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1. Fundamentals of Fluid
Mechanics

2.  It is a physical science concerned with the behavior of the fluids which are in either at
rest, motion, and forces acting on them.

4.  UNIT OPERATIONS AND UNIT PROCESS

6.  Fluids are substances that deform
continuously and permanently when they
are subjected to forces that vary spatially
in magnitude or direction.
 Fluids can be classified as either liquids,
which are relatively dense and maintain a
definite volume, and gases, which are less
dense and expand to fill their container.
 Fluids, both liquids and gases, are
distinguished from solids by their inability
to withstand deforming forces: in contrast
to solids, they continue to deform for as
long as the deforming forces are applied.

9.  Force is an external agent capable of changing a body’s state of rest or motion. It
has a magnitude and a direction.
 The direction towards which the force is applied is known as the direction of the
force, and the application of force is the point where force is applied.
 Definition of force:
Law?

10.  Stress: The internal restoring force acting per unit area of the cross-section of the
deformed body is called stress.
 Stress = (Applied force / Area) = F / A
 Its unit is Newton / m2
 Or Pascal.
 Normal stress:

11. Stress = (Applied force / Area)
= F / A

12.  If normal stress acts away from the area and there is an increase in length then it
is known as tensile stress.

13.  If the normal stress acts into the area and there is a decrease in length under the
effect of applied force then, it is compressive stress.

14.  shear stress, force tending to cause deformation of a material by slippage along
a plane or planes parallel to the imposed stress.
 The resultant shear is of great importance in nature, being intimately related
to the downslope movement of earth materials and to earthquakes.
 Shear stress may occur in solids or liquids; in the latter it is related to fluid
viscosity.

17. APPLY HYDROSTATIC EQUILIBRIUM
PRINCIPLE, DEVELOP THE
EXPRESSION TO ESTIMATE THE
PRESSURE DIFFERENCE IN A VERTICAL
COLUMN. (10 M)

18. HYDROSTATIC
EQUILIBRIUM
Gravity

19.  The hydrostatic law states that the rate of increment of pressure is
equal to the specific weight of the fluid at any point in a static fluid
system.
 In hydrostatic equilibrium conditions, the force exerted by the fluid is
balanced by its weight. Maintaining the hydrostatic balance is the key
concept of buoyancy.

20. Manometer
Continuous Gravity Decanter
Centrifugal Decanter

22. The air around you has weight, and it
presses against everything it touches.
That pressure is called atmospheric pressure, or air
pressure.
 Atmospheric pressure is the force exerted on a surface by
the air above it as gravity pulls it to Earth.
 Atmospheric pressure is commonly measured with a -------
------------.

23. The atmospheric pressure is not the same
throughout. At sea level, the pressure 760 mm of
mercury, and it --------------- as we move upwards.

24.  Evangelista Torricelli (1643) invented a device called the barometer to measure
atmospheric pressure.
 It consists of a one-metre glass tube closed at one end, filled with mercury, and
then dipped into a bowl of mercury.
 The level of mercury inside the tube settles at 760 mm when we are at sea level.
 The space above the mercury column is a vacuum which is also known as
Torricelli Vacuum.

26.  A Manometer is a device to measure pressures.
 A common simple manometer consists of a U
shaped tube of glass filled with some liquid.
 Typically the liquid is mercury because of its
high density.

27.  Manometric liquid is the liquid that is filled in a manometer to
measure the pressure of other liquid or gases.
 The balancing liquids in a manometer are selected based on the
range of pressure measurement and the required sensitivity.
 A manometric liquid, besides density, should also have a defined
meniscus,
 low surface tension and should be immiscible into fluid whose
pressure is to be measured.
 For low range and high sensitivities liquids of low specific gravity:
CCl4 ( Sp. Gr. 1.595), Acetyl tetra Bromide (2.95) and antimony
pentachloride (2.99) are used.

29. Manometer measure the pressure difference
between 2 points in a pipe or between 2 pipes

33. It resembles to a U-tube Manometer. One limb is
a tube of uniform bore (6 mm internal diameter)
which is kept inclined at a low angle to the
horizontal line
• The other limb is transformed to a large reservoir
with cross-sectional area 300-400 times larger than
that of the cross-sectional area of inclined limb.
• Any change in the level of manometer fluid in the
reservoir can be neglected in comparison with the
change in fluid level in the inclined tube.
• Hence, a scale along the inclined limb directly
reads pressure difference.

