1 / 49

Chapter 14

Chapter 14. Fluids. Fluids at Rest. (Fluid = liquid or gas). Density ( r ). unit: kg/m 3 we will consider only r = m / V = constant (incompressible fluid) we will also assume g = constant. Pressure ( p ). A fluid exerts a force dF normal to any area dA you consider in it.

pandora
Download Presentation

Chapter 14

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 14 Fluids

  2. Fluids at Rest (Fluid = liquid or gas)

  3. Density (r) • unit: kg/m3 • we will consider only r = m/V = constant • (incompressible fluid) • we will also assume g = constant

  4. Pressure (p) • A fluid exerts a force dF normal to any area dA you consider in it. • For a fluid at rest, the force is equal and opposite on each side.

  5. Pressure (p) • Why is there a force? • Microscopically: the fluid particles are in motion and collide with dA • Macroscopically: the fluid is at rest

  6. Pressure (p) • pressure p is a scalar (no intrinsic direction) • reason: it acts normal to any surface dA

  7. Pressure (p) • units used:pascal, millibar, atm • 1 Pa = 1 N/m2 1 millibar = 100 Pa 1 atm = 1.013×105 Pa

  8. Terminology • ‘gauge pressure’ = p – patm • (can be > 0 or < 0) • (e.g., read on a car tire pressure gauge) • p = absolute pressure (> 0) = atmospheric pressure + gauge pressure = patm + gauge pressure

  9. Pressure and depth • pressure: pcoordinate: y • pressure decreases with ‘elevation’ y: Derive this result and integrate it

  10. Pressure and depth • coordinate: ydistance: h > 0 • p increases with depthfor any shape of vessel Demonstration: depth and shape of container

  11. Exercise 14-10 • The dangers of a long snorkel tube: • Find the gauge pressure at the depth shown. Will this cause the snorkeler’s lungs to collapse? Demonstration: atmospheric pressure

  12. Pascal’s Law • If any change in pressure Dp is applied at one point, it is transmitted to all points in the fluid and to walls enclosing it.

  13. Example: Hydraulic Lift At equilibrium, p = F1/A1 = F2/A2 Demonstration

  14. Two Pressure Gauges Notes on (b) first Notes on (a) and Exercise 14-9

  15. Homework Hints: Exercise 14-55

  16. Buoyancy and Buoyant Force

  17. A (fully or partially) submerged object feels an upward force equal to the weight of fluid it displaces

  18. (a) fluid element with weight wfluid(b) body of same shape feels buoyant force B = wfluid Demonstration

  19. Surface Tension • Molecules of liquid attract each other (else no definite volume) • center: net force = 0 • surface: net force is directed inward

  20. Surface Tension • So the surface acts like a membrane under tension (like a stretched drumhead) • The surface resists any change in surface area • Strength characterized by ‘surface tension’ Demonstration

  21. Surface Tension g • g = F/d = cohesive force per unit length • surface tension forceF = g d • We can measure g by just balancing F Notes on measuring g Do Example 14-23

  22. cohesion: attraction of like molecules example: liquid-liquid forces (surface tension)

  23. adhesion: attraction between unlike moleculesexample: liquid-glass forces

  24. (a) adhesion > cohesion: water wets glass(b) adhesion < cohesion: mercury beads up

  25. Capillarity • For these two cases, the surface tension force F pushes the column of liquid either up or down: • (a) up for water • (b) down for mercury Notes on capillary tubes

  26. Homework Announcements • Homework Set 5: Correction to hints for 14-55 (handout at front and on webpage) • Recent changes to classweb access (see HW 5 sheet at front and webpage) • Homework Sets 1, 2, 3: returned at front(scores to be entered on classweb soon)

  27. Midterm Announcements • Friday: • review required topics • practice problems (from class, HW, new?) • Monday: (midterm) • you can bring a sheet of notes (both sides) • you will be given a list of equations

  28. Fluid Flow (Fluid Dynamics)

  29. Flow line =path of fluidelement Flow tube =bundle of flow lines passingthrough area A (just a useful construct) Flow Fluid

  30. Steady flow: At any given point in the fluid, its properties (v, r, p) don’t change in time Simplifying Assumptions

  31. Steady flow: different flow lines never cross each other fluid entering a flow tube never leaves it Simplifying Assumptions

  32. Incompressible fluid: r = constant No friciton: no ‘viscosity’ Simplifying Assumptions

  33. the same volume dV of fluid enters and exits tube: dV = volume passing through A in dt = Av dt Notes Continuity EquationA1v1 = A2v2

  34. along the flow: A = area of flow tubev = speed of fluid if one increases, theother must decrease Continuity EquationA1v1 = A2v2 Notes and Demonstration: water flow

  35. Where the flow lines are crowding together, the fluid speed is increasing Continuity EquationA1v1 = A2v2

  36. only valid for:steady flow, incompressible fluid,no viscosity! Notes Bernoulli’s Equation

  37. if v1= v2= 0: reduces to previous result for fluid at rest Bernoulli’s Equation

  38. if y1= y2then for p and v: if one increases, theother must decrease Bernoulli’s Equation Demonstration

  39. Applications of Bernoulli’s Equation

  40. Notes Venturi Meter (Example 14-10) horizontal flow tube

  41. Note: if viscosity is present, then v decreases with distance from tube center

  42. Notes Venturi Meter:Homework Problem 14-90 (c) Demonstration

  43. Wing Lift

  44. Can’t predict flow lines but they indicate low pressure above wing, so net force up Demonstration: propellor

  45. Efflux Speed: vertical flow tube Notes

  46. First: you must fill the tube There is a limit:H + h < 10 m Siphon:flow tube points up, then down

  47. Warm-up demonstrations Curve Ball:viscosity makes it possible

  48. Viscosity drags air with spinning ball: low pressure=net force so the ball curves Demonstration

  49. Homework Announcements • Homework Set 5: Correction to hints for 14-55 (handout at front and on webpage) • Recent changes to classweb access (see HW 5 sheet at front and webpage) • Homework Sets 1, 2, 3: returned at front(scores to be entered on classweb soon)

More Related