Course Introduction January 4, 008 Course Introduction Larry Caretto Mechanical Engineering 390 Fluid Mechanics January and 4, 008 Today s Class First class day items: roll, outline, etc. Class goals and learning objectives Assessment quiz Discussion o dimensions and units Physical quantities have dimensions Several units measure same dimension Use SI system o units (meter, kilogram,... Also use engineering units (eet, pounds... Thursday Class Fluid properties Density Bulk modulus Viscosity Vapor pressure Viscosity Surace Tension Start discussion o luid statics on using next set o notes 3 Basic Inormation Larry Caretto, Jacaranda (Engineering) 3333, lcaretto@csun.edu, 818.677.6448 Oice hours Monday and Wednesday, 4:30 to 5:15 pm; Tuesday and Thursday :45 to 3:45 pm; other times by email, phone, drop-in, or appointment http://www.csun.edu/~lcaretto/me390 Munson, Young, and Okiisii, Fundamentals o Fluid Mechanics (ith edition), Wiley, 006. 4 Email Campus policy requires students to monitor their CSUN email addresses These addresses will be used class email list me390-c@csun.edu Setup your CSUN email account i you have not done so already I desired, orward CSUN email to another address 5 Course Learning Objectives Understand the and be able to ormulate and solve problems using basic luid properties: density, speciic weight, viscosity and mechanical quantities: pressure, velocity, orce and stress solve problems to determine pressures in static luids and manometers understand limits o and solve problems with Bernoulli equation 6 ME 390 Fluid Mechanics 1
Course Introduction January 4, 008 More Learning Objectives understand deinition and be able to use concepts o system and control volume use continuity equation to use mass conservation in problem solving solve problems to determine orces in moving luids using control volumes use dimensionless parameters and apply the concept o similitude or luid mechanics experimentation 7 Still More Learning Objectives understand the dierences between laminar and turbulent lows and be able to determine i a low is laminar or turbulent based on the Reynolds number or the low solve problems in laminar and turbulent lows in pipes be amiliar with the basic ideas o boundary layers and irrotational lows outside these boundary layers 8 Learning Objectives Concluded solve problems o lit and drag in external lows understand the important variables used to solve problems in open channel and compressible lows solve problems in one o the ollowing areas (a) compressible lows (b) open channel lows Thermodynamics Oten a prerequisite or luids, but not presently a prerequisite at CSUN Students advised to complete ME 370 prior to taking ME 390 Instead o a 370 review this course will use just-in-time Thermodynamics Cover speciic topics as required or course in nature o review 9 10 Class Operation Tuesday: lecture on new material Review text and notes beore class Thursday: group problem solving Tuesday: 30-minute quiz at start o class ollowed by new material lecture Starts next week Introduction during irst week First quiz is on Tuesday, February 5 Quizzes Twelve during the semester Based on group work and homework Homework assigned, but not collected or graded Solutions available on line Count ten highest quiz grades or inal No makeup quizzes; inal quiz grade based only on quizzes taken i ewer than ten First ew quizzes closed book; remainder will be open book and equation sheet 11 1 ME 390 Fluid Mechanics
