E4014 Construction Surveying

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 DiscussionsHydrostatics
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 DiscussionsFluid

• 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 DiscussionsFluid 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 DiscussionsFluid 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 DiscussionsFluid 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 DiscussionsPressure 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 newtons per square metre in SI
  units
• An alternative metric unit is the bar, which is
  105 N/m2.

10
Definitions DiscussionsPressure - Example

11
Definitions DiscussionsPressure 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/m2,
• equivalent to a head of 10.35m of water
• or 760 mm of mercury approximately, and decreases
  with altitude

12
Definitions DiscussionsPressure 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 DiscussionsPressure Scales

• Absolute Pressure
• the intensity of pressure measured above the
  absolute zero, which is a perfect vacuum

14
Definitions DiscussionsPressure Scales

• absolute pressure atmospheric pressure gauge
  pressure, or
• p(abs) p(atm) p(g)

15
Definitions DiscussionsPressure Scales

• absolute pressure atmospheric pressure gauge
  pressure, or
• p(abs) p(atm) p(g)

16
Definitions DiscussionsDimensions 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 DiscussionsDimensions Units

• Seven base dimensions, each with its own base unit

18
HydrostaticsIntroduction
19
HydrostaticsIntroduction
20
HydrostaticsHydrostatic laws - Horizontal
Pressure Variation

• Horizontal Hydrostatic Law
• Pressure has a constant value at a given
  horizontal level in a continuous fluid mass

21
HydrostaticsHydrostatic laws - Horizontal
Pressure Variation

22
HydrostaticsHydrostatic laws - Vertical Pressure
Variation
23
HydrostaticsHydrostatic laws - Vertical Pressure
Variation
24
HydrostaticsHydrostatic laws - Vertical Pressure
Variation
25
HydrostaticsHydrostatic laws - Vertical Pressure
Variation
26
HydrostaticsHydrostatic laws - Example

27
HydrostaticsHydrostatic laws - Example

68670 Pa
28
HydrostaticsHydrostatic laws - Example

68670 Pa
29
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
68670 Pa
30
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
19620 Pa
68670 Pa
31
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
19620 Pa
68670 Pa
32
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
9810 Pa
19620 Pa
68670 Pa
33
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
9810 Pa
9810 Pa
19620 Pa
68670 Pa
34
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
9810 Pa
9810 Pa
19620 Pa
PH due to benzine 51796.8 Pa
68670 Pa
35
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
9810 Pa
9810 Pa
19620 Pa
PH due to benzine 51796.8 Pa
68670 Pa
61606.8 Pa
36
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
9810 Pa
9810 Pa
19620 Pa
PH due to benzine 51796.8 Pa
68670 Pa
61606.8 Pa
37
HydrostaticsHydrostatic laws - Example

PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
9810 Pa
9810 Pa
19620 Pa
PH due to benzine 51796.8 Pa
PJ due to benzine 77695.2 Pa
68670 Pa
61606.8 Pa
38
HydrostaticsHydrostatic laws - Example

-16088.4 Pa
PF due to water 49050.0 Pa
PG due to water 58860.0 Pa
9810 Pa
9810 Pa
19620 Pa
PH due to benzine 51796.8 Pa
PJ due to benzine 77695.2 Pa
68670 Pa
61606.8 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
46
Hydrostatics Hydrostatic Pressure on Horizontal
Surfaces - example
47
Hydrostatics Hydrostatic Pressure on Horizontal
Surfaces - example

• Pressure 5886.0 N/m2

AreaBase 6.0m2
48
Hydrostatics Hydrostatic Pressure on Horizontal
Surfaces - example

• Pressure 5886.0 N/m2

AreaBase 6.0m2
49
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces
50
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces
F
51
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces
F
52
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces
F

• ICG formula for common shapes

53
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces
F
54
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces - Example
55
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces - Example
56
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces - Example
57
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces - Example
58
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces - Example
59
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces - Example
60
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces - Example
61
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 ApG

• where F is the magnitude of the force, A is the
  surface area of the immersed surface and pG is
  the pressure at the centroid

63
Hydrostatics Hydrostatic Pressure on Inclined
Surfaces

• Formula to calculate the pressure at the centroid

Where hCG 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 yCP is the depth to the centre of the
  pressure measured along the inclined surface (not
  vertically), yCG is the depth to the centre of
  gravity of the surface measured along the
  inclined surface and ICG 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.