Measurements in Fluid Mechanics
058:180 (ME:5180)
Time & Location: 2:30P - 3:20P MWF 3315 SC
Office Hours: 4:00P – 5:00P MWF 223B-5 HL
Instructor: Lichuan Gui
lichuan-gui@uiowa.edu
Phone: 319-384-0594 (Lab), 319-400-5985 (Cell)
http://lcgui.net
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.
2
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
3
Text book
Measurement in Fluid Mechanics, Stavros Tavoularis, 2005, Cambridge, 2005
Reference books
Particle Image Velocimetry, Raffelet. al., 2ndEdition, 2007, Springer
Particle Image Velocimetry, Adrian and Westerweel, 2011, Cambridge
Flow Visualization, Wolfgang Merzkirch, 2nd Edition, 1987, Academic
4
Lecture 1. Fluid properties and continuum hypothesis
5
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 easily deformation materials and take the shape of any container
- fluids include liquids and gases
Liquids - relatively high density and difficult to change volume
Gases
- relatively low density and easily to change volume
- tend to occupy the entire available volume of their container
- fluids are composed of molecules that collide with one another and solid objects.
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
6
Measurements in Fluid Mechanics
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)
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.
Measurements in Fluid Mechanics
- Methods and techniques used in the process or for result analysis of
determining force, motion and other physical quantities of fluids
7
Measurements in Fluid Mechanics
International System of Units (SI)
8
Measurements in Fluid Mechanics
International System of Units (SI)
9
Measurements in Fluid Mechanics
International System of Units (SI)
10
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 - acts throughout the volume
- e.g. gravity and electromagnetic forces
Surface force - acts across an internal or external surface element
- decomposed in to two perpendicular components
F
Normal component (Fn)
Tangential or shear component (Fs)
- force per unit area () SI unit: pascal (Pa=1N/m2)
A
Fs
n=Fn/A
Shear stress
s=Fs/A
11
Measurable fluid properties
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
- Symbol: P
SI unit: pascal (Pa=1N/m2), bar (=105Pa)
Viscosity - resistance to deformation because of shear stress (µ, )
SI unit: Pas=kg/(sm)
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
12
Measurable fluid properties
Temperature - quantitatively expresses the common notions
of hot and cold ( T )
SI unit: kelvin (K)
Energy - the ability a physical system has to do work on other
physical systems ( E )
SI units: joule [J]
Work - the amount of energy transferred by a force acting
through a distance in the direction of the force. ( W )
SI units: joule [J]
Heat
SI units: joule [J]
- an energy transfer to the body in any other way
than due to work performed on the body ( Q )
Power - the rate at which work is performed or energy
is converted. ( P )
SI units: watt [W]
Thermal conductivity - material's ability to conduct heat ()
SI unit: W/(mK)
13
Measurable fluid properties
Heat flux - the rate of heat energy transfer through a given surface SI unit: W/m2
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
Specific heat capacity under constant pressure ( CP )
SI unit: J/(kgK)
Specific heat capacity under constant volume ( CV )
SI unit: J/(kgK)
Internal energy - total energy contained by a thermodynamic system ( U )
SI unit: J
Enthalpy (H) - total energy of a thermodynamic system
H=U+pV
Entropy ( S ) - thermodynamic property that can be used to determine
energy available for useful work in thermodynamic process
dS=Q/T
14
Measurable fluid properties
Position
- Cartesian coordinate system (x, y, z)
P=xi+yj+zk
- Cylindrical coordinate system (, , z)
P=cosi+sinj+zk
- Spherical coordinate system (r, , )
P=rsincosi+rsinrsinj+rcosk
15
Measurable fluid properties
Displacement - shortest distance from the initial to the final position of a point (x, y, z)
P=xi+yj+zk
Velocity - the rate and direction of change
in the position of an object
z
x
y
V=P/t=x/ti+y/tj+z/tk
Acceleration - rate of change of velocity over time
a=V/t=[V(t+t)-V(t)]/t
16
Measurable fluid properties
Volume flow rate
Q=
Vn
𝐴
𝑉𝑛 𝑑𝐴
Mass flow rate
A
Vorticity - tendency for elements of the fluid to "spin."
Strain rate - rate of change in strain with respect to time ( )
- length under applied stress
- original length
v - speed of deformation
17
Measurable fluid properties
Angular position
()
Angular displacement (  )
SI unit: radian
Angular velocity (  )
=d/dt
Angular acceleration (  )
=d/dt=d2/dt2
Momentum - product of the mass and velocity of an object (P=mv).
Angular momentum
Torque (  )
=rF
L=rP= rmv
SI unit: kgm/s or Ns
SI unit: Nms or kgm2s−1
SI unit: Nm
18
Homework
- Read textbook 1.1-1.2 on page 3-5
-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.
- Due on Friday, 08/24
- Send MS Word or PDF file to lichuan-gui@uiowa.edu
19