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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
At the end of this topic student should:
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
At the end of this topic student should:
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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for your ttention