1. III. Fluid Statics

2. Contents 1. Pressure in Static Fluid 2. Governing Equation 3. Units and Scales of Pressure 4. Pressure Measurement 5. Fluid Force on Plane Surface 6. Fluid Force on Curved Surface 7. Relative Equilibrium

3. 1. Pressure in Static Fluid

4. There is only inward-normal stress (pressure) on any contact area at a point in static fluid

5. The magnitude of the pressure at any point in static fluid is independent of the direction

7. Forces

8. Forces Balance

9. Force Balance

10. 1. 1.There is only inward-normal stress (pressure) on any contact area at a point in static fluid (by definition) 2. 2.The magnitude of the pressure at any point in static fluid is independent of the direction (by force balance) Stress state in static fluid can be described by a SCALAR

11. State of Stress In generalIn static fluids

12. 2. Basic Equation

13. Forces on a fluid element

14. Force balance

15. Force Balance

16. Governing Equation

17. The gradient of pressure is balanced by the body force

18. In the case of conservative force Y = Force potential

19. When gravity force is the only external force ( z axis is vertically upward )

20. Let h = -z ( h is the depth below a datum ) Pressure in a static fluid is linearly proportional to the depth below a datum

23. z = constant Horizontal plane in static fluid is necessarily equi-pressure plane p = constant

25. ? ?

26. Piezometric head in a static fluid is constant Position Head Pressure Head Piezometric head

27. 1 2

28. 3. Units and Scales of Pressure

29. Reference of pressure is taken at ZERO Absolute Pressure P A Relative Pressure P R Reference of pressure is taken at p 0 P R = Gage pressure P atm - P A = Vacuum pressure

31. Pressure measured by fluid force per unit area Pressure measured by equivalent height of liquid 1 atm = 1.034 at = 101325 Pa = 760 mm Hg = 10.34 m H 2 O Pressure measured by atmospheric pressure

32. 4. Pressure Measurement

33. Barometer

34. Piezometer h

35. Manometer h1h1h1h1 h2h2h2h2

36. Manometer for negative pressure h1h1h1h1 h2h2h2h2

37. Differential Manometer hBhBhBhB hAhAhAhA DhDhDhDh DzDzDzDz

38. 5. Fluid Force on Plane Surface

40. x y

41. Centroid

42. Centroid

43. Centre of pressure

44. PropertiesofAreas

45. Example Rock-fill Porous Water Impermeable Curtain Impermeable Layer Concrete Cover 2 1 h l

46. Example On the slope On the bottom

47. 6. Fluid Force on Curved Surface

49. S AzAz AxAx AyAy p

50. Fluid Force

53. Example 30° d

54. Horizontal Force No net force h

55. Vertical Force

56. Force Balance

57. Buoyancy

58. Stability of Floating Bodies

59. 7. Relative Equilibrium

60. Static state of fluid in a moving coordinate system is called relative equilibrium

61. Basic Equation D’Alembert’s Principle

62. Uniform Acceleration Equi-pressure surface

63. Uniform Rotation Equi-pressure surface