rest (fluid

statics) or in motion (fluid dynamics).

The analysis is relate continuity of

massand energywith forceand

momentum.

FLUID is a substance which deformscontinuously under the action of shearing

force (however small it is may be)


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IMPORTANTOF FLUID

MECHANICSTO

ENGINEER

To determine the

stability of floating andsubmerged objects

pontoons, ships

To determine the

hydrostatic forces

dams

To determine flow and

energy losses in pipe

To design fluid

machinespumps

and turbines

To determine flow rate,

energy dissipation from

spillway and flow in

open channels such as

rivers

IMPORTANT OF FLUID MECHANICS


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DIFFERENCE BETWEEN SOLID AND FLUID

Have

preferredshape

Hard & noteasily

deformed

Cannotdeformedcontinuouslyunder shear

force

SOLIDDoes nothave anypreferredshape

Soft & easilydeformed

Deformedcontinuouslyunder shear

force

FLUID


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3 CONDITIONS OF FLUIDS

The study ofincompressible fluidunder static conditions(hydrostatics)

That dealing with thecompressible staticgases- aerostatics

STATICS

Deals with thevelocities,accelerations andpattern of flow only

Force and energycausing velocities andaccelerations are notdeal under this head.

KINEMATICS

Deal with therelationshipbetweenvelocities andaccelerations of fluidwith the FORCES @ENERGY causingthem.

DYNAMICS


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CONCEPT OF FLUID

In FLUID:

-The molecules can move freely but are constrained through a traction forcecalled cohesion.

-This force is interchangeable from one molecule to another.

For GASES:

-It is very weak which enables the gas to disintegrate and move away from itscontainer.

-A gasis a fluid that is easily compressed and expandsto fill its container.

-It fills any vessel in which it is contained. There is thus no free surface.

For LIQUIDS:

-It is stronger which is sufficient enough to hold the molecule together and canwithstand high compression, which is suitable for application as hydraulic fluid suchas oil.

-On the surface, the cohesion forms a resultant force directed into the liquid regionand the combination of cohesion forces between adjacent molecules from atensioned membrane known as free surface.


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1.1 FLUID AS CONTINUUM

Continuum mechanics and its concept

It is a branch ofmechanicsthat deals with theanalysis of the kinematicsand mechanicalbehaviour of materials modelled as a continuum.(eg. solids and fluids), (eg. liquids and gases)

A continuum concept assumes that the substanceof the body is distributed uniformlythroughout, andcompletely fills the space it occupies.

Fluid properties is depends on their molecularstructure.However, engineering applications hardlyanalyses fluids at molecular level.

It is the fluids bulk behavior of main concern in

engineering applications.


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CONTINUUM CONCEPTS

Atoms are widely spaced in the

gas phase.

However, we can disregard the

atomic nature of a substance.

View it as a continuous,

homogeneous matter with no

holes, that is, a continuum . This allows us to treat properties

as smoothly varying quantities.

Continuumis valid as long as sizeof the system is large in

comparison to distance between

molecules.


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Fluid as acontinuum

A continuous substancewhere quantities such as

velocity and pressure canbe taken as constant atany section irrespective ofthe individual fluid particle

velocity.


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PRESSURE

Pressure acts

perpendicular to the

surface and increases

at greater depth.

area

forcepressure

Pressureis the force per unit area, where the force is perpendicular to the area.

A measure of the amount of force exerted on a surface area

1 2 UNITS AND DIMENSION USED IN


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1.2 UNITS AND DIMENSION USED IN

ENGINEERING FLUIDS

WHAT IS

UNITS?

WHAT IS

DIMENSION

?

Standardized system ofmeasurements used todescribe the magnitude ofthe dimensionA properties that can bemeasured

Measurable properties used todescribe a body/systemThe standard element, in terms ofwhich these dimensions can bedescribed quantitatively assignednumerical values.


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VARIOUS SYSTEM OF UNIT

Parameter SI UNITS c.g.s system of unit Imperial units ( BritishGravitational system; EnglishUnits)

Length Meters (m) Centimeters (cm) Foot (ft)

Mass kilogram(kg) Gramme (g) Pound ( Ib)

Time Seconds (s) Seconds (s) Seconds (s)

Temperature

Degree Celcius(oC)

Degree Fahrenheit ( oF)

Theprimary quantitieswhich are also referred to as basic dimensions, such asLfor length, Tfor time, Mfor mass and Ffor force.

Student also expected to be familiar with the various systems of units used inengineering. These systems include :

As any quantity can be expressed in whatever way you like it is sometimes easy to become

confused as to what exactly or how much is being referred to. This is particularly true in the

field of fluid mechanics.


