Lecture 1 Course overview and fundamental principlesLearning Teaching & Assessment Strategy ... Flow...
Transcript of Lecture 1 Course overview and fundamental principlesLearning Teaching & Assessment Strategy ... Flow...
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Lecture 1Course overview and fundamental
principles
Dr Tim Gough: [email protected]
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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!
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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).
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
• 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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
• 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!
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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]
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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!!!
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Lecture 1Fundamental principles
Dr Tim Gough: [email protected]
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Nanotechnology and microfluidics
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Motion of animals
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Everyday occurrences
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Car aerodynamics
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Flight mechanics
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Meteorology ‐ Hurricane Katrina – near New Orleans – August 2005
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Earth's atmosphere – one month's worth of data
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Fluid mechanics
Jupiter – great red spot
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Flight
Chanute’s biplane hang glider ‐ 1896 Wright flyer I – 17th December 1903Flight time 59 seconds !!!
Rumpler Taube (dove) from 1910
Zanonia Macrocarpa seeds
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Handley Page V/1500 ‐ 1918Sopwith Triplane ‐ 1916
Concorde ‐ 1969Spitfire ‐ 1936
Flight
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Vestas V27 wind turbine
Nysted offshore wind farm ‐ Denmark
Hydroelectric power plant – NY, USA Tidal power – N. Ireland
Power generation / conversion
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Ground transport
Mercedes Benz T80 ‐ 1939
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Ground transport
Flow patterns in 4‐stroke internal combustion engine(modelled using Ansys Fluent 6.3)
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Rolls Royce Avon 200 gas turbine
Rolls Royce Bergen C‐gas engine
Other turbines / engines
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
• Outflow from Glen Canyon Dam, Arizona, US mfm 38
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
• 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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Bridge design
November 7th 1940
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Interactions
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
• 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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
• Though we will be dealing with fluids of constant density during this module, we need to be aware that …
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Viscosity
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Viscosity
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Increasing temperature
Mineral oil 15W40 rheology
Viscosity measurements
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Mineral oil 15W40 rheology
Viscosity measurements
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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...).
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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).
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Viscosity of non‐Newtonian fluids
Frequency sweep at varying T for EVA copolymer
Increasing T
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Pressure
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Typical pressure distribution around car
Wall pressure variation over car
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Wall pressure variation over car
• Note high pressure at front of car.
• Low pressure over roof of car.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Measuring pressure
Pressure regulator
Aneroidbarometer
U‐tube manometer
And others…
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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:‐
.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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?
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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?)
. /
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
= 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
.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
• 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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
The Reynolds number
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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 is the ratio of inertial to viscous forces in a flow
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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 is the ratio of inertial to viscous forces in a flow
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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 !!!
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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:
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Reynolds experiment
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Reynolds number
Low Reynolds number
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Reynolds number
Medium Reynolds number
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
'High' Reynolds number
Reynolds number
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Critical Reynolds number
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.
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
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?
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ENG2038M – Fluid Mechanics 2ENG2038M – Fluid Mechanics 2
Critical Reynolds number
Increasing Reynolds number