Brad Peterson, P.E.

SFRIDAYS – 14:00 to 15:40

FRIDAYS – 16:10 to 17:50

BRAD PETERSON P E PTOEBRAD PETERSON, P.E., PTOE

Brigham Young University 1975 Brigham Young University, 1975 Highway and Bridge Design Montana Utah Idaho Wyoming Montana, Utah, Idaho, Wyoming Worked 27 Years in Helena, Montana

W k d 4 Y i S lt L k Cit Ut h Worked 4 Years in Salt Lake City, Utah Partner in a 400-Person Civil-Design

Firm Left firm in July 2009

It’s a Small WorldIt s a Small World

USAUSA

My House in SummerMy House in Summer

My House in WinterMy House in Winter

My Family:My Family:

Fluid Mechanics, Friday, y

Class Time (14:00 or 16:10)

Name in Chinese Characters

Chi N i Pi iChinese Name in Pinyin

English Name (if you use one)g ( y )

Student Identification Number

Year in School (1st , 2nd , 3rd, 4th, Masters, PhD, Other)

M j d th U i itMajor and the University

CLASS INFO:CLASS INFO: Class Website: Class Website:

https://sites.google.com/site/njut2009fall/

Mr. Peterson’s Email Address: bradpeterson@engineer combradpeterson@engineer.com

Class GoalClass GoalPrimarily:Primarily:

To learn and practice the concepts and principles of Fluid Mechanicsprinciples of Fluid Mechanics.

S d ilSecondarily:To increase skills in the English language as

l t d t th i i i i lrelated to these engineering principles.

Guidelines:Guidelines:

Attend all classes Check with the Attend all classes. Check with the instructor on how you can make up a class before you miss the classclass, before you miss the class.

Be punctual (be on time). SHOE Speak Here Only English SHOE - Speak Here Only English. Do not be fearful about making mistakes

h ki E li hwhen speaking English.

Guidelines:Guidelines: Participate in class discussions and ask Participate in class discussions and ask

questions when you do not understand. Check for and download information at Check for and download information at

the class website. DO NOT smoke eat spit use cell DO NOT smoke, eat, spit, use cell

phone or sleep in class.

Guidelines:Guidelines: Be prompt in handing in written Be prompt in handing in written

assignments – due at the beginning of each class.

Learn and have fun!

GradingGrading In-Class Tests – 30% In Class Tests 30%

Homework 30% Homework – 30%

Final Exam – 40%

CLASS SCHEDULECLASS SCHEDULE Lesson 1, Properties of Fluids Lesson 2, Fluid Statics Lesson 3, Hydrostatic Force on Surfaces Lesson 4, Buoyancy and Flotation

L 5 T l ti d R t ti f Li id M Lesson 5, Translation and Rotation of Liquid Masses Lesson 6, Dimensional Analysis and Hydraulic Similitude Lesson 7, Fundamentals of Fluid Flow

L 8 Fl i Cl d C d it Lesson 8, Flow in Closed Conduits Lesson 9, Complex Pipeline Systems Lesson 10, Flow in Open Channels L 11 Fl f C ibl Fl id Lesson 11, Flow of Compressible Fluids Lesson 12, Measurement of Flow of Fluids Lesson 13, Forces Developed by Moving Fluids Lesson 14 Fluid Machinery Lesson 14, Fluid Machinery

Class Text:Class Text:

About the Class TextAbout the Class Text Clear concise and straightforward Clear, concise and straightforward But not long – <400 pages vs. 800+ If feasible purchase a copy If feasible, purchase a copy Useable now, and for entire career See my website for one purchase site Local bookstores may also have it? Or

can get it?

Other Sources of InfoOther Sources of Info www google com www.google.com www.wikipedia.com Other search engines and data bases Other search engines and data bases

Some info is good, some not-so-good. Be careful and let’s discuss, if questions.

Lesson 1 Properties of FluidsLesson 1, Properties of Fluids

1. Fluid Mechanics 8. Vapor Pressure1. Fluid Mechanics2. Definition of a Fluid3. Systems of Units

9. Surface Tension10. Capillarityy

4. Specific or Unit Weight

11. Modulus of Elasticity12. Isothermal Conditions

5. Mass Density6. Specific Gravity

13. Adiabatic or Isentropic Conditions

7. Viscosity 14. Pressure Disturbances

Items of ImportanceItems of Importance For this lesson, items considered of For this lesson, items considered of

most importance for civil engineering students (items dealing with liquids and

ifi ll ) ll hspecifically water) are generally shown in white text like this.

It l t d t d li id th Items related to gases and liquids other than water are dealt with in less detail and are shown in green text Theand are shown in green text. The student is encouraged to research these topics individually, as needed.

1 1 Fluid Mechanics1.1. Fluid Mechanics Deals with the properties of fluids at Deals with the properties of fluids, at

rest and in motion.

