Download - fluid mechanics 1 lecture 1 2009-10
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Fluid Mechanics 1
Simon Tait
ro essor o v ng neer ngUniversity of Bradford
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Fluid Mechanics 1
Aim:
o un erstan t e as c concepts t at escr ethe mechanical behavior of fluids.
Learning Teaching & Assessment Strategy:1 Lectures to introduce and develo fundamental
theories and describe application;
(2) Example classes to provide explanation ofsupp e u or a ques ons;
(3) Laboratory classes to develop basic skills.
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Fluid Mechanics 1
Expected workload:
tu y ours:Lectures: 22.00
.Formal Exams: 2.00Laborator /Practical: 3.00
n epen en u y: . rs wee
.
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Fluid Mechanics 1
Assessment:
o u e ssessment:Examination - closed book at end of semester, 100%
Duration - 2.0 hours
Descriptionxam w compu sory ques ons, one ase onlaboratory activities
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Fluid Mechanics 1
Syllabus
. n s an mens ons2. Properties of fluids3. Hydrostatics forces on immersed surfaces
4. Buoyancy forces5. Stability of floating bodies6. Pressure Measurement7. Fluids in motion laminar and turbulent flows8. Principle 1 - Mass continuity
10. Principle 3 Momentum Conservation
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Fluid Mechanics 1
Week 1-6: Monday 1600-19:00 Weeks 7-12 Monday 1400-
1700 Note no classes in week 8
You will gain most benefit from the Example Classes if you havecompleted the tutorial sheets beforehand.
Laboratory experiment schedules:
Details will be released in week 4. One exam question will bebased on the work of the laboratory session.
Points to be noted:(1) Class registration is required for the lectures, example
classes and laboratory experiments to comply with the.
(2). Location: Chesham B1.07. E-mail: [email protected] first!.
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Week Activity Content of Activity Expected StudentProgress
1 Lecture Introduction to module;consideration of units anddimensions, properties of fluids(2 hours)
Tutorial
Handed out
2 Lecture Hydrostatics forces on
immersed bodies (2 hours)TutorialSheet 2
Handed out
3 Lecture
Buoyancy forces and stabilityof immersed bodies (2 hours)
Example
Complete
Sheets 1 and 2 (1 hour)
1 and 2 beforeExample Class
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Week Activity Content of Activity ExpectedStudent
4 LecturePressure Measurement(1 hour)
Formative
Sessionxam sty e quest on
Tutorial Sheet 3
5 Lecture Pressure Measurementcontinued. Fluids inmo on. am nar anturbulent flows. (2 hours)
6 Lecture
continuity
Tutorial Sheet 4
Handed out
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Fluid Mechanics 1
Dimensions and Units
3 fundamental dimensions:
Length (L), mass (M), time (T)
Fundamental units - metres m kilo rams k seconds s
Always use these units
Other units are based on these three fundamental units
. . =
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Fluid Mechanics 1
Dimensional Homogeneity
For dimensional homogeneity both sides of an equation musthave the same units.
All terms of an equation must have the same units.
Careful consideration of units can confirm that an equation iscorrect.
or examp e; ens y - g m
mmassVvolume
.
fundamental units (kg, m and s).
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Fluid Mechanics 1
Fluid mechanics is a sub set of Mechanics concerned with the
statics and dynamics of liquids and gasses.
It is governed by the three principles used in general mechanics
1. Conservation of mass flow (mass continuity).
2. Conservation of ener
3. Conservation of momentum
Generally the difficult part of fluid mechanics is deciding which ofthe above principles is applicable to a particular engineeringproblem.
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Fluid Mechanics 1
Difference between solids and fluids:
1. Within the elastic limit for a solid, the strain is proportional tothe applied stress, whereas for a fluid the rate of strain is
proportional to the stress.2. For a solid the strain is independent of the time of
app ca on o e orce.
3. For a solid, within the elastic limit, deformation is reversible.
stress is applied. It does not recover its original shape whenthe stress is removed.
