fluid mechanics 1 lecture 1 2009-10

8/7/2019 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

[email protected]


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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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Density 3 forms

2. Specific Weight (w)

Defined as the weight per unit volume (N/m3)

mgV

gw =


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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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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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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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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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Two types of viscosity

Absolute viscosity () Ns/m2

Dynamic viscosity ()

msmkgmNsmmNs2

2

3

2====


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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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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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Bulk modulus = Change in pressure/volumetric strain

dp=

V

dV

dpVK =


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d

VdV=

.

For water value of K doubles as pressure increasesfrom 1 to 3500 atmospheres


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d

VdV=

Units N/m2 - same as pressure

water 2.05109 N/m2

9 2 .

fluid mechanics 1 lecture 1 2009-10

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