Course Introduction January 4, 008 Grading Quiz grades 45% Midterm (March 13) % Final (May 13) 33% Plus/minus grading will be used Grading criteria in course outline No make-up quizzes or exams See the Course Outline Download rom course web site http://www.csun.edu/~lcaretto/me390 Contains lecture schedule and homework assignments (homework also on web) Also read inormation on the ollowing items Class participation and courtesy Collaboration versus plagiarism: students ound cheating receive F grade in course Students are responsible or changes to outline announced in class 13 14 Galileo Galilei (1564-164) You cannot teach people anything; you can only help them ind it within themselves. http://space.about.com/od/astronomyhistory/a/galileoquotes.htm Goals or this Course My goal is to help all students ind within themselves suicient knowledge o luid mechanics so that they will all get an A grade in the course What is your goal or this course? What will you do to achieve that goal? 15 16 How to get your A Spend six to ten hours per week outside class studying or the course Prepare or lecture and be ready to ask questions Read the assigned reading beore class Download, print, and review the lecture presentations beore class Use these as notes so that you can ollow the lecture; write additional notes on these presentations 17 How to Get your A, Part II Study with ellow students and try to answer each other s questions Do the homework as well as you can beore reviewing the on-line solutions Contact me by email, telephone or oice visits to ask questions Develop a good working relation with other members o your sel-study group 18 ME 390 Fluid Mechanics 3
Course Introduction January 4, 008 What I will do to help Arrive at class a ew minutes early to answer any questions you may have Give lectures that stress application o basics to problem solving Return quizzes and exams promptly so that you can learn rom your errors Be available or questions by email, oice visits or phone calls Send entire class emails as appropriate 19 Preliminary Assessment Designed to help instruction One set o questions on student background Second set o questions is ungraded quiz Take about 10 minutes or this assessment Hand yours in when inished Will call time when most students are done 0 Dimensions and Units Any physical quantity has a unique dimension: e.g., mass, length, time, Several units may be available or any dimension Length is measured in meters, eet, miles, athoms, urlongs, yards, light-years, etc. You cannot measure length in units with the dimension o mass Systems o Units Arbitrary units or undamental dimensions, e.g. mass (M), length (L), time (T), and temperature (Θ). Units or other physical quantities rom the physical relations to quantities with undamental units Velocity dimensions are length/time, L/T Acceleration dimensions are length/time Force dimension o (mass)(length)/(time) 1 More Dimensions Pressure = orce per unit area = [orce] / [length] = [(mass) (length) / (time) ] / (length) = (mass) / [(time) (length)] or MT - L -1 Common dimensions or energy terms are (mass)(length) /(time) or ML T - Work = orce times distance = (orce)(length) = (mass)(length) /(time) or ML T - Kinetic energy = mv / = (mass)(velocity) Still More Dimensions Another energy term Potential energy = mgh = (mass)(acceleration)(length) = (mass)(length) /(time) Power = (energy)/(time) = (mass) (length) /(time) 3 or ML T -3 Thermodynamic work is PdV This is like Fdx where P = F/A and dv = Adx (A is area) PdV dimensions are (length) 3 (orce)/(area) = (mass)(length) /(time) or ML T - which also is (mass)(length) /(time) 3 4 ME 390 Fluid Mechanics 4