34.  An inclined tube manometer is a sensitive manometer used to calculate
differential pressure in fluids where the pressure values are to be measured
with greater accuracy, such as in vacuum systems or low-pressure gas
pipelines.
 This level of accuracy is generally an expectation in standards institutions like
the International Standards Organisation (ISO) or the American Society of
Mechanical Engineers (ASME).
 This manometer can be used and is commonly used to measure negative
pressure, also known as vacuum pressure.
 These sorts of manometers improve readability by elongating an upright
differential head in a column. The manometer is useful for preserving accurate
pressure points of steam in industries.

35.  For greater sensitivity, the inclined tube manometers can be filled with alcohol which also gives
better meniscus than water.
 The instrument can be made suitable to measure a wide range of pressures by changing the
inclination of tube.
 Smaller angle of inclination can be used for measuring lower range of pressures.
 For a large range of pressure, arrangement is made for varying the inclination of the tube.
 For low-pressure measurements, a ------------- value for the angle of inclination `α` is chosen,
 whereas for measurements in the high-pressure range, the value of `α` is ------------.
 The pressure measured by such a manometer is given by the equation………………….

38. a) What are the various pressure measuring devices?
b) A simple U-Tube manometer is used to measure the head or
pressure drop across a flow meter. The heavier fluid is
mercury with a density of 13.6g/cm3 and the top fluid is
water. The reading on the manometer is 32.7cm. Calculate the
pressure difference.

41.  Rotational flow: A flow is called a rotational flow when fluid particles rotate about
their centre of mass in the flow field.
 Irrotational flow: A flow is called an irrotational flow when fluid particles does not
rotate about their centre of mass in the flow field.
 In case of irrotational flow there is no torque i.e there is no tangential force and
this is generally associated with non-viscous fluid.

44. Ideal fluid :
An incompressible fluid with zero viscosity.
The flow of ideal fluid is called as Potential flow.
2 characteristics:
• Irrotational flow: No eddies formation
• No friction is created: No dissipation of
mechanical energy to heat

46. Reynolds Experiments
1883

47.  In early 1883, Reynolds performed his classic experiment on fluid flow,
investigating different flow rates of water by squirting a jet of dyed water into
water flowing through a large glass pipe.
 There was a control valve at one end of the pipe to allow him to control the
velocity.
 He noted that at low velocities, the layer of dyed water kept its shape as it flowed
through the pipe, while at higher velocities, the dyed layer broke apart and
diffused through the rest of the water.
 This was the transition point between what is now known as laminar (smooth)
flow and turbulent (disorderly) flow.

48. 2100
2100

49. Transition flow: 2100<Re<4000

51.  Shear stress occurs when the force is applied parallel to a surface.
 Such a force is called a shear force.
 Now, we know that strain is defined as the change in dimension such as length to
original dimension of the body.
 Shear strain is the change occurring in the dimension due to shear stress.
 Shear rate: rate of change of velocity at which point one fluid layer passes over
another layer. (velocity gradient)

54. RHEOLOGY IS THE STUDY OF THE
FLOW OF MATTER, PRIMARILY IN A
FLUID STATE, BUT ALSO AS "SOFT
SOLIDS"

56.  A fluid with------------------ (large/low) viscosity resists motion
because its molecular makeup gives it a lot of internal friction.
 A fluid with ------------ (large/low) viscosity flows easily because its
molecular makeup results in very little friction when it is in motion.

57.  Viscosity is the physical property that characterizes the flow resistance
of simple fluids.
 Newton’s law of viscosity defines the relationship between the shear
stress and shear rate of a fluid subjected to a mechanical stress.
 The ratio of shear stress to shear rate is a constant, for a given
temperature and pressure, and is defined as the viscosity or coefficient
of viscosity.
 Newtonian fluids obey Newton’s law of viscosity. The viscosity is
independent of the shear rate.