1 2 Definition of a Fluid1.2. Definition of a Fluid Capable of flowing Capable of flowing Conforms to shape of a vessel Cannot sustain shear forces Cannot sustain shear forces Little resistance to change of form. Two Classifications:

Liquid, not compressible, definite volume Gas, compressible, expands to volume of

vessel.

Important Fluid PropertiesImportant Fluid Properties Specific Weight Specific Weight Density Viscosity Viscosity

1 3 Systems of Units1.3. Systems of Units British Engineering (or FPS) British Engineering (or FPS)

Not used in this class

1.3. Systems of Units (Cont) International System of Units (SI)

Length = meter (m)g ( ) Mass = kilogram (kg) Time = second (s)

All th it d i d f th th All other units derived from these, thus:○ Area = m2

○ Volume = m3

○ Acceleration = m/s2

○ Acceleration of gravity (g) = 9.81m/s2

○ Force = Newton (N) = mass X acceleration = kg . m/s2○ Force Newton (N) mass X acceleration kg . m/s

○ Work = joule (J) = N . m○ Pressure = pascal (Pa) = N/m2

1 4 Specific or Unit Weight1.4. Specific or Unit Weight Specific (or unit) weight (Ƴ) = Weight of Specific (or unit) weight (Ƴ) Weight of

a unit volume of a substance For liquids Ƴ is constant For liquids, Ƴ is constant

S ifi i ht f t 9 79 kN/ 3 Specific weight of water = 9.79 kN/m3

1 5 Mass Density1.5. Mass Density Mass per unit volume = Ƴ/g Mass per unit volume Ƴ/g For Water, mass density = 1000 kg/m3

Weight, Acceleration Of Gravity & Mass

2Acceleration of gravity at sea level 9.81 /g m s

decreases slightly as elevation increasesg

2In our textbook g is assumed to be 9 81 /m sIn our textbook, g is assumed to be 9.81 /m s

Weight, Acceleration Of Gravity & Mass (cont)

3

3

Weight of water 9.81 / at 09 79 / t 20

o

o

kN m CkN C

3

3

9.79 / at 20 9.73 / at 40

o

o

kN m CkN m C

3 9.40 / at 100okN m C

3Our textbook uses 9.79 /kN m

Weight, Acceleration Of Gravity & Mass (cont)

339.81 /Mass density of water =1000kg / at 0okN m m C 2

33

Mass density of water =1000kg / at 09.81 /

9.79 / =998kg / at 20o

m Cm s

kN m m C

2

33

=998kg / at 209.81 /9.73 / 992k /

m Cm skN m

t 40oC32 =992kg /

9.81 /m

m s

33

at 40

9.40 / 958k / t 100

o

o

C

kN m C32

3

=958kg / at 1009.81 /

Our textbook uses 1000 / for mass of water

om Cm s

kg m

Our textbook uses 1000 / for mass of waterkg m

Weight, Acceleration Of Gravity & Mass (unit check)

3

2

9.81 /Mass of water 9 81 /

kN m 2

2 3

9.81 /9810( / ) /

m skg m s m

2 9.81 /

m s

3 =1000kg / at 0om C

Weight, Acceleration Of Gravity & Mass (conclusion)

2Some sources use g 9.8 /m s3and, for water 9.8 /

however:kN m

2

however:Our textbook uses: g 9.81 /m s

3and, for water 9.79 /kN m

1 6 Specific Gravity1.6. Specific Gravity Ratio of weight of a body to the weight Ratio of weight of a body to the weight

of an equal volume of a standard substance

Water is usually the standard substance 9 79 kN/m39.79 kN/m

Specific Gravity =

____weight of substance___weight of equal volume of waterweight of equal volume of water

1 7 Viscosity1.7. Viscosity That property which determines the That property which determines the

amount of a fluid’s resistance to a shearing force.g

Absolute viscosity = μ = τ /(dV/dy)where τ = F/A = shear stresswhere τ = F/A = shear stress

Ki ti Vi it 2/ ft2/ Kinematic Viscosity = ʋ = m2/s or ft2/sec

Viscosity (cont)y ( )

U = velocityU velocityA = area of platey = spacing between platesy = spacing between platesU / y = dV / dy Experiments have shown that:F α (AU/y = A▪dV/dy) or F/A α dV/dy

Viscosity (cont)Viscosity (cont)Since shear stress = F/A = τ

d if ti lit t t iand if a proportionality constant μ is introduced, then:

F/A dV/d bF/A α dV/dy becomes:τ = μ x dV / dy or,μ = τ / (dV/dy)μ ( y)

Units for μ are Pa-s or lb-sec/ft2Units for μ are Pa s or lb sec/ft

1 8 Vapor Pressure1.8. Vapor Pressure Produced when evaporation takes place Produced when evaporation takes place

within and enclosed space Depends on temperature Depends on temperature Increases as temperature increases

1 9 Surface Tension1.9. Surface Tension Molecules on the surface of a liquid Molecules on the surface of a liquid

have more energy that molecules within. This creates surface tension.

