1. FLUIDS AND THEIR PROPERTIES

2. Introduction
Fluid mechanics is the science that deals with the action of forces on fluids at rest as well as in motion.
If the fluids are at rest, the study of them is called fluid statics.
If the fluids are in motion, where pressure forces are not considered, the study of them is called fluid Kinematics
If the fluids are in motion and the pressure forces are considered, the study of them is called fluid dynamics.

3. Velocity field-Continuum Hypothesis
The flow is made of tightly packed fluid
particles that interact with each other. Each particle consists of numerous molecules, and we can describe the field variables velocity, acceleration, pressure, and density of these particles at a given time.

4. What is a Continuum?
This assumption works well in applications where the features we are interested in studying are much larger than the distance between molecules. The mean free path of air at standard conditions is approximately 0.1 m. As long as the smallest features of the problem are greater than this scale, the continuum approximation is a good one. In liquids the mean free path is usually a few angstroms (an angstrom is 10-10m, making cases where we must account for non-continuum effects rare for an engineer.

5. Fluid Thus Fluid exist in two form:- Liquid Gas
Matter exists in two states- the solid state and the fluid state. This classification of matter is based on the spacing between different molecules of matter as well as on the behavior of matter when subjected to stresses.
Because molecules in solid state are spaced very closely, solids possess compactness and rigidity of form. The molecules in fluid can move more freely within the fluid mass and therefore the fluids do not possess any rigidity of form.
The primary property that differentiates fluid from solid behavior is that fluids cannot support shear forces at equilibrium. If I take a block of solid material between my hands and shear it, the solid resists the motion. I can deform the material, but the solid can resist and stop the motion. Fluid on the other hand, will just flow and cannot stop the shearing force.
Thus Fluid exist in two form:-
Liquid
Gas

6. 1.What is Fluid?
Fluid is a substance that is capable of flowing. It has no definite shape of its own. It assumes the shape of its container.
Both liquids and gases are fluids.
Examples of fluids are :
i. water
ii. milk
iii. kerosene
iv. petrol
v. emulsions etc.

7. Hydrostatics
No relative motion between adjacent layers. Thus, no shear stress (tangential stress) to deform the fluid.
The only stress in fluid statics is normal stress (perpendicular to surface)
Normal stress is due to pressure (Pressure: gravity field-weight of fluid)
Variation of pressure is due only to the weight of the fluid → fluid statics is only relevant in presence of gravity fields.
Connected vessels:

8. Properties of Fluids Density = r (decreases with rise in T)
mass per unit volume ( lbs/ft3 or kg/m3 )
for water density = 1.94 slugs/ft3 or 1000 kg/m3
Specific Weight = g (Heaviness of fluid)
weight per unit volume g = rg
for water spec wt = 62.4 lbs/ft3 or 9.81 kN/m3
Specific Gravity = SG
Ratio of the density of a fluid to the density of water
SG = rf / rw SG of Hg = 13.55

9. Ideal Gas Law relates pressure to Temp for a gas
P = rRT
T in 0K units
R = 287 Joule / Kg-0K
Pressure
Force per unit area:
lbs/in2 (psi), N/m2, mm Hg, mbar or atm
1 Nt/m2 = Pascal = Pa
Std Atm P = 14.7 psi = kPa = 1013 mb
Viscosity fluid deforms when acted on by shear stress
m = 1.12 x 10-3 N-s/m2
Surface tension - forces between 2 liquids or gas and liquid - droplets on a windshield.

10. Atmospheric Pressure Pressure = Force per Unit Area
Atmospheric Pressure is the weight of the column of air above a unit area. For example, the atmospheric pressure felt by a man is the weight of the column of air above his body divided by the area the air is resting on
P = (Weight of column)/(Area of base)
Standard Atmospheric Pressure:
1 atmosphere (atm) lbs/in2 (psi) Torr (mm Hg) millibars = kPascals
1kPa = 1Nt/m2

11. Variation of Pressure with Depth
In the presence of a gravitational field, pressure increases with depth because more fluid rests on deeper layers.
To obtain a relation for the variation of pressure with depth, consider rectangular element
Force balance in z-direction gives
Dividing by Dx and rearranging gives

12. Variation of Pressure with Depth
Pressure in a fluid at rest is independent of the shape of the container.
Pressure is the same at all points on a horizontal plane in a given fluid.

13. A water tower is an elevated structure supporting a water tank constructed at a height sufficient to pressurize a water supply system for the distribution of potable water, and to provide emergency storage for fire protection. Water towers are able to supply water even during power outages, because they rely on hydrostatic pressure produced by elevation of water (due to gravity) to push the water into domestic and industrial water distribution systems; however, they cannot supply the water for a long time without power, because a pump is typically required to refill the tower. A water tower also serves as a reservoir to help with water needs during peak usage times. The water level in the tower typically falls during the peak usage hours of the day, and then a pump fills it back up during the night.

14. Scuba Diving and Hydrostatic Pressure

15. Scuba Diving and Hydrostatic Pressure
Pressure on diver at 100 ft?
Danger of emergency ascent? 1
100 ft 2
Boyle’s law
If you hold your breath on ascent, your lung
volume would increase by a factor of 4, which would result in embolism and/or death.

16. Pascal’s Law
Pressure applied to a confined fluid increases the pressure throughout by the same amount.
In picture, pistons are at same height:
Ratio A2/A1 is called ideal mechanical advantage

17. Pascal’ law
Hydrostatics

18. The Manometer
An elevation change of Dz in a fluid at rest corresponds to DP/rg.
A device based on this is called a manometer.
A manometer consists of a U-tube containing one or more fluids such as mercury, water, alcohol, or oil.
Heavy fluids such as mercury are used if large pressure differences are anticipated.

19. Mutlifluid Manometer For multi-fluid systems
Pressure change across a fluid column of height h is DP = rgh.
Pressure increases downward, and decreases upward.
Two points at the same elevation in a continuous fluid are at the same pressure.
Pressure can be determined by adding and subtracting rgh terms.

20. Measuring Pressure Drops
Manometers are well--suited to measure pressure drops across valves, pipes, heat exchangers, etc.
Relation for pressure drop P1-P2 is obtained by starting at point 1 and adding or subtracting rgh terms until we reach point 2.
If fluid in pipe is a gas, r2>>r1 and P1-P2= rgh

21. The Barometer
Atmospheric pressure is measured by a device called a barometer; thus, atmospheric pressure is often referred to as the barometric pressure.
PC can be taken to be zero since there is only Hg vapor above point C, and it is very low relative to Patm.
Change in atmospheric pressure due to elevation has many effects: Cooking, nose bleeds, engine performance, aircraft performance.

22. Fluid Statics
Fluid Statics deals with problems associated with fluids at rest.
In fluid statics, there is no relative motion between adjacent fluid layers.
Therefore, there is no shear stress in the fluid trying to deform it.
The only stress in fluid statics is normal stress
Normal stress is due to pressure
Variation of pressure is due only to the weight of the fluid → fluid statics is only relevant in presence of gravity fields.
Applications: Floating or submerged bodies, water dams and gates, liquid storage tanks, etc.

23. Buoyancy and Stability
Buoyancy is due to the fluid displaced by a body. FB=rfgV.
Archimedes principal : The buoyant force acting on a body immersed in a fluid is equal to the weight of the fluid displaced by the body, and it acts upward through the centroid of the displaced volume.

24. Buoyancy and Stability
Buoyancy force FB is equal only to the displaced volume rfgVdisplaced.
Three scenarios possible
rbody<rfluid: Floating body
rbody=rfluid: Neutrally buoyant
rbody>rfluid: Sinking body

25. Example: Galilean Thermometer
Galileo's thermometer is made of a sealed glass cylinder containing a clear liquid.
Suspended in the liquid are a number of weights, which are sealed glass containers with colored liquid for an attractive effect.
As the liquid changes temperature it changes density and the suspended weights rise and fall to stay at the position where their density is equal to that of the surrounding liquid.
If the weights differ by a very small amount and ordered such that the least dense is at the top and most dense at the bottom they can form a temperature scale.

