Lecture 1 Course overview and fundamental principlesLearning Teaching & Assessment Strategy ... Flow...

ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2

Lecture 1Course overview and fundamental

principles

Dr Tim Gough: [email protected]


Aims

To examine the principles of fluid flow, with an emphasis on the analysis of flows that are common in engineering fields.

Learning Teaching & Assessment Strategy

Theoretical understanding and problem solving through large lectures, staff‐led tutorial/example class and directed study, practical skills of data interpretation and justification gained from lab sessions, assessed by examination.

Fluid Mechanics 2 – ENG2038M

Overview of course

• Best way of passing FM2 is to attend everything, read everything and do all tutorials!


Intended Learning Outcomes

On successful completion of this module you will be able to...

1. Understand and review more general flows and principles, and examine their applications to common engineering fields.

2. Interpret and justify laboratory experimental data by using available information and propose solutions to problems arising from that analysis.

Assessment

• 100 % formal examination

• Closed book 2 hours duration

• Four compulsory questions and one based on laboratory activities.

Overview of course


Study hours

Lectures 22 hours

Seminars/tutorials 10 hours

Laboratory/practical 4 hours

Examination 2 hours

Directed study 62 hours

Total 100 hours

• i.e. The major part of this course is done away from the lecture theatre and laboratories.

• Use library and internet resources for this directed study element.

• Assessment is purely by examination.

• This consists of four compulsory questions and one based on labs.

Overview of course


General information (1)• Attendance compulsory.

• Registers will be taken through new swipe card system.

• All slides will be put on Blackboard at the end of each lecture in pdfformat.

• This may include embedded videos (save to disk!) but may just containlinks to websites and DVD resources (in library).

• Tutorial sheets should be completed in tutorial session on Thursday andoutside class time. Completed questions brought to each lecture.

• Laboratory classes will be arranged shortly when final numbers havebeen set.

• You will need access to a decent scientific calculator for all classes (notthe one on your phone please as you can’t use this is assessments).


Fluid Mechanics 1 (ENG1032M) syllabus

• Units and dimensions• Properties of fluids• Hydrostatics ‐ forces on immersed surfaces• Buoyancy forces• Pressure measurement• Stability of floating bodies• Fluids in motion ‐ laminar and turbulent flows• Principle 1 ‐Mass continuity• Principle 2 ‐ Energy Conservation ‐ Bernoulli`s equation• Principle 3 ‐Momentum Conservation

Laboratory ‐ Use of energy principles to measure flow rate


• Understanding of fundamental principles: Flow acceleration, continuity and energy equations and their applications.

• Reynolds number and head losses in real flows.

• Features of laminar and turbulent flows in pipes and conduits with velocity profiles, pressure drops, friction factors and Moody diagram, and turbulence mechanics.

• Pipe systems including pipes in series, pipes in parallels and branching pipelines.

• Pipe connections with pump and siphon.

• Dimensional analysis and similitude.

• Momentum equation and fluid force on structures.

Fluids 2 syllabus (may not be in this order)

This can be also found on University modcat system


Reading list – possible selection

• Fluid Mechanics 6th edition: Douglas, Gasiorek, Swaffield and Jack.• http://www.amazon.co.uk/Fluid‐Mechanics‐Dr‐J‐

Douglas/dp/0273717723/ref=sr_1_1?ie=UTF8&qid=1376323678&sr=8‐1&keywords=fluid+mechanics+douglas

• Fluid Mechanics 7th edition: Munson, Okiishi, Huebsch and Rothmayer.• http://www.amazon.co.uk/Fluid‐Mechanics‐Bruce‐R‐

Munson/dp/1118318676/ref=sr_1_2?s=books&ie=UTF8&qid=1376323798&sr=1‐2&keywords=fluid+mechanics+munson


• Multimedia Fluid Mechanics 2nd edition: Homsy et al.• http://www.amazon.co.uk/Multimedia‐Fluid‐Mechanics‐DVD‐ROM‐

Homsy/dp/0521721695/ref=sr_1_1?s=books&ie=UTF8&qid=1376323936&sr=1‐1&keywords=fluid+mechanics+homsy

Reading list – possible selection

• However, Fluid Mechanics 2 is mainly based on Newtonian Fluid Mechanics.