Illustrated by glass of water and needle.

1 10 Capillarity1.10. Capillarity Causes liquid to rise or fall in a tube Causes liquid to rise or fall in a tube. Caused by surface tension and by

adhesion to walls of the tubeadhesion to walls of the tube. Adhesion > Cohesion – liquid rises in tube Cohesion > Adhesion liquid falls in tube Cohesion > Adhesion – liquid falls in tube Draw picture to illustrate. Capillarity is important using tubes smaller Capillarity is important using tubes smaller

than 10mm diameter

1 10 Capillarity (picture)1.10. Capillarity (picture)

1 11 Bulk Modulus of Elasticity1.11. Bulk Modulus of Elasticity

Expresses the compressibility of a fluid Expresses the compressibility of a fluid. Ratio of change in unit pressure to

corresponding volume changecorresponding volume change.

Pressure DisturbancesPressure Disturbances Isothermal Conditions Isothermal Conditions Adiabatic or Isentropic Conditions Pressure Disturbances Pressure Disturbances

These apply mostly to gases and may be discussed at a later date, as needed.

Problem 1Problem 1If 6 m3 of oil weighs 47 kN calculate itsIf 6 m of oil weighs 47 kN, calculate its

specific weight Ƴ and specific gravity.

Problem 1 SolutionProblem 1, Solutionspecific weight Ƴ = 47 kN = 7 833 kN/m3specific weight Ƴ 47 kN 7.833 kN/m

6 m3

specific gravity = Ƴoil = 7.833 kN/m3 = 0.800Ƴwater 9 79 kN/m3Ƴwater 9.79 kN/m

Problem 2Problem 2 If 1 m3 of concrete has a mass 2 4 Tons If 1 m of concrete has a mass 2.4 Tons,

calculate its specific weight Ƴ and specific gravity.p g y

Problem 2 Solution (Cont)Problem 2, Solution (Cont)

33

9.81 /specific weight 2300 22.56 /1N kgkg kN mm

3

1

22 56 /

m

kN 3

3

22.56 /specific gravity 2.309.79 /

con

water

kN mkn m

Problem 3Problem 3 A cylinder of 0 122 m radius rotates A cylinder of 0.122 m radius rotates

concentrically inside a fixed cylinder of 0.128 m radius. Both cylinders are y0.305 m long. Determine the viscosity of the liquid that fills the space between q pthe cylinders if a torque of 0.881 N-m is required to maintain an angular velocity of 60 revolutions per minute.

Problem 3 SolutionProblem 3, Solution Sketch on the Board Sketch on the Board Torque is transmitted through the fluid

layers to the outside cylinderlayers to the outside cylinder. Since the gap between the cylinders is

small calculation can be made withoutsmall, calculation can be made without integration.

Problem 3 Solution (cont)Problem 3, Solution (cont)Tangential velocity of inner cylinder =Tangential velocity of inner cylinder

rω = 2π x 0.122 m x 1 rps) = 0.767 m/s

dV/dy = (0.767 m/s) / (0.128 – 0.122) = 127 8 1127.8 s-1

Problem 3 Solution (cont)Problem 3, Solution (cont)τ = F/A torque = F x armF = τA F =torque/arm

τA = torque/armτ = torque / (arm x A)q ( )

τ = 0.881 / [(0.125) x (2π x 0.125 x 0.305)] =29.4 Pa

μ = τ / (dV/dy) = 29.4 / 127.8 = 0.230 Pa-s

CLASS SCHEDULECLASS SCHEDULE Lesson 1, Properties of Fluids – 2009 September 04 Lesson 2, Fluid Statics – 2009 September 11 Lesson 3, Hydrostatic Force on Surfaces Lesson 4, Buoyancy and Flotation

L 5 T l ti d R t ti f Li id M Lesson 5, Translation and Rotation of Liquid Masses Lesson 6, Dimensional Analysis and Hydraulic Similitude Lesson 7, Fundamentals of Fluid Flow

L 8 Fl i Cl d C d it Lesson 8, Flow in Closed Conduits Lesson 9, Complex Pipeline Systems Lesson 10, Flow in Open Channels L 11 Fl f C ibl Fl id Lesson 11, Flow of Compressible Fluids Lesson 12, Measurement of Flow of Fluids Lesson 13, Forces Developed by Moving Fluids Lesson 14 Fluid Machinery Lesson 14, Fluid Machinery

Vocabulary for Next WeekVocabulary for Next Week Fluid Pressure Absolute Pressure Fluid Pressure Pressure Gages Pressure Head

Absolute Pressure Gage Pressure Barometers

Compressible Vacuum

Standard Atmospheric

Piezometers Manometers

Pressure