instructor: lichuan gui lichuan-gui@uiowa

Measurements in Fluid Mechanics058:180 (ME:5180)

Time & Location: 2:30P - 3:20P MWF 3315 SC

Office Hours: 4:00P – 5:00P MWF 223B-5 HL

Instructor: Lichuan [email protected]

Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

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Lectures - around 40 lectures in class room followed by discussions if necessary- lecture note available on web after each class (http://icon.uiowa.edu & http://lcgui.net )

Homework- homework problems assigned MWF, due FMW- Paper version accepted in class, PDF/DOC files accepted by e-mail- late submission with legitimate reason, explained in writing

Class project - write computer program with Matlab (sample programs provided)

- process digital particle image (PIV) recordings with algorithms introduced in class

- start at the beginning of PIV lectures (Matlab program practice & examples earlier)

- details may be discussed in the class or office hours

- presentation in class when the class lectures are completed

- report include introduction, method description, program structure, source code, and results.

Examinations- two in-semester 50-minute and one final 120-minute examinations- closed notes and books- one-page formula sheet allowed.

http://icon.uiowa.edu/

http://lcgui.net/

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Grading

The final course grade will be based on the total points earned during the

semester. The distribution of points is as follows:

Homework problems 25% = 25

Class project 25% = 25

Two in-semester exams 12.5% each = 25

Final examination 25% = 25

TOTAL = 100 points

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Text book

Measurement in Fluid Mechanics, Stavros Tavoularis, 2005, Cambridge, 2005

Reference books

Particle Image Velocimetry, Raffelet. al., 2ndEdition, 2007, SpringerParticle Image Velocimetry, Adrian and Westerweel, 2011, CambridgeFlow Visualization, Wolfgang Merzkirch, 2nd Edition, 1987, Academic

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Lecture 1. Fluid properties and continuum hypothesis

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Measurements in Fluid Mechanics

Mechanics - the branch of physics concerned with the behavior of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

Fluid

- fluids are composed of molecules that collide with one another and solid objects.

- fluids include liquids and gases

- fluids are easily deformation materials and take the shape of any container

Liquids

Gases

- relatively high density and difficult to change volume

- relatively low density and easily to change volume

- tend to occupy the entire available volume of their container

Continuum hypothesis

- the continuum assumption considers fluids to be continuous.

- fluid property values continuously distributed within volume of fluid

- local values defined at an infinitely small fluid element i.e. a mathematical point

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Measurement - the process or the result of determining the ratio of a physical quantity, such as a length or a mass, to a unit of measurement, such as the meter or the kilogram.


- Methods and techniques used in the process or for result analysis of determining force, motion and other physical quantities of fluids

Fluid mechanics - the study of fluids and the forces on them

- fluid mechanics can be divided into

fluid statics - the study of fluids at rest

fluid kinematics - the study of fluids in motion;

fluid dynamics - the study of the effect of forces on fluid motion

experimental fluid dynamics (EFD)

computational fluid dynamics (CFD)

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International System of Units (SI)

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Measurable fluid properties

Mass - quantity of material ( m ) SI unit: kilogram (kg), gram (g)

Volume - quantity of space ( V ) SI unit: cubic meter (m3), liter (=0.001 m3)

Density - mass per unit volume ( ) SI unit: kg/m3

Specific volume - volume divided by mass (v) SI unit: m3/kg

Force - any influence that causes a free body to undergo a change in speed, a change in direction, or a change in shape ( F ) SI unit: newton (N)

Body force

Surface force - e.g. gravity and electromagnetic forces- acts throughout the volume

- acts across an internal or external surface element - decomposed in to two perpendicular components

Normal component (Fn) Tangential or shear component (Fs)

F

FsA

- force per unit area () SI unit: pascal (Pa=1N/m2)

Shear stress

n=Fn/A

s=Fs/A

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Stress tensor

Normal stresses: 11 , 22 , 33

Shear stress: 12 , 13 , 21 , 23 , 31 , 32 (12 = 21 , 13 = 31 , 23 = 32)

External forces: F1 , F2 ,, Fn

Pressure - force per unit area applied in a direction perpendicular to the surface

- average normal stress along any three orthogonal directions

SI unit: pascal (Pa=1N/m2), bar (=105Pa)- Symbol: P

Viscosity - resistance to deformation because of shear stress (µ, ) SI unit: Pas=kg/(sm)

Surface tension - property of the surface of a liquid that allows it to resist an external force.

SI unit: N/m

Index of refraction - a measure of the speed of light in substance

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Temperature - quantitatively expresses the common notions of hot and cold ( T )

SI unit: kelvin (K)

Work

Energy - the ability a physical system has to do work on other physical systems ( E )

SI units: joule [J]

- the amount of energy transferred by a force acting through a distance in the direction of the force. ( W )

SI units: joule [J]

Power - the rate at which work is performed or energy is converted. ( P )

SI units: watt [W]

Heat - an energy transfer to the body in any other way than due to work performed on the body ( Q )

SI units: joule [J]

Thermal conductivity - material's ability to conduct heat () SI unit: W/(mK)

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Specific heat capacity under constant pressure ( CP )

Specific heat capacity under constant volume ( CV )

Heat capacity


- measurable physical quantity that characterizes the amount of heat required to change a substance's temperature by a given amount. ( C )

SI unit: J/K

SI unit: J/(kgK)

SI unit: J/(kgK)

Internal energy - total energy contained by a thermodynamic system ( U ) SI unit: J

Enthalpy (H) H=U+pV

Entropy ( S ) dS=Q/T

Heat flux - the rate of heat energy transfer through a given surface SI unit: W/m2

- thermodynamic property that can be used to determine energy available for useful work in thermodynamic process

- total energy of a thermodynamic system

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Position

- Cartesian coordinate system (x, y, z)

- Cylindrical coordinate system (, , z)

- Spherical coordinate system (r, , )

P=xi+yj+zk

P=cosi+sinj+zk

P=rsincosi+rsinrsinj+rcosk


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P=xi+yj+zk

Displacement - shortest distance from the initial to the final position of a point (x, y, z)

xy

zVelocity

V=P/t=x/ti+y/tj+z/tk

- the rate and direction of change in the position of an object

Acceleration - rate of change of velocity over time

a=V/t=[V(t+t)-V(t)]/t


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Volume flow rate Q

Mass flow rate A

Vn Measurable fluid properties

Vorticity - tendency for elements of the fluid to "spin."

Strain rate - rate of change in strain with respect to time ( )

v - speed of deformation

- length under applied stress- original length

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Angular position ( )

Angular displacement ( )


Angular velocity ( ) =d/dt

Angular acceleration ( ) =d/dt=d2/dt2

Momentum - product of the mass and velocity of an object (P=mv). SI unit: kgm/s or Ns

Angular momentum L=rP= rmv SI unit: Nms or kgm2s−1

SI unit: radian

Torque ( ) =rF SI unit: Nm

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Homework

-Questions and Problems: 1 and 2 on page 17 1. Provide definitions for the following measureable flow properties: angular momentum, entropy, thermal conductivity, molecular diffusivity, and surface tension. 2. List the established names for the SI units of force, pressure, energy, and power and their relationships to primary units. Also list the conversion factors of these units to corresponding units in the British gravitational system.

- Read textbook 1.1-1.2 on page 3-5

- Send MS Word or PDF file to [email protected]

- Due on Friday, 08/24

mailto:[email protected]

instructor: lichuan gui lichuan-gui@uiowa

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