58.  NEWTONIAN FLUIDS
 A Newtonian fluid's viscosity remains constant, no matter the amount of shear applied for a
constant temperature. These fluids have a linear relationship between viscosity and shear stress.
 Examples:
• Water
• Mineral oil
• Gasoline
• Alcohol

60. Thins or Thickens Yes or No

61.  The space between the parallel plates kept 3 mm apart is filled with oil of dynamic viscosity
0.2 Pa.Sec. what is the shear stress if the upper plate is moving at a velocity of 1.5 m/Sec.
 An incompressible fluid (kinematic viscosity, 7.4 × 10–7 m2/s, specific gravity, 0.88) is held
between two parallel plates. If the top plate is moved with a velocity of 0.5 m/s while the
bottom one is held stationary, the fluid attains a linear velocity profile in the gap of 0.5 mm
between these plates; the shear stress in Pascals on the surface of top plate is?

62. 1.Viscosity denotes resistance to flow.
2.Viscosity in gases is caused by molecules passing through layers of flow and
transferring momentum between them.
3.Gas viscosity increases with temperature, whereas liquid viscosity decreases with
temperature. Because intermolecular forces weaken with temperature, viscosity
decreases.
4.Temperature increases typically cause an increase in molecular interchange because
molecules move faster at higher temperatures. The coefficient of viscosity is a
measure of the fluid's resistance to flow.

63. Critical
Reynolds
Number?

64. • The critical Reynolds number can be used to define
the transition from laminar to turbulent flow for a
particular system as the fluid flow rate increases.
• There is no single critical Reynolds number, but rather
it tends to lie in a broad range from approximately
2300 to 4000 for many enclosed systems

65. BOUNDARY LAYERS
 Boundary layer is defined as a part of a moving fluid in which the fluid motion is
influenced by the presence of solid boundary.
Boundary Layer:
The imaginary surface layer which
separates the fluid that is directly
affected by the plate from which local
velocity is constant or equal to initial
velocity of the approach fluid.

66. : Fluid velocity at solid fluid interface is zero.
Interview Question

67. Laminar zone: Boundary layer near to the
wall surface is small : Laminar.
Turbulent flow in boundary layer
Viscous Sub
Layer
Buffer Layer Turbulent Zone

68.  Viscous sublayer is a region closest to the wall.
 The flow is not strictly laminar in the viscous sublayer because it experiences random
fluctuations in velocity.
 But because fluctuations in velocity normal to the boundary must decrease to zero at the
boundary.
The buffer layer is a zone just outside the viscous sublayer in which the gradient of time-
average velocity is still very high but the flow is strongly turbulent.
It’s a transition zone from the laminar to turbulent.
As flow goes away from the wall, shear stress decreases and turbulence activity appears.
 Turbulent layer: The region outside the buffer layer and extending all the way to the free
surface is called the outer layer.
 turbulent eddies here are more efficient at transporting momentum normal to the flow
direction than are the much smaller eddies nearer the boundary.

70.  Consider a straight tube with fluid entering at a
uniform velocity.
 Initially boundary layer occupies only a small part of
tube.
 In the boundary layer the velocity is increased from
zero at the wall to constant velocity existing in the
core.
 As the stream moves farther down the tube, the
boundary layer occupies an increasing portion of
cross section.
 Finally, the boundary layer occupies entire cross
section and a constant velocity distribution. This flow
is called as Fully developed flow.

71.  The length of the tube necessary to the boundary layer to reach the center of the
tube and fully developed flow to be established is called Transition length.

73.  Consider the far side of a submerged object, where the fluid leaves the solid
surface.
 If the flow is parallel to the plate:
 At the edge of flat plate, the boundary layer is formed.
 After the fluid leaves the plate, the boundary layer disappear and fluid moves at a
uniform velocity.

74.  If the flow is perpendicular to the plate:
 The boundary layer forms as before flowing
over the plate.
 Because of boundary layer formation, when
the fluid reaches the edge of plate, the
momentum prevents it from making sharp
turn around the edge and it separates from
plate and proceeds.
 Due to this, there is a large eddies formation
called vortices are formed.
 This zone is called Wake.

75. 1. Hydrostatic equilibrium derivation.
2. U-Tube manometer derivation.
3. Rheological properties of fluids
4. Qns on Boundary layer
5. Problems on Utube manometer and Newtons law of viscosity
6. Explain with necessary expressions.
 i.Steady and Unsteady flow.
 ii.Uniform and non-uniform flow.
 iii.Laminar and turbulent flow.
 iv.Compressible and Incompressible flow.
 v.Rotational and Irrotational flow.
3. Define boundary layer thickness.