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DERIVED UNIT


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1.3 DENSITY, RELATIVE DENSITY

SPECIFIC WEIGHT, SPECIFIC GRAVITY,

SPECIFIC VOLUME AND VISCOSITY


Be able to apply basic knowledge of various fluid

properties.(CO1-PO1)Be able to acquire various fluid properties in identify and solving

problems related to fluid engineering problem.(CO1-PO3)

Be able to formulate the relationship between shear, stress and

velocity gradient from the Newtonslaw of viscosity. (CO1-PO3)


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1. DENSITY

Regardless of form (solid, liquid,

gas) we can define how much mass

is squeezedinto a particular space

Densityof a material is defined by

the amount of matterper unit

volume.

Density of material may be referred

to in many ways.


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1.1 MASS DENSITY,

Definition

Density of a fluid, , is defined as the mass per unit volume It is denoted by the Greek

symbol, .

==V m3kgm-3

kgm

water= 1000 kgm-3

air=1.23 kgm-3


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1.2 SPECIFIC WEIGHT,

Definition

Specific weight of a fluid, , is defined as the weight of the fluid per unitvolumeForce exerted by gravity, g, upon unit volume of substance

=wV

= g

Units: N/m3

= the density of the material (kgm-3)g = acceleration due to gravity (ms-2)

Water =9.81 X 103N/m3

1 3 RELATIVE DENSITY


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1.3 RELATIVE DENSITY

@ SPECIFIC GRAVITY, SG

Definition

A ratio of the specific weight of a substance to the specific weight ofwater at standard temperature (4C) and atmospheric pressure.

Units: dimensionless

Cw

s

Cw

sSG

4@4@

Unit is none, since ratio is a pure number.SGis a dimensionless quantity


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2. SPECIFIC VOLUME, V

Definition

The reciprocal of the mass density i.e. the volume per unit massor theinverse of density

Units: m3/kg

v = 1/ = V/m


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Dynamic

Kinematic

3. VISCOSITY


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3.1 DYNAMIC VISCOSITY,

Definition

Dynamic viscosity, , is defined as the Shear force per un it area(shear stress, ) needed to drag a layer of fluid with a unit velocity past

another layer at a unit distance away from it in the fluid

Measure of internal friction of fluid particles

Molecular cohesiveness

Resistance fluid has to shear (or flow)

Units:

Water:

Air:


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3.2 KINEMATIC VISCOSITY,

Definition

It defined as the ratio of dynamic viscosity to mass density

v

= dynamic viscosity= mass density

Will be found to be important in cases

in which significant viscous and

gravitational forces exist.

Typical values:

Water = 1.14x10-6m2/s;Air = 1.46x10-5m2/s;

Units: m2/s or stokes (10,000 St = 1m2s-1)


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NEWTON LAW OF VISCOSITY

When fluid moves, it generates shearing stress

If no movement between the moving fluid particles no shearstresses developed

Fluid particles which in contact with solid boundaries will adhere tothese boundaries will have same velocities as the solidboundaries

Movement of a fluid over solid boundary can be visualized aslayers of a fluid moving one above the other.

The velocity of fluid layers increases as the distance from the solidboundary increases

y

vFlowing passing over a solid boundary

TEMPERATURE VS VISCOSITY


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TEMPERATURE VS VISCOSITY(LIQUID AND GASES)

Liquids

Gases

Viscosity

Temperature

Viscosity is caused by the cohesive

forces between the molecules in liquidsand by the molecular collisions in

gases, ant it varies greatly with

temperature.

The viscosity of liquid decreases with

temperature, whereas the viscosity of

gases increases with temperature. This is because in a liquid the

molecules possess more energy at

higher temperature and they can

oppose the large cohesive

intermolecular forces more strongly.

As a result, the energized liquid

moleculescan move more freely.

In gases, the intermolecular activities

are negligibleand the gas molecules at

high temperature move randomly at

higher velocity.


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Viscosity in gases

Due to intermolecular collisionbetween randomly moving particles

For gas, temperature , amount ofintermolecular collision , viscosity

Viscosity in liquid

Due to intermolecular collisionbetween liquid particles

For liquid, temperature ,intermolecular collisionis weakened,viscosity

VISCOSITY IN GASES & LIQUIDS


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NEWTON LAW OF VISCOSITY

It is important to evaluate the magnitude of the shearstress generated by the moving fluid

NewtonsLaw of viscosity: = shear stress

= viscosity of fluid

du/dy = shear rate, rate of strainor velocity gradient

dy

du (1.1)

The viscosity is a function only of the condition of the fluid, particularly itstemperature.

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

NEWTONIAN &


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NEWTONIAN &NON NEWTONIAN FLUID

Fluid Newtons lawof viscosity

Newtonian fluidsobey refer

Example: Air, Water, Oil, Gasoline, Alcohol, Kerosene, Benzene, Glycerine

FluidNewtons law

of viscosity Non Newtonian fluids

not obey refer


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NON NEWTONIAN FLUID

*The slope of a curve at a point is the apparent viscosity of the fluid at that point


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EXAMPLE 1

1. The lower plate as shown below is fixed while the upper

one is free to move under the action of a mass of 50g.Castor oil with absolute viscosity 650 x 10-3 Ns/m2

occupies the space between these two plates. The area

of contact of the upper plate with the oil is 0.7m2, find the

velocity of the upper plate when the distance separating

the plates is 0.5cm.

