3. Stream line or steady flow of a
liquid is a steady flow in which
each layer of liquid follows the
same path and has the same
velocity as that of its
predecessor.
Stream line or Steady Flow
Dr. Pius Augustine, SH College, Kochi
4. When the velocity of a point in the liquid
changes with time the flow is called unsteady
flow.
Unsteady flow is called turbulent flow, when
there are bents in the path of a fast moving
liquid.
Velocity of liquid change continuously and
haphazardly both in magnitude and direction
Turbulent flow
Dr. Pius Augustine, SH College, Kochi
5. The path followed by an element of a
moving fluid is called line of flow.
A collection of identical streamlines is
called a tube of flow.
Infinitesimally small volume element of
the liquid is called particle of liquid
Line of Flow, Tube of Flow, Particle of a Liquid
Dr. Pius Augustine, SH College, Kochi
6. Steady flow: Particular point -velocity of
fluid particle is same
Volume of liquid crossing any section per
second is same
Velocity high at narrow region
Dr. Pius Augustine, SH College, Kochi
7. A stream line may be defined as a curve, the tangent
to which at any point gives the direction of the flow of
liquid at that point.
v1 = constant, v2 = constant , v3 = constant
v1 ≠ v2 ≠ v3
V1
V2
V3
Dr. Pius Augustine, SH College, Kochi
8. Two stream lines never cross ?
if intersect, there will be two tangents and
two different velocity at same point which
is not possible.
Dr. Pius Augustine, SH College, Kochi
9. Laminar flow
Liquid flow in which different layers or
laminae glide over one another at a slow and
steady velocity, without intermixing, is
called laminar or viscous flow.
Dr. Pius Augustine, SH College, Kochi
10. Magnitude of velocities of various layers is
represented by the length of arrowed lines
Dotted curve : velocity profile or velocity
shape
Velocity profile is parabolic for tube of flow
Laminar flow
Dr. Pius Augustine, SH College, Kochi
11. velocity gradient
Velocity of layers increase from zero at the
walls (bottom) to maximum along the axis.
Rate of change of velocity with distance is
called velocity gradient.
Dr. Pius Augustine, SH College, Kochi
12. Just for information….
Normal blood flow in the human aorta is
laminar, but a small disturbance such as a
heart pathology can cause the flow to
become turbulent.
The turbulence makes noise, which is why
listening to blood flow with a stethoscope is
a useful diagnostic technique.
Dr. Pius Augustine, SH College, Kochi
13. Q. Water near the bed of a deep river
is quiet while that near the surface
flows. Give reason?
Dr. Pius Augustine, SH College, Kochi
14. If water in one flask and castor oil in
other are violently shaken and kept
on a table, which will come to rest
either?
Dr. Pius Augustine, SH College, Kochi
15. Viscosity
It is the property of a liquid by which it
opposes the relative motion between its
different layers.
It is a measure of resistance of a fluid
Dr. Pius Augustine, SH College, Kochi
16. Viscous force acts tangentially in a direction
opposite to the relative motion between the
different layers of the liquid.
Viscosity of a lubricating oil is one of the
factors which decides whether it is suitable
for use in the engine of a machine.
Dr. Pius Augustine, SH College, Kochi
18. Reynold’s number (Osborne Reynold)
Velocity of flow of a liquid upto which the
flow is streamlined (above which, flow
becomes turbulent) is called critical velocity.
Critical velocity vc = Rη/ρD
R - Reynold’s number
η - coefficient of viscosity
D - diameter of tube, ρ - density of liquid
Dr. Pius Augustine, SH College, Kochi
19. Reynold’s number (Osborne Reynold)
Critical velocity vc = Rη/ρD
Flow is streamline if R< 2000
Flow is turbulent if R > 3000
Reynold’s number is dimensionless
Derivation - dimensional analysis
Dr. Pius Augustine, SH College, Kochi
20. Reynold’s number
It is a dimensionless number.
It is a critical variable which determines
the process taking place inside a
cylindrical tube, when fluid flows
through it.
Law of similarity? And Reynold’s number
Dr. Pius Augustine, SH College, Kochi
21. well I won't go any faster with fuel
Dr. Pius Augustine, SH College, Kochi
22. Viscosity and density of some liquids
Fluid η Pl ρ SI
Hydrogen 8.4 *10-6 0.082 at 300K
Air 17.4 *10-6 1.161 at 300K
Water 0.8 * 10-3 1000
Mercury 1.526 * 10-3 13600
Blood at 370C (3 to 4) * 10-3 1060
Castor oil 0.985 956
Glycerol 1.49 1126
Honey 2 - 10 1420
ketchup 50 – 100
Molten glass 10 - 1000
Dr. Pius Augustine, SH College, Kochi
23. Critical velocity vc = Rη/ρD
Note : higher viscous, low dense liquid flowing
through narrow tube may be streamline (higher
critical velocity)
Low viscous, high dense liquid flow even through
wider tube may be turbulent
Above Vc, most of energy needed to drive liquid
is dissipated in setting up whirlpools, vortices
and eddies
Dr. Pius Augustine, SH College, Kochi
25. Expression for Viscous Force (Newton’s equation)
Magnitude of viscous force F on a certain layer of
liquid is propotional to
i] area A ii] velocity gradient dv/dx
F = -η A dv/dx
η – constant depend upon the nature of the liquid and is
called coefficient of viscosity of the liquid
-ve sign indicates that viscous force acts in a direction
opposite to direction of flow of liquid
Dr. Pius Augustine, SH College, Kochi
26. Coefficient or absolute or dynamic viscosity η
F = -η A dv/dx. η = F
A dv/dx
Coefficient of viscosity may be defined as the
tangential viscous force per unit area
required to maintain unit velocity gradient
normal to the direction of flow.
Dr. Pius Augustine, SH College, Kochi
27. Unit of η
F = -η A dv/dx. η = F
A dv/dx
SI unit: Pa-s or Nsm-2 called poiseuille (Pl)
CGS uint : poise
Reyn is british unit for dynamic viscosity
1Pl = 10 poise or decapoise
Dimension : ML-1T-1
Dr. Pius Augustine, SH College, Kochi
28. The velocity of water in a river is 18 km/hr
near the surface. If the river is 5 m deep,
find the shearing stress between the
horizontal layers of water. The coefficient of
viscosity of water = 10-2 poise.
dv/dx = (18 km/hr)/5m = 1.0 s-1.
Stress = F/A = η A (dv/dx)
Dr. Pius Augustine, SH College, Kochi
29. What is the effect of temperature on coefficient of
viscosity of a liquid ?
η of liquid decreases with increase
in temperature.
η of gases increases with increase
in temperature.
Dr. Pius Augustine, SH College, Kochi
30. Viscosity of water at different temperatures
Temperature oC η * 10-3 Pa-s
10 1.308
20 1.002
30 0.7978
40 0.6531
50 0.5471
60 0.4668
70 0.4044
80 0.3550
90 0.3150
100 0.2822
Decreaseswithincreaseintemperature
Dr. Pius Augustine, SH College, Kochi
31. Q. Oils of different viscosities are used in
different seasons, for lubrication. Why ?
Q. Why do the machine parts get jammed in
winter ?
Dr. Pius Augustine, SH College, Kochi
32. Can you stop it
Dr. Pius Augustine, SH College, Kochi
33. Effect of pressure on viscosity
Viscosity of liquids and gases
increases with pressure.
Dr. Pius Augustine, