# ME3250 Fluid Dynamics I

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1 ME3250 Fluid Dynamics I Section I, Fall 2012 Instructor: Prof. Zhuyin Ren Department of Mechanical Engineering University of Connecticut

2 Course Information Website: Username: s12, Password (case sensitive): Fluids Instructor: Prof. Zhuyin Ren Office: UTEB-356, Phone: Office hours: 11:00 am-12:00am, Tuesday/Thursday Teaching Assistant: Chao Xu Textbook: Fundamentals of Fluid Mechanics, Munson et al, 7 th Ed., John Wiley & Sons, NY. Homework including one project: Assigned every Thursday; due the following Thursday Grades: HW: 15 %; Midterms & Pop quizzes 55 %; Final 30 % No exams dropped, no make-ups for quizzes

3 Chapter 1. Introduction Concept of fluid Gases, Liquids, Granular solids etc A definition: a fluid is a substance that deforms continuously when acted by a shearing stress of any magnitude i.e. fluid can flow Fluid statics: fluid in rest (chap. 2) Fluid kinematics & dynamics: fluid in motion (chap. 3-12)

4 Examples Involving Fluid & Flow es/water_faucet.jpg _cup-of-coffee.jpg ns/0/01/seagull_in_flight.jpg 2_f68f0816a4.jpg cts/graphcuttextures/data/interactio n/littleriver.jpg ain/content/wp/en- commons/thumb/1/16/300px- Georgia_Aquarium_- _Giant_Grouper_edit.jpg y/ / jpg ia/2216/us%20navy%20- %20Submarine.jpg

5 Types of Flows/Fluids Static vs. dynamic Compressible vs. incompressible Viscous vs. inviscid Laminar vs. turbulent Homogeneous vs. heterogeneous Non-reacting vs. reacting Newtonian vs. non-newtonian Laminar Turbulent Non-Newtonian Newtonian It is important to know fluid properties & their measurement to understand different flows m/images/water_drop.jpg s/uncategorized/ketchup_1.jpg

6 Dimensions & Units Basic units: Length, L; Mass, M; Time, T; Temperature, θ; Derived units: Velocity, v: L/T; Acceleration, a: L/T 2 ; Force: f=m*a: ML/T 2 ; Work/energy: f*l: ML 2 /T 2, Density: Specific weight: Pressure: Stress: Momentum: Dimensional Homogeneity The LHS and RHS of an equation must have the same dimension All additive separate terms in an equations must have the same dimension Example: V = V 0 + a * t [L/T] = [L/T] [L/T 2 ] * [T]

7

8 Systems of Units International System (SI) Length, meter, m Time, second, s Mass, kilogram, kg Temperature, Kelvin, k English Engineering System (EE) Length, foot, ft Time, second, s Mass, pound, lbm Force, pound, lbf Temperature, Rankine, R British Gravitational System (BG) Length, foot, ft Time, second, s Force, pound, lbf Temperature, F Mass: slug, defined based on Newton s 2 nd law f = m * a 1 lbf = 1 slug * 1(ft/s 2 ) f = (m * a)/g c g c = [(lbm*f/s 2 )/lbf]

9 Base Units in SI: a Complete List Table 1. SI base units SI base unit Base quantity Name Symbol length meter m mass kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K amount of substance mole mol luminous intensity candela cd NIST:

10 Example Derived Units in SI SI derived unit Derived quantity Name Symbol area square meter m 2 volume cubic meter m 3 speed, velocity meter per second m/s acceleration meter per second squared m/s 2 wave number reciprocal meter m -1 mass density kilogram per cubic meter kg/m 3 specific volume cubic meter per kilogram m 3 /kg current density ampere per square meter A/m 2 magnetic field strength ampere per meter A/m amount-of-substance concentration mole per cubic meter mol/m 3 luminance candela per square meter cd/m 2 mass fraction kilogram per kilogram, which may be represented by the number 1 kg/kg = 1 NIST:

11 Measures of Fluid Properties Mass/weight Viscosity Compressibility Vapor pressure Speed of sound Surface tension Density: Specific volume: Mass/weight lim 0 =1/ 3 3 Specific weight: = Specific gravity: =

12 Measures of Mass/Weight (cont.) Density of water as a function of temperature In most cases water is considered incompressible, i.e. its density changes negligibly with pressure

13 Ideal Gas Law Ideal gas law: WU2 P is absolute pressure (vs. gauge pressure) ρ is density T is temperature (K) R = R u /W, where R u is the universal gas constant (8.31J/K-mol), W is the average molecular weight Which of the following can be approximated as ideal gas? Atmospheric air Cotton candy p = ρrt Exhaust gas from jet engine Fuel spray in IC engine cylinder

14 Slide 13 WU2 Pressure in a fluid at rest is defined as the normal force per unit area exerted on a plan surface immersed in a fluid and is created by the bombardment of the surface with the fluid molecules. Windows User, 1/6/2012

15 Measurement of Fluid Viscosity The wiki definition: Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or extensional stress With similar external force, fluids with higher viscosity deforms slower (can be used to measure viscosity) Fluid viscosity manifest itself in many ways, a prominent one is the shearing flow F F Sharing stress: = No-slip boundary condition: Fluid velocity remains the same as that of the wall on the boundary

16 Shearing Flow (Viscous) = = h µ: Absolute viscosity, or dynamic viscosity [τ]: N/m 2 Kinematic viscosity: = [m2 /s] [du/dy]: (m/s)/m = 1/s Unit of µ: N s/m 2 Reynolds number: Re = ρul = µ ul ν (dimension of Re?)

17 Newtonian Fluid vs. Non-Newtonian Fluid Newtonian Fluid: µ is constant Non-Newtonian: µ is not a constant

18 Dependence of Viscosity on Temperature Opposite trend for liquid vs gas: Gas: µ with increasing T Liquid: µ with increasing T

19 Compressibility of Fluids Bulk modulus measures the compressibility of fluids Dimension same as pressure E dp dp = = v dρ / ρ dv / v Compression/expansion of ideal gas p = ρrt Isothermal compression/expansion (T = const) p = ρ RT = const Isentropic compression/expansion ( 12/airplane/compexp.html) p c p cv R const k + p =, = = k = const E v =? k /( k 1) ρ c c T v v E v =?

20 Speed of Sound Sound wave is a propagating pressure wave Pressure fluctuation is small (Fig. 1.1) Approximately isentropic dp c = = dρ E v ρ For ideal gas (+isentropic) Mach number Ma<1, subsonic Ma>1, supersonic Ma = V c c = krt = kp ρ

21 Surface Tension Surface tension tends to reduce surface area of a liquid, σ: force per unit length [pictures from wikipedia]

22 Example of Surface Tension Figure 1.7 (p. 25) Forces acting on one-half of a liquid drop.

23 Example of Surface Tension Non-Wetting Wetting Figure 1.8 (p. 25) Effect of capillary action in small tubes. Wetting vs. Non-wetting liquid

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