Hint:

Answer: du = 5.4mm/s

A

F

dy

du

= 650 x 10-3Ns/m2 y =

0.5cm

m=50g

pulley

Stationary

EXAMPLE 2


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2. A vertical gap 25mm wide of infinite extent contains oil

of relative density 0.95 and viscosity 2.4Pa.s. A metalplate 1.5m x 1.5m x 1.6mm, weighing 55N is to be lifted

through the gap at a constant speed of 0.06 m/s.

Determine the force required.

Hint:

Answer: F = 110.4 N

0.06m/s

dydy

F

W

25 mm

A

F

dy

du

EXAMPLE 2

EXAMPLE 3


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EXAMPLE 3

3. Crude oil at 20C fills the space between two concentric

cylinders of diameters 150mm and 156mm respectively.Both cylinders are 250mm in height. If the inner cylinder is

to be rotated at a constant speed of 12 rev/min while

keeping the outer cylinder stationary, calculate the torque

required. The fluid properties of the crude oil at 20C are:

i) specific gravity = 0.86

ii)kinematic viscosity = 8.35 x 10-6m2/s

Hint: Linear velocity,

Answer: T = 0.002NmrFT

A

F

dy

du

rv

EXAMPLE 4


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EXAMPLE 4

4. A vertical cylinder of diameter 180mm rotates

concentrically inside another cylinder of diameter181.2mm. Both the cylinders are 300mm high. The

space between the cylinders is filled with a liquid whose

viscosity is unknown. Determine the viscosity of the fluid

if torque of 20 Nm is required to rotate the inner cylinder

at 120 rpm.

Answer : =0.696 Ns/m2


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1.4 COMPRESSIBILITY AND BULK MODULUS,

VAPOUR PRESSURE, SURFACE TENSION,

AND CAPILLARITY


Be able to define thefluid parameters.(CO1-PO1)

Be able to apply bulk modulus, surface tension and capillarity insolving fluid engineering problem.(CO1-PO1)

Be able to use the Newtons law of viscosity which are the

relationship of shear stress and velocity gradient in solving fluid

engineering problems (CO1-PO3)

4 SURFACE TENSION


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4. SURFACE TENSION,

Surface tension

defined as the force acting a unit length ofa line drawn in the liquid surface

Surface tension

Surface tension tend to reduce the surface

area of a body of liquid The internal pressure within the droplet, p

and the surface tension forces,must be inequilibrium.

p


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Surface tension

Taking vertical equilibrium of the forces actingon the droplet

The magnitude of surface tension forces arevery small compared to other forces

Normally are neglected

22 rpr

rp

2

2

pr Units : N/m

5 VAPOR PRESSURE P


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5. VAPOR PRESSURE, Pv

Vapor pressure

defined as the pressure at which a liquidturns to vapour

thepressure exerted by its vapor in phaseequilibrium with its liquid at a giventemperature

Themolecules which moves above thesurface of the liquid exert pressure in theconfined surface

Vapor pressure

Pvapour= P saturat ion

Units: N/m2 or Pascal

6 CAPILLARITY


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6. CAPILLARITY

When a liquid comes into contact with a solid surface:

- Adhesion forces: forces between solid and liquid- Cohesion forces:forces within liquid

If cohesive forces > adhesive forces, the meniscus in a glass tube

will take a shape as in figure (a) and (b).

Figure (a) and (b)


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Capillary effectis

the riseor fallof a

liquid in a small-

diameter tube

gdh

cos4

grh

cos2

dh

cos4@ @

Units= m @ mm

where h= height of capillary rise (or depression)

= surface tension

= wetting (contact) angle

= specific weight of liquid

r= radius of tube

7. COMPRESSIBILITY &


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7. COMPRESSIBILITY &BULK MODULUS

Definition

The change of pressure corresponding to frictional changein volume of fluid where temperature remains constant

Gases are much more compressible compared to liquids

Liquids are considered incompressible

The compressibility of a fluid is expressed by its bulk modulus ofelasticity, K, which describes the variation of volume withchange of pressure, i.e.

Typical values : Water = 2.05x109N/m2; Oil = 1.62x109N/m2

strainvolumetricpressureinchangeK

/pK

VdVpK/

Units: N/m2

EXAMPLE 6


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6. 1 When the pressure exerted on a liquid isincreased from 550 kN/m2 to 1000 kN/m2, the

volume is decreased by 1%. Determine the bulk

modulus of the liquid.

Answer: K = 45x106N/m2

EXAMPLE 6


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6.3 Determine the bulk modulus of a liquid if itundergoes a 0.1% decrease in volume when

subjected to a pressure change from 100kPa to

6.5Mpa.

Answer: 6.4GPa

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