Course Introduction January 4, 008 SI Units Basic deinitions or undamental units Mass: kilogram (kg) = international prototype Time: second (s) = time or 9 19 631 770 periods o radiation rom Cs 133 Length: meter (m) = length light travels in 1/99 79 458 o a second Temperature: kelvin (K) = 1/73.16 o the triple point o water Current: ampere (A) deined in terms o electrostatic orce Other Units Light intensity and molar units Units or velocity and acceleration are m/s and m/s Units or orce are kg m/s 1 newton (N) = 1 kg m/s Units or energy are kg(m/s) = N m 1 joule (J) = 1 N m = 1 kg m /s 5 6 Still More Units Some Preixes Power: (energy)/(time) = joules/second 1 watt (W) = 1 J/s = 1 N m/s = 1 kg m /s 3 Pressure: (orce)/(area) = newtons per square meter (1 atm = 101,35 Pa) 1 pascal (Pa) = 1 N/m = 1 kg/(m s ) Note that Sir Isaac Newton has a capital N; 1 newton o orce does not, unless it is abbreviated as 1 N (true or all units named ater individuals) pico, p 10-1 tera, t 10 1 nano, n 10-9 giga, g 10 9 micro, μ 10-6 mega, M 10 6 milli, m 10-3 kilo, k 10 3 7 8 Engineering Units Second is the basic unit o time The oot = 0.3048 m (exactly) is the basic unit o length Pound is conusing because it can be used to represent two dimensions Mass: pound-mass (lb m = 0.45359 kg) Force: pound orce (lb = 3.174 lb m t/s ) What is SI equivalent or pound orce? 1 lb = 4.448 N 9 Why Use a Pound Force? From the deinition o a pound orce, the weight, W = mg, o a pound mass in a standard gravitational ield is 1 lb 3.174 t lb s W = mg = ( m lbm ) = m lb s 3.174lb t This is convenient, but the same name or two dimensions is conusing and the conversion actor is awkward m 30 ME 390 Fluid Mechanics 5
Course Introduction January 4, 008 Two Engineering Unit Systems English engineering units use mass as pound mass and orce as pound orce 1 lb = 3.174 lb m t/s British gravitational (BG) system uses slug as the mass unit 1 lb = 1 slug t/s Which mass is larger, slug or lb m? What is their conversion actor? 1 lb s /t = 3.174 lb m = 1 slug 31 More Engineering Units oot-pound is work (energy unit) British thermal unit (Btu = 778.16 t-lb ) Pressure in lb /in (psi) 1 atm = 14.696 psi = (144)(14.696) lb /t (ps) Horsepower as power unit 1 hp hr =,545 Btu = 1.98x10 6 t lb 1 kw hr = 3,41 Btu The metric unit, calorie = 1/5 Btu The ood Calorie is a kilocalorie 3 Calculating Units What is kinetic energy o a 100 lb m mass moving at 10 t/s mv / = (100 lb m )(10t/s) / = 5000 lbm t s- Unit conversion (100 lb lb m) 10 t s KE = = 165. 4 s 3.174lb t Note algebraic cancellation o units m t lb Calculating Units II What is kinetic energy o a 3 slug mass moving at 10 t/s mv / = (3 slugs)(10t/s) /=15 slug t s- Unit conversion (3 slugs) 10 t lb s KE = = 150 t lb s 1slug t Note algebraic cancellation o units Especially simple i numeric value is one! 33 34 Units quiz What is the change in potential energy when a mass o 0 slugs is raised a distance o 15 t? Do you need more data to answer this question? What is g? Use 5 t/s or this problem 5 t lb s PE = mgh = (0 slug) 1500 s 1slug t ( 15 t) = t lb Another Quiz Some European engineering calculations use the kilogram-orce, deined in the same way as the pound orce and measure pressure in kg /cm What exactly is the deinition o a kg? How many newtons are in a kg? How many pascals are in a kg /cm? 35 36 ME 390 Fluid Mechanics 6
Course Introduction January 4, 008 Solutions to Another Quiz One kg is the orce required to accelerate 1 kg at an acceleration o standard gravity, g = 9.80665 m/s kg 1 cm 9.80665 m 1 N s 1 kg = 1 kg = 9. 80665 N s kg m kg = 1 cm 9.80665 N 100 cm kg m Pa m 1 N kg 5 1 10 Pa 1 atm cm = 98066.5 Pa 37 A Few Other Units Volume is sometimes measured in liters (or litres), L, where 1 L = 1000 cm 3 = 0.001 m 3 Gallons, gal, is another volume measure; 7.4805 gal = 1 t 3 Speed is sometimes measured in miles per hour, mph; 30 mph = 44 t/s and 1 mph = 0.44704 m/s 1 hogshead = 63 gallons 38 Working With Units Carrying units in the calculation is a good approach or correct results I you do not want to do that, here are some hints or correct unit results In the BG system convert all lengths to eet time to seconds, and pressures to lb /t (ps); 1 lb = 1 slug t/s In the SI system always use m, Pa and N (instead o mm, cm, kpa, kn, etc.; 1 N = 1 kg m/s ) 39 Temperature Units SI unit: absolute temperature in K Degrees Celsius, o C = K 73.15 Degrees Fahrenheit, o F = 1.8( o C) + 3 Rankine, R = o F + 459.67 is absolute temperature or Fahrenheit scale T(R) = 1.8 T(K) What is a ΔT o 5 o F in Rankine? 