1. E4014 - Construction Surveying HYDRAULICS

2. Introduction surveyors –usually not be directly involved in the design of hydraulics systems –most certainly will be responsible for the setting out of such systems. surveyor may need to alter the design of a system ‘on-site’ – the principles involved in this field must be understood.

3. Introduction It is with this in mind and the desire to make you better able to understand the requirements of the engineer or design draftsman responsible for the project that this module is included.

4. Definitions & Discussions Hydrostatics & Hydrodynamics Hydrostatics –The study of the properties of fluids which are at rest or in equilibrium (e. g. storage systems such as dams and reservoirs). Hydrodynamics –The study of the properties of fluids which are in motion in pipes and channels (e.g. water or sewerage reticulation and drainage systems).

5. Definitions & Discussions Fluid –can offer no permanent resistance to any force causing change of shape. – flow under their own weight –take the shape of any solid body with which they are in contact.

6. Definitions & Discussions Fluid cont –change of shape is caused by shearing forces; therefore if shearing forces are acting in a fluid it will flow. –Conversely, if a fluid is at rest there can be no shearing forces in it, and all forces are perpendicular (normal) to the planes on which they act.

7. Definitions & Discussions Fluid cont Fluids are divided into liquids and gases. Liquid –difficult to compress; –a given mass occupies a fixed volume irrespective of the size of the container holding it –a ‘free surface’ is formed as a boundary between the liquid and the air above it.

8. Definitions & Discussions Fluid cont Fluids are divided into liquids and gases. Gas –easily compressed; –expands to fill any vessel in which it is contained – does not form a free surface.

9. Definitions & Discussions Pressure & Intensity of Pressure Pressure –force exerted by a fluid on the surfaces with which it is in contact, or by one part of a fluid on the adjoining part. intensity of pressure at any point – force exerted on the unit area at that point measured in newton’s per square metre in SI units An alternative metric unit is the bar, which is 10 5 N/m 2.

10. Definitions & Discussions Pressure - Example

11. Definitions & Discussions Pressure Scales Atmospheric Pressure –The earth is surrounded by an atmosphere many miles high. –The pressure due to this atmosphere at the surface of the earth depends upon the head of air above the surface. –Atmospheric pressure at sea level is about 101.325 kN/m 2, equivalent to a head of 10.35m of water or 760 mm of mercury approximately, and decreases with altitude

12. Definitions & Discussions Pressure Scales Vacuum – A perfect vacuum is a completely empty space in which, therefore, the pressure is zero Gauge Pressure –the intensity of pressure measured above or below atmospheric pressure

13. Definitions & Discussions Pressure Scales Absolute Pressure –the intensity of pressure measured above the absolute zero, which is a perfect vacuum

14. Definitions & Discussions Pressure Scales –absolute pressure = atmospheric pressure + gauge pressure, or –p(abs) = p(atm) + p(g)

15. Definitions & Discussions Pressure Scales –absolute pressure = atmospheric pressure + gauge pressure, or –p(abs) = p(atm) + p(g)

16. Definitions & Discussions Dimensions & Units Dimensions –various physical properties that all matter possess –describe the state of things Units –internationally agreed measurable quantities of the various dimensions –SI ( System International ) kilogram, metre, cubic metre, metre per second, kelvin, ampere, and joule

17. Definitions & Discussions Dimensions & Units Seven base dimensions, each with its own base unit

18. Hydrostatics Introduction

20. Hydrostatics Hydrostatic laws - Horizontal Pressure Variation Horizontal Hydrostatic Law –Pressure has a constant value at a given horizontal level in a continuous fluid mass

21. Hydrostatics Hydrostatic laws - Horizontal Pressure Variation

22. Hydrostatics Hydrostatic laws - Vertical Pressure Variation

26. Hydrostatics Hydrostatic laws - Example

27. Hydrostatics Hydrostatic laws - Example 68670 Pa

28. Hydrostatics Hydrostatic laws - Example 68670 Pa

29. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa

30. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa

31. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa

32. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa 9810 Pa

33. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa 9810 Pa

34. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa 9810 Pa P H due to benzine = 51796.8 Pa

35. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa 9810 Pa P H due to benzine = 51796.8 Pa 61606.8 Pa

36. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa 9810 Pa P H due to benzine = 51796.8 Pa 61606.8 Pa

37. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa 9810 Pa P H due to benzine = 51796.8 Pa 61606.8 Pa P J due to benzine = 77695.2 Pa

38. Hydrostatics Hydrostatic laws - Example 68670 Pa P F due to water = 49050.0 Pa 19620 Pa P G due to water = 58860.0 Pa 9810 Pa P H due to benzine = 51796.8 Pa 61606.8 Pa P J due to benzine = 77695.2 Pa -16088.4 Pa

39. Hydrostatics Pressure Units Expressed in two ways –pressure head the height of the free surface of a particular liquid above the surface in question –traditional pressure units Pascals (Pa) = Newtons/square metre

40. Hydrostatics Pressure Units - Example

41. Hydrostatics Pressure Units - Example

42. Hydrostatics Pressure Units - Example

43. Hydrostatics Hydrostatic Pressure on Surfaces A fluid in contact with a solid surface will exert a force on every small area of the surface. The total pressure on the surface can be represented by a point force equal to the product of the pressure on the small element and its area.

44. Hydrostatics Hydrostatic Pressure on Surfaces The point at which this force must act is the centroid.

45. Hydrostatics Hydrostatic Pressure on Horizontal Surfaces - example

47. Pressure = 5886.0 N/m 2 Area Base = 6.0m 2

48. Hydrostatics Hydrostatic Pressure on Horizontal Surfaces - example Pressure = 5886.0 N/m 2 Area Base = 6.0m 2

49. Hydrostatics Hydrostatic Pressure on Inclined Surfaces

50. F

51. F

52. I CG formula for common shapes F

53. Hydrostatics Hydrostatic Pressure on Inclined Surfaces F

54. Hydrostatics Hydrostatic Pressure on Inclined Surfaces - Example

62. Hydrostatics Hydrostatic Pressure on Inclined Surfaces When the surface is not horizontal it can be shown that ‘the hydrostatic force on an immersed plane surface is the product of the surface area and the pressure at its centroid’ F = Ap G where F is the magnitude of the force, A is the surface area of the immersed surface and p G is the pressure at the centroid

63. Hydrostatics Hydrostatic Pressure on Inclined Surfaces Formula to calculate the pressure at the centroid Where h CG = vertical depth to the centre of gravity (or centroid) of the immersed surface So...

64. Hydrostatics Hydrostatic Pressure on Inclined Surfaces the position of the centre of pressure of an inclined surface. where y CP is the depth to the centre of the pressure measured along the inclined surface (not vertically), y CG is the depth to the centre of gravity of the surface measured along the inclined surface and I CG is the second moment of inertia of the immersed surface about its horizontal centroidal axis.

65. Hydrostatics Hydrostatic Pressure on Surfaces A fluid in contact with a solid surface will exert a force on every small area of the surface. The total pressure on the surface can be represented by a point force equal to the product of the pressure on the small element and its area.