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Fluid Mechanics 1
Fluids can be liquids or gasses
a change in shape, but will flow under their own weight andtake up the shape of the container.
This change in shape is the result of shearing forcesandtherefore shearing forces occur in movingfluids.
a u s a res en ere are no s ear ng orces.
This splits fluid mechanics into two:
1. Fluids at rest - hydrostatics
2. Fluids in motion
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Fluid Mechanics 1
Fluids can be liquids or gasses:
What is the difference between a liquid and a gas?
Liquids have a definite volume, they are very difficult tocom ress and form a free surface between the li uid and theair (gas) above it.
Gases are easily compressible and will easily expand to fill acontainer without forming a free surface.
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Fluid Mechanics 1
n eng neer ng e erm y rau cs s some mes oose y useto cover the whole field of fluid mechanics it can be spilt into
two main topics:
1. Hydrostatics
Is concerned with water at rest. It will readily give exact
solutions.2. Hydrodynamics
Is concerned with the behaviour of water in motion. Itsstudy began towards the end of the 17th Century and during
th thexpressions for a viscous fluid. These theoreticalexpressions need to be modified using empirically obtained
.
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Fluid Mechanics 1 Properties of Fluids
Density 3 forms
1. Mass density ()
Defined as the mass per unit volume (kg/m3)
mmassVvolume
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Fluid Mechanics 1 Properties of Fluids
Density 3 forms
2. Specific Weight (w)
Defined as the weight per unit volume (N/m3)
mgV
gw =
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Fluid Mechanics 1 Properties of Fluids
Density 3 forms
3. Specific gravity (or relative density) (s)
Defined as the ratio of the weight of a substance to the weight ofan equa vo ume o wa er a .
waterforwaterforws
==
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Fluid Mechanics 1 Properties of Fluids
a s e erence e ween mass m an we g w
It is important that you have a clear understanding between thedifference between mass and weight (force).
Mass represents the amount of matter in a body or volume ofli uid. This is a constant
Weight varies according to the local value of gravity (g). This is
potentially variable
mw =
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Fluid Mechanics 1 Properties of Fluids
a s e erence e ween pressure an we g w
The average pressure (P) is defined as the weight (w) appliedover an area (A).
wP =
Pressure has units of Newtons per metre squared (N/m2)
Sometime these are called Pascals (Pa)
1Pa = 1N/m2
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Fluid Mechanics 1 Properties of Fluids
a s scos y
The shear stress () is related to the velocity gradient betweenadjacent fluid layers (du/dy).
dydu
dydu =
Where is the coefficient of absolute viscosity
has units of Ns/m2
, ,
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Fluid Mechanics 1 Properties of Fluids
Two types of viscosity
Absolute viscosity () Ns/m2
Dynamic viscosity ()
msmkgmNsmmNs2
2
3
2====
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Fluid Mechanics 1 Properties of Fluids
Values of viscosity dependent
on temperature
Absolute viscosit Ns/m2
Dynamic viscosity () m2/s
Water at 20C Ns3m
2
2
s101
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Fluid Mechanics 1 Properties of Fluids
Bulk Modulus (K) Measure of Compressibility
All materials whether solids, liquids or gasses arecompressible
Remember liquids are difficult to compress but not
ons er a cu e o u su ect to a c ange npressure dpon all its surfaces.
by dV
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Fluid Mechanics 1 Properties of Fluids
Bulk Modulus (K) Measure of Compressibility
Bulk modulus = Change in pressure/volumetric strain
dp=
V
dV
dpVK =
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Fluid Mechanics 1 Properties of Fluids
Bulk Modulus (K) Measure of Compressibility
d
VdV=
.
For water value of K doubles as pressure increasesfrom 1 to 3500 atmospheres
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Fluid Mechanics 1 Properties of Fluids
Bulk Modulus (K) Measure of Compressibility
d
VdV=
Units N/m2 - same as pressure
water 2.05109 N/m2
9 2 .