5 R What is 15 o C in Rankine? 15 o C = 88.15 K = 59 o F = 518.67 R 40 Density and Related Properties Density, ρ, is mass per unit volume (ρ = 1/v, where v is speciic volume used more commonly in thermodynamics) Units or density are (SI) kg/m 3, (EE) lb m /t 3, and (BG) slug/t 3 Speciic weight, γ = ρg, typically tabulated at standard gravity, g = 9.80665 m/s = 3.174 t/s, in N/m 3 or SI and lb /t 3 or both EE and BG 41 Density and Related Properties II Speciic gravity, SG, o a substance: ratio o the substance density to the density o a reerence substance at a speciied temperature Reerence substance is usually water or liquids and air or gases Water reerence temperature: 4 o C (39.4 o F) where ρ water = 1000 kg/m 3 = 1.94 slugs/t 3 The speciic gravity o mercury at 68 o F is 13.56 (relative to water at 39.4 o F). What is its density at this temperature? 4 ρ Hg = 1.356x10 4 kg/m 3 = 6.3 slugs/t 3 ME 390 Fluid Mechanics 7
Course Introduction January 4, 008 Density and Related Summary Density: ρ = mass per unit volume with units o kg/m 3 or slugs/t 3 Speciic weight: γ = ρg with units o N/m 3 or lb /t 3 (varies with local g) Speciic gravity: SG = ρ/ρ re = γ/γ re Liquid ρ re : water at 4 o C with ρ = 1000 kg/m 3 and γ = 9806.65 N/m 3 or water at 60 o F with ρ = 1.94 slugs/t 3 and γ = 6.4 lb /t 3 Gas ρ re : air at 15 o C (59 o F) with ρ = 1.3 kg/m 3 = 0.0038 slugs/t 3 and γ = 6.4 lb /t 3 43 Pressure States o Matter (Phases) Solid Liquid Triple Point Critical Point Gas Temperature Triple point: unique point or each substance where solid, liquid and vapor coexist No liquid-gas transition above critical point 44 Transitions Between Phases Vapor Pressure Pressure Melting line Solid Forphase transitions pressure and temperature are Liquid related Vapor pressure is Gas the pressure at which liquid-vapor Sublimation curve transition occurs Temperature Boiling line 45 Pressure exerted by a liquid in equilibrium with a vapor Value depends on the nature o the liquid and temperature For water the vapor pressure at 100 o C is 101.35 kpa Vapor pressure is pressure at which liquids change to gas at constant temperature Figure on page 3 Fundamentals o Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi,Copyright 005 by John Wiley & 46 Volume Change Compressibility Changing the pressure on a luid can change its volume The volume change can be done in dierent ways In an isothermal process the temperature is constant An isentropic (constant entropy) process is one in which no heat is added to the luid and there is no riction; this ideal process is approached or short times Isothermal bulk modulus P P ET = V = ρ V ρ Isentropic bulk modulus No heat added to luid P P Es = V = ρ V ρ E T E s or liquids T s T s Figure on page 0Fundamentals o Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi,Copyright 005 by John Wiley & 47 Figure on page 0Fundamentals o Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi,Copyright 005 by John Wiley & 48 ME 390 Fluid Mechanics 8