26. Example: Floating Drydock
Auxiliary Floating Dry Dock Resolute (AFDM-10) partially submerged
Submarine undergoing repair work on
board the AFDM-10
Using buoyancy, a submarine with a displacement of 6,000 tons can be lifted!

27. Example: Submarine Buoyancy and Ballast
Submarines use both static and dynamic depth control. Static control uses ballast tanks between the pressure hull and the outer hull. Dynamic control uses the bow and stern planes to generate trim forces.

28. Examples of Archimedes Principle

29. The Golden Crown of Hiero II, King of Syracuse
Archimedes, B.C.
Hiero, B.C.
Hiero learned of a rumor where the goldsmith replaced some of the gold in his crown with silver. Hiero asked Archimedes to determine whether the crown was pure gold.
Archimedes had to develop a nondestructive testing method

30. The Golden Crown of Hiero II, King of Syracuse
The weight of the crown and nugget are the same in air: Wc = rcVc = Wn = rnVn.
If the crown is pure gold, rc=rn which means that the volumes must be the same, Vc=Vn.
In water, the buoyancy force is B=rH2OV.
If the scale becomes unbalanced, this implies that the Vc ≠ Vn, which in turn means that the rc ≠ rn
Goldsmith was shown to be a fraud!

31. 2. Types of Fluids
Fluids can be classified into five basic types. They are:
Ideal Fluid
Real Fluid
Pseudo-plastic Fluid
Newtonian Fluid
Non-Newtonian Fluid

32. 2.1 Ideal Fluid An Ideal Fluid is a fluid that has no viscosity.
It is incompressible in nature.
Practically, no ideal fluid exists.

33. 2.2 Real Fluid
Real fluids are compressible in nature. They have some viscosity.
Real fluids implies friction effects.
Examples: Kerosene, Petrol, Castor oil

34. What is viscosity? Rheology Viscosity
Deformation and flow of matter under the influence of applied stress
Viscosity, elasticity, and plasticity
Viscosity
Measure of the resistance to deformation of a fluid under shear stress

35. Shear Stress Experiment
Internal friction between layers of flow
(Wikipedia 2006)

36. Molecular Origins Gases Liquids
Molecular diffusion between layers of flow
Independent of pressure
Increases with increasing temperature
Newtonian
Liquids
Additional forces between molecules but exact mechanics unknown
Independent of pressure except at very high pressure
Decrease with increasing temperature
Newtonian and non-Newtonian

37. Hydrogen bonding in water
Chemistry 140 Fall 2002
Hydrogen bonding in water
Solid ice has lower density than liquid water. H-bonding holds the ice in a rigid but open structure.
Maximum density of water at 3.98 C.
around one molecule in solid phase in liquid phase

38. Examples for Hydrogen Bonding

39. Characterization of Fluids
Newtonian Fluid
Non-Newtonian Fluids are usually complex mixtures
(de Nevers 2005)

40. Introduction Kinematic Viscosity :
Viscosity is a quantitative measure of a fluid’s resistance to flow.
Dynamic (or Absolute) Viscosity:
The dynamic viscosity(η) of a fluid is a measure of the resistance it offers to relative shearing motion.
η= F/ [A×(u/h)]
η= τ /(u/h) N-s/m²
Kinematic Viscosity :
It is defined as the ratio of absolute viscosity to the density of fluid.
ν= η/ρ m²/s ; ρ= density of fluid

41. Viscosity Measurements
Capillary Viscometers
It gives the ‘kinematic viscosity’ of the fluid. It is based on Poiseuille’s law for steady viscous flow in a pipe.

42. Viscosity Measurements
Rotational Viscometers
These viscometer give the value of the ‘dynamic viscosity’.
It is based on the principle that the fluid whose viscosity is being measured is sheared between two surfaces.
In these viscometers one of the surfaces is stationary and the other is rotated by an external drive and the fluid fills the space in between.
The measurements are conducted by applying either a constant torque and measuring the changes in the speed of rotation or applying a constant speed and measuring the changes in the torque.
There are two main types of these viscometers: rotating cylinder and cone-on-plate viscometers

43. Viscosity Measurements
Rotating cylinder viscometer

44. Viscosity Measurements
Cone-on-plate viscometer

45. Effects of temperature
The viscosity of liquids decreases with increase the temperature.
The viscosity of gases increases with the increase the temperature.

