Basic Fluid Mechanics. Prof. Young I Cho

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1 Basic Fluid Mechanics MEM 220 Prof. Young I Cho Summer 2009

2 Chapter 1 Introduction What is fluid? Give some examples of fluids. Examples of gases: Examples of liquids: What is fluid mechanics? Mechanics of fluids (gas and liquid) What is the meaning of mechanics? Mechanical behavior of water? What do we mean? Examples of fluid at rest? Milk (Gasoline) carrying truck: What is the issue?

3 What is fluid? Definition of fluid? Answer: Fluid is a substance that What is Shear force? Unit of force [N] [lbf] [dyne] What is stress? How is stress different from force? Stress = What is Shear stress?

4 Normal stress? How is it different from shear stress? What do we call the normal stress? P Example kg of mass What is the force acting on the bottom of the tank? What is the pressure at the bottom of the tank that is produced by the water? Given: Area of bottom = 1.5 ft 2. Repeat when the elevator is accelerating upward at 7 ft/s 2.

5 What is the difference between gas and liquid? Gas: Liquid: Gas is light because Liquid is heavy because What happens to gas when we heat it? Kinetic energy (½mv 2 ) increases or decreases. Why? What happens to liquid when we heat it? The distance between two molecules increases or decreases. Why?

6 Mean free path? It is the distance that Air: λ = 10 9 m Liquid : λ = 10 6 m Ifwe vacuum outair air, reducing pressure, the mean free path increases or decreases. Vacuum out a part of air Air: λ = atm Air: λ = greater or less than 10 9 m Thermal conductivity of gas is proportional to Mean free path of the gas. (Yes or No) Fluorescent lamp

7 1.4 Fluid properties Density = Specific volume = Specific weight = Specific gravity = 1.5 Ideal gas law PV = constant (Thermodynamics): PV = mrt What do we learn from this eq?

8 Pressure. What is pressure? It is a stress. Pressure always acts normal to a solid surface. Absolute pressure (PV = mrt) When we measure tire pressure of a car with a pressure gage, We measure gage or absolute pressure. Total Recall.

9 1.6 Viscosity What is viscosity? to flow Thickness, heaviness, stickiness Examples of very thick fluids: Blood is about times thicker than water.

10 Figure 1.8 (p. 17) Dynamic (absolute) viscosity of some common fluids as a function of temperature. 1.6 Viscosity Why do we do oil change when engine is hot? What happens if we try to change engine oil when engine is cold? Why does liquid viscosity decrease with increasing temperature?

11 Gas viscosity? Consider air flow through a pipe. Heating of a pipe where air flows inside. What happens? Air Intense local heating

12 Meltdown in nuclear powerplant. Why?

13 Meltdown in nuclear powerplant. Why? Gas viscosity it increases with increasing i temperature. t

14 Shear stress and shear rate relation Consider fluid between two parallel plates. Top plate is pulled with a force P. Figure 1 4 (p 14) Figure 1.4 (p. 14) (a) Deformation of material placed between two parallel plates. (b) Forces acting on upper plate.

15 Velocity profile u(y) is shown. No slip boundary conditions? What? Do you see velocity slope? Vl Velocity gradient? If we increase P, we increase U and shear stress. That increases velocity slope. Fi 15 ( 15) Figure 1.5 (p. 15) Behavior of a fluid placed between two parallel plates.

16 Shear stress vs. shear rate. What is a Newtonian fluid? What is a shear thinning fluid? Figure 1.7 (p. 16) Variation of shearing stress with rate of shearing strain for several types of fluids, including common non Newtonian fluids. Velocity gradient

17 Andrede s equation Viscosity as a function of temperature HW 158(p 1.58 (p.33) Table B2 B.2 At 10 o C, μ = mpa.s; at 30 o C, μ = 0.8 mpa.s; Find m at 25 o C. EXAMPLE 1.4 EXAMPLE 1.5

18 1.7 Compressibility of gases Compress Is air compressible or incompressible? PV = constant (Thermodynamics): What do we learn from this eq? Flat tire in bike: When we pump air to inflate the tire, are we compressing air? Why does tire pressure increase? Air When we compress air, does pressure increase? In MEM 220, we treat air as an incompressible fluid. Why? Later in MEM 320 Fluid Dynamics, we treat air as compressible fluid. Why?

19 1.8 Vapor pressure Vacuum out air Air at 1 atm (760 mmhg) Air at 13.4 mmhg Water initially at room temperature Water initially at room temperature Heating When water boils (evaporates), what is the temperature of water? Heating When water boils (evaporates), what is the temperature of water?

20 1.8 Vapor pressure Cavitation Can cold sea water boil at the tip of a propeller? (Chapter 3 Bernoulli Eq.)

21 1.9 Surface Tension Capillary rise It is a force existing at Why does mercury fall? Water Hg Why does water rise In a capillary glass tube? Figure 1.10 (p. 25) (a) Rise of column in a capillary glass tube. (b) Free body diagram for calculating column height. (c) Depression of column for a nonwetting liquid.

22 1.9 Surface Tension Object: to calculate l capillary rise Figure 1.9 (p. 25) Forces acting on one half of a liquid id drop. Water Example: Consider a glass capillary tube with an inside diameter of 11mm Example: Consider a glass capillary tube with an inside diameter of 1.1 mm. Estimate capillary rise h. Answer: see Eq.(1.22)

23 Sequoia National Park Trees are ft high. They must have water at the top. How do they get water at the top? the General Grant Tree, CA

24 HW 1.60 (p. 34) At the interface of two fluids, what is equal?

25 HW 1.67 Objective: to estimate shearing force on the reader head Fig. P 1.67 Hint: How do we describe shear stress? Shear force = shear stress x ( )

26 HW 1.70 Rotating viscometer (Co axial cylinders) Objective: to determine the expression of torque.

27 Rotating viscometer To measure viscosity it of liquidid

28 Water Stride bug Figure P (p. 37)

29 Water Stride bug

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