• Isaac Newton published Principia Mathematica in 1687.

• Hence lots of other books are (cheaply) available (White, Massey etc) and any edition will do!


Contact and communication

Formal contact hours

• 1x two hour lecture per week – Tuesday 11 am Chesham B4.02

• 1x one hour tutorial session per week – Thursday 11 am Richmond Workshop WB24

• 1x laboratory class – to be timetabled shortly

Other communication

• All information (lecture notes, tutorials etc) on to Blackboard after lecture

• Announcements will be made via Blackboard and e‐mail (check!)

• If you want a meeting, arrange by e‐mailing [email protected]


Contact and communication

• Please note that there will be no tutorial sessions in week 3 (03‐10‐13) and week 7 (31‐10‐13).

• Also there will be no lecture in week 7 (29‐10‐13).

• These are due to external research commitments.

www.esrf.eu www.diamond.ac.uk

• Extra tutorial questions will be set. Please keep an eye on your email!!!


Lecture 1Fundamental principles

Dr Tim Gough: [email protected]


Basic physical concepts

• A fluid is defined as a substance that continually deforms under anapplied shear stress.

• Fluids flow under applied stresses and will take the shape of acontainer.

• Broadly there exist three phases of matter – solids, liquids andgases.

• Fluids consist of liquids and gases.

Solids Liquids Gases

Fluids


Differences between solids and fluids

1. Within the elastic limit for a solid, the strain is proportional to the applied stress, whereas for a fluid the rate of strain is proportional to the applied stress.

2. For a solid the strain is independent of the time of the force’s application.

3. For a solid, within the elastic limit, deformation is reversible. However, for a fluid, the material will continue to flow as long as the stress is applied. A fluid does not recover its original shape when the stress is removed.

Elastic solids

Newtonian fluids


Fluid mechanics• Typical fluids include:

• Air, water, oils, honey, molten polymers, glass(?).

• Typical applications of fluid mechanics:

• Flight, sailing, car aerodynamics, wind loadings on buildings, weather prediction, river flows, waves breaking, engines and lots lots more.


Fluid mechanics

Gas bottles

Water in beaker Windermere

Free surface• Fluids can be either liquids or

gases.

• Liquids have a defined volume. • They are very difficult to

compress.• They form a free surface

between the liquid and the gas (air) above the liquid.

• Gases are easily compressible and will expand to fill a container without forming a free surface.


Fluid mechanics

• Similarly to solid mechanics, fluid mechanics can be divided into two parts:

• Fluid staticsFluids at rest (i.e. not moving)

• Fluid dynamicsFluids in motion


Fluid dynamics

• The two most commonly studied (and useful) fluids are water and air since they occur in such abundance in nature.

• Understanding how the atmosphere works, how rivers and seas flow are all critical in:

Hydraulics (water)

• Hydrostatics – concerned with water at rest.

• Hydrodynamics – concerned with behaviour of water in motion.

Air

• Aerodynamics – concerned with behaviour of air in motion.


Fluid mechanics

Nanotechnology and microfluidics


Fluid mechanics

Motion of animals


Fluid mechanics

Everyday occurrences


Fluid mechanics

Car aerodynamics


Fluid mechanics

Flight mechanics


Fluid mechanics

Meteorology ‐ Hurricane Katrina – near New Orleans – August 2005


Fluid mechanics

Earth's atmosphere – one month's worth of data


Fluid mechanics

Jupiter – great red spot


Fluid mechanics• Most of these examples are of fluid mechanics in action in the

natural world.

• As engineers we need to both understand the effects of these processes but also we want to control and use them to our advantage.

• i.e. We need to engineer a solution involving fluid mechanics to provide us with useful work.

To affirm that the airplane is going to revolutionize the future is to be guilty of the wildest exaggeration.

Scientific American, 1910

‘No balloon and no aeroplane will ever be practically successful.’

Lord Kelvin, 1902


Flight

Chanute’s biplane hang glider ‐ 1896 Wright flyer I – 17th December 1903Flight time 59 seconds !!!