Course Introduction January 4, 008 Ideal Gases From chemistry: PV = nrt (V is volume) n = m / M is the number o moles or mass in kg n is in kilogram moles (kmol); or mass in lb m, n is in pound moles (lbmol) R = 8.31447 kj/kmol K = 10.7316 psia t 3 / lbmol R is universal gas constant R = R/M is engineering gas constant that is dierent or each gas Real gases like ideal gases at low pressures P = nrt / V = (m/m)rt / V = (m/v)(r/m)t 49 P = ρrt E Ideal Gases II Isothermal: P = ρrt P = ρ ρ 1 P = ρ = ρ RT ρ T = T Isentropic: P/ρ k = C P k 1 k Es = ρ = ρckρ = kcρ = kp ρ s k is heat capacity ratio, a gas property, = 1.4 or air P Figure on page 0Fundamentals o Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi,Copyright 005 by John Wiley & 50 Introduction to Viscosity τ is shear stress on plate (opposite sign rom shear stress on luid) Velocity gradient, du/dy ( u/ y) u τ = μ y τ is shear stress on luid Figure 1. (p. 13) (a) Deormation o material placed between two parallel plates. (b) Forces acting on upper plate. Young, and Theodore Okiishi,Copyright 005 by John Wiley & 51 Figure 1.3 (p. 14) Behavior o a luid placed between two parallel plates (top one moving, bottom stationary.) Young, and Theodore Okiishi,Copyright 005 by John Wiley & 5 Viscosity Newtonian Fluids have a linear variation o shearing stress with rate o shearing strain slope is viscosity Figure 1.4 (p. 15) u τ = μ y How does μ or water change with temperature? Young, and Theodore Okiishi,Copyright 005 by John Wiley & 53 Viscosity II Newtonian and non-newtonian Variation o shear stress with rate o shearing strain or several types o luids, including common non- Newtonian luids. Figure 1.5 (p. 16) Young, and Theodore Okiishi,Copyright 005 by John Wiley & u τ = μ y 54 ME 390 Fluid Mechanics 9
Course Introduction January 4, 008 What is τ or Velocity Proile? Figure E1.5 (p. 19) Young, and Theodore Okiishi,Copyright 005 by John Wiley & 55 Viscosity Dimensions What are viscosity dimensions? (τ = μ u/ y) What are dimensions o other variables? τ has dimensions o FL - = (MLT - )L - = ML -1 T - u / y has dimensions o (L/T) / L = T -1 μ has dimensions o τ / ( u/ y) = FL - / T -1 What are μ dimensions in terms o mass? Dimensions o μ are FTL - = ML -1 T -1 SI units: N s/m = kg/m s; BG units: lb s/t = slug/t s; EE units: lb s/t = 3.174 lb m /t s 56 Viscosity III Viscosity o gases increases with temperature Viscosity o liquids decreases with temperature Figure 1.6 (p. 17) Surace Tension Forces generated at liquid-gas or liquid-liquid interaces Surace tension, σ, a luid property, with dimensions F/L Figure 1.7 Forces acting on one-hal o a liquid drop. Young, and Theodore Okiishi,Copyright 005 by John Wiley & 57 Young, and Theodore Okiishi,Copyright 005 by John Wiley & 58 Surace Tension Eects Surace Tension Eects II Figure 1.8 Capillary action in small tubes. (a) Rise o column or a liquid that wets the tube. (b) Freebody diagram or calculating column height. (c) Depression o column or a nonwetting liquid. Young, and Theodore Okiishi,Copyright 005 by John Wiley & 59 Vertical orce balance: γπr h = πrσcosθ Surace tension depends on luid and temperature, wetting angle, θ, depends on luid and surace σcosθ h = γr Young, and Theodore Okiishi,Copyright 005 by John Wiley & 60 ME 390 Fluid Mechanics 10
Course Introduction January 4, 008 Surace Tension Problem Find the capillary rise or water at 60 o F (γ = 6.4 lb /t 3, σ = 0.00503 lb /t) in a circular tube with a diameter o 0.5 in? For water in clean glass, θ = 0 o 0.00503 lb σcosθ t h = = γr 6.4 lb t 3 ( cos0) 0.5 in 144 in t = 0.093 in Tube Diameter vs. Capillary Rise σcosθ h = γr Water at 0 o C 0.5 in = 1.7 mm gives h = 0.093 in =.36 mm 61 Figure E1.8, Fundamentals o Fluid Mechanics, 5/E by Bruce Munson, Donald Young, and Theodore Okiishi,Copyright 005 by John Wiley & 6 Typical Units Quantity Density Pressure & shear stress Velocity Viscosity Speciic weight = ρg SI units kg/m 3 kpa = kn/m m/s N s/m = kg/m s EE units lb m /t 3 BG units slug/t 3 1 psi = 1 lb /in = 144 ps = 144 lb /t t/s lb s/t = lb s/t = 3. lb m /t s slug/t s N/m 3 lb /t 3 Tabulated values at standard gravity 63 ME 390 Fluid Mechanics 11