46. Effects of temperature
The lubricant oil viscosity at a specific temperature can be either calculated from the viscosity - temperature equation or obtained from the viscosity-temperature ASTM chart.
Viscosity-Temperature Equations

47. Effects of temperature
fig: Viscosity-temperature characteristics of selected oils

48. Effects of pressure

49. Viscosity - shear relationship
For Newtonian fluids, shear stress linearly vary with the shear rate as shown in Figure. Viscosity is constant for this kind of fluid.
τ = η (u/h)
Non Newtonian fluid doesn’t
follow the linear relation
between viscosity and shear rate.

50. Viscosity – shear relationship
Pseudoplastic Behaviour
Pseudoplastic or shear thinning and is associated with the thinning of the fluid as the shear rate increases.
Thixotropic Behaviour
Thixotropic or shear duration thinning, is associated with a loss of consistency of the fluid as the duration of shear increases.
The opposite of this behavior is
known as inverse thixotropic.

51. Applications Selection of lubricants for various purpose.
- we can choose an optimum range of viscosity for engine oil.
- for high load and also for speed operation high viscous lubricants is required.
In pumping operation
- for high viscous fluid high power will require.
- for low viscous fluid low power will require.
In making of blend fuel
- less viscous fuels easy to mix.
In the operation of coating and printing.

52. 2.3 Pseudo-plastic Fluid
A fluid whose apparent viscosity or consistency  decreases instantaneously with an increase in  shear rate.
Examples are:
i. quick sand
ii. ketch-up etc.

53. 2.4 Newtonian fluid
Fluids that obey Newton’s law of viscosity are known as Newtonian Fluids. For a Newtonian fluid, viscosity is entirely dependent upon the temperature and pressure of the fluid.
Examples: water, air, emulsions

54. 2.5 Non-Newtonian Fluids
Fluids that do not obey Newton’s law of viscosity are non-Newtonian fluids.
Examples: Flubber, Oobleck (suspension of starch in water), Pastes, Gels & Polymer solutions.

56. 3. Properties of Fluids
Properties of fluids determine how fluids can be used in engineering and technology. They also determine the behaviour of fluids in fluid mechanics. They are:
Density
Viscosity
Surface Tension
Capillary Action
Specific Weight
Specific Gravity

57. 3.1 density
Density is the mass per unit volume of a fluid. In other words, it is the ratio between mass (m) and volume (V) of a fluid.
Density is denoted by the symbol ‘ρ’. Its unit is kg/m3.

58. 3.2 Viscosity
Viscosity is the fluid property that determines the amount of resistance of the fluid to shear stress.
It is the property of the fluid due to which the fluid offers resistance to flow of one layer of the fluid over another adjacent layer.

59. 3.2.1 Dynamic Viscosity
The Dynamic (shear) viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different speeds. 

60. 3.2.2 Kynematic Viscosity
The kinematic viscosity (also called "momentum diffusivity") is the ratio of the dynamic viscosity μ to the density of the fluid ρ.

61. 3.3 Surface Tension
The property of fluids to resist tensile stresses on their surface is called as Surface Tension.

62. 3.4 Capillary Action
Capillary action is the property of fluid to flow in a narrow spaces without assistance of and in opposition to external forces like gravity.
The effect can be seen in the drawing up of liquids between the hairs of a paint-brush, in a thin tube, in porous materials such as paper and plaster, in some non-porous materials such as sand or in a cell.
It occurs because of intermolecular forces between the liquid and surrounding solid surfaces.

64. 3.5 Specific Weight
Specific weight is the weight possessed by unit volume of a fluid. It is denoted by ‘w’. Its unit is N/m3.
Specific weight varies from place to place due to the change of acceleration due to gravity (g).

65. 3.6 Specific Gravity
Specific gravity is the ratio of specific weight of the given fluid to the specific weight of standard fluid.
It is denoted by the letter ‘S’. It has no unit.