Rumpler Taube (dove) from 1910

Zanonia Macrocarpa seeds


Handley Page V/1500 ‐ 1918Sopwith Triplane ‐ 1916

Concorde ‐ 1969Spitfire ‐ 1936

Flight


Vestas V27 wind turbine

Nysted offshore wind farm ‐ Denmark

Hydroelectric power plant – NY, USA Tidal power – N. Ireland

Power generation / conversion


Transport

Bugatti type 51 (1933)CD = 0.74 CDA = 0.96

VW type 1 beetle (1938)CD = 0.48 CDA = 0.87

Jaguar D type (1955)CD = 0.49 CDA = 0.59

Citroen DS (1957)CD = 0.37 CDA = 0.81

VW microbus (1958)CD = 0.45 CDA = 1.04

Ford Sierra (1982)CD = 0.34 CDA = 0.67


Ground transport

Mercedes Benz T80 ‐ 1939


Ground transport

Brabham BT‐46B fan car ‐ 1978 Ducati wind tunnel

See http://www.bloodhoundssc.com for further details BMW Sauber F1 studied using Ansys Fluent


Ground transport

Flow patterns in 4‐stroke internal combustion engine(modelled using Ansys Fluent 6.3)


Rolls Royce Avon 200 gas turbine

Rolls Royce Bergen C‐gas engine

Other turbines / engines


• Outflow from Glen Canyon Dam, Arizona, US mfm 38


• Coupling between flowing fluids andsolid bodies can have disastrousconsequences.

• Tacoma Narrows Bridge WashingtonState, US opened June 30th 1940 .World’s third largest suspensionbridge.

• Bridge unaffected by winds over 50mph. On the 7th of November steadywinds of about 40 mph werepresent.

Bridge design


Bridge design

November 7th 1940


Interactions


Density

• Density, , is the mass per unit volume of a material.

• It's measured in kg/m3.

Water = 1000 kg/m3

Air = 1.2 kg/m3

Steel = 7700 kg/m3

Densities of some common materials

• Sometimes expressed as specific weight (g) or specific gravity whichis the ratio of material density to that of water (different units).

Density = mass / volume


• We usually deal with density fairly simplistically but remember that temperature, pressure and relative humidity all play a big part in this...

Density

• How does density change with temperature ?

• How does density change with pressure (or height)?

International standard atmosphere


Density

• Clearly the other key factor is the fluid itself.

• Common material densities include (at 20 oC and 1 atmosphere):

Fluid Density (kg/m3)

Water 998

Petrol 670

Ethyl alcohol 790

Olive oil 900

Sea water 1030

Glycerin 1260

Mercury 13550

• So it is critical when studying a problem to use the correct density at the correct temperature, pressure etc.


• Though we will be dealing with fluids of constant density during this module, we need to be aware that …


Viscosity


Viscosity

• Viscosity is a measure of the resistance of one layer of fluid to movement over the neighbouring layer.

• Similar in some ways to friction for solids.

• Though small for air it is a very important property and gives rise to many phenomena in flight and aerodynamics.

Some typical viscosities

Fluid Viscosity (Pa.s)

Water (at 25oC) 8.90 x 10‐4

Air (at 25oC) 1.86 x 10‐5

Olive oil 0.081


Viscosity


Viscosity – for a Newtonian fluidViscosity

is shear stress (in N/m2) is viscosity (in Ns/m2 or Pa.s)V is velocity (in m/s)y is distance (in m)

• Viscosity is normally given the symbol,

• It is defined by:

is simply the change in velocity with distance.

This is known as the strain rate and has units of 1/s.


Viscosity

• Typically viscosity is expressed in two forms – it is very important to know the difference between these:

Dynamic viscosity Kinematic viscosity

• Here is the dynamic viscosity and has the SI unit of Pa.s.

• Can also be expressed as Poise, centiPoise and many others.

Fluid Dyn. viscosity (Pa.s)

Water (at 25oC) 8.90 x 10‐4

Air (at 25oC) 1.86 x 10‐5

Olive oil 0.081

• Kinematic viscosity, , is simply the dynamic viscosity of the fluid divided by the density. It has SI units of m2/s.

Fluid Kin. viscosity (m2/s)

Water (at 25oC) 8.71 x 10‐7

Air (at 25oC) 1.57 x 10‐5

Olive oil 9.53 x 10‐5


Increasing temperature

Mineral oil 15W40 rheology

Viscosity measurements


Mineral oil 15W40 rheology

Viscosity measurements


Viscosity

Note logarithmic y axis

• Clearly the kinematic viscosity also varies significantly with pressure and temperature.

• Because of the complex interplay between density and dynamic viscosity of fluids, kinematic viscosity typically increases with temperature for gases and decreases with temperature for liquids.


Viscosities of common engineering fluids

Fluid Dynamic viscosity (Pa.s)

Air 1 x 10‐5

Water 1 x 10‐3

Mercury 1.5 x 10‐3

Olive oil 0.1

Glycerol 1.5

Honey 10

Bitumen 1 x 108

Molten glass 1 x 1012

• There are 17 orders of magnitude on this table.

• As engineers we may be in charge of using any of these fluids (and many more...).


Viscosity of non‐Newtonian fluids

Qualitative flow curves for various fluids

• Newtonian fluids exhibit a constant viscosity independent of shear rate.

• The viscosities of Non‐Newtonian fluids (such as blood, heavy oils, molten polymers and lots more) may either increase or decrease with increasing shear rate.

• Clearly these values are also dependent on temperature, pressure and other variables as well (very complicated very quickly).


Viscosity of non‐Newtonian fluids

Frequency sweep at varying T for EVA copolymer

Increasing T


Pressure


Pressure

Pressure is defined as force per unit area:

• In SI units this is measured in Newtons per metre2 (N/m2).

• This unit is also known as a Pascal (Pa).

• It can also be expressed in terms of bars or pounds per square inch(psi).

Pressure = force / area


Pressure

Q ‐What pressure does each exert on the floor ?

ElephantMass = 5000 kg

One foot area = 0.142 m2

Victoria BeckhamMass = 45 kg

One heel area = 0.0001 m2


P = 1250 x 9.81 / 0.142P = 86356 N/m2

P = 22.5 x 9.81/0.0001P = 2207250 N/m2

So Victoria Beckham applies 25 times the pressure of the elephant !!!

Pressure

ElephantMass = 5000 kg

Foot area = 0.142 m2

Victoria BeckhamMass = 45 kg

Heel area = 0.0001 m2


Typical pressure distribution around car

Wall pressure variation over car


Wall pressure variation over car

• Note high pressure at front of car.

• Low pressure over roof of car.


Measuring pressure

Pressure regulator

Aneroidbarometer

U‐tube manometer

And others…


Piezometers and static pressure

• If fluid is at rest it still exerts a pressure.

• This is called the absolute static pressure and is defined as:

Patmos. is atmospheric pressure (N/m2) is density of measuring fluid (kg/m3)g is gravitational acceleration (m/s2)h is height of fluid column (m)

This is the absolute static pressure.

h is also known as the ‘head’ of fluid

.


Static pressure

• The pressure at a point in a fluid in equilibrium is due partly to the atmospheric pressure at the free surface and partially due to the weight of the fluid.

• The pressure above atmospheric pressure is called the gauge static pressure and is defined as:‐

.


Piezometers

• The simplest form of pressure measuring device is the pressure tube or piezometer.

• This simply consists of a single vertical tube, open at the top, inserted into a pipe or vessel containing liquid under pressure which rises in the tube to a height depending on pressure.

• When the top of the tube is open to the atmosphere, the measured pressure is the ‘gauge’ pressure.

• Q ‐What is the maximum gauge pressure of water that can be measured by a piezometer tube 2m high?


Piezometers

• Q ‐What is the maximum gauge pressure of water that can be measured by a piezometer tube 2m high?

hmax = 2 metreswater = 1000 kg/m3

g = 9.81 m/s2

Q – What if the fluid was mercury (Hg = 13600 kg/m3?)

. /


1 standard atmosphere is 101325 N/m2 (or Pascals)

• Suppose this diver is 100m below the surface.

• What is:a) the total static pressureb) the gauge static pressure

• Assume the density of the sea water is 1025 kg/m3.

Pressure at depth


= 101325 + (1025 x 9.81 x 100)= 1106850 N/m2

= 1106.85 kPa

= 1025 x 9.81 x 100= 1005525 N/m2

= 1005.53 kPa

Pressure at depth

.


• For a non‐viscous flow (known as inviscid) along a streamline Bernoulli related pressure and velocity by:

ps is the static pressure (N/m2) is the fluid density (kg/m3)z is height above a reference plane (m)V is the fluid velocity (m/s)

What about when the fluid is moving ?

This is known as Bernoulli's theorem.


Bernoulli's theorem

• For the flows we will look at the change in height z is negligible so wecan reduce this to:

• What this tells us is that:

• If we raise the static pressure we lower the velocity.

• If we lower the static pressure we increase the velocity.


Bernoulli's theorem

• The two terms are called the static pressure (as we discussed earlier) and the dynamic pressure.

• Dynamic pressure is defined as:‐

• So Bernoulli states that static pressure + dynamic pressure is constant along a streamline.


The Reynolds number


Reynolds number

Reynolds number is the ratio of inertial to viscous forces in a flow

Inertial forces:We know that inertial (i.e. dynamic) pressure is:

We can say that inertial force is: So remembering that:

12


Reynolds number

• Viscous forces:

• These are generated when the fluid (air) is sheared.

• So for a Newtonian fluid (including air and water) we've seen that shear stress is:

And we know that stress has the same units as pressure (Pa or N/m2).



Reynolds number

where: is density in kg/m3

V is velocity in m/sL is a length in m is viscosity in Pa.s



Reynolds number

• So what are the units of Reynolds number?

• Using the previous definitions work out what these are.

is density in kg/m3

V is velocity in m/sL is a length in m is viscosity in Ns/m2

Units is kg/m3

V is m/sL is m is kgms/s2m2

It has no dimensions !!!


Non‐dimensional numbers

Reynolds number (Re) – ratio of viscous to inertial forces

• Other important non‐dimensional numbers:

• Mach number (M) – inertial forces to elastic forces.

• Froude number (Fr) –inertial to gravitational forces.

And lots more!!!

See http://en.wikipedia.org/wiki/Dimensionless_number for some of them.


Reynolds experiment

So why is Reynolds number important ?

Let's look at the flow of water through a pipe of diameter D

Flow velocity VD

• Here the main length scale is the diameter of the pipe, D, so we rewrite the Reynolds number as:


Reynolds experiment


Reynolds number

Low Reynolds number


Reynolds number

Medium Reynolds number


'High' Reynolds number

Reynolds number


Critical Reynolds number for pipe flow

• Remembering the definition ofReynolds number:

• Reynolds worked out that, for pipe flow, there existed a critical valueof Re:

If Re < 2000 the flow is laminar

If 2000 < Re < 4000 the flow is transitional

If Re > 4000 the flow is turbulent

Nearly all flows of engineering interest are turbulent.


Critical Reynolds number

Q. An air conditioning pipe of 2.5 metres diameter transports exhaust gas at a fully developed velocity of 10 m/s calculate the Reynolds number.

• Is this laminar, transitional or turbulent?

• Here we take the diameter of the pipe to be the characteristic length scale of the flow.

Assume gas density is 1.25 Kg/m3

and viscosity is 0.001 Ns/m2.



Re = 1.25 x 10 x 2.5 / 0.001

Re = 31250

Turbulent flow

Q. An air conditioning pipe of 2.5 metres diameter transports exhaust gas at a fully developed velocity of 10 m/s calculate the Reynolds number.

• Is this laminar, transitional or turbulent?

• Here we take the diameter of the pipe to be the characteristic length scale of the flow.


Turbulent flow over a flat plate

flow

• For pipe flow the characteristic length scale was the diameter D.• What is the characteristic length scale of this flow?



Increasing Reynolds number

Lecture 1 Course overview and fundamental principlesLearning Teaching & Assessment Strategy ... Flow...

Documents

Transcript of Lecture 1 Course overview and fundamental principlesLearning Teaching & Assessment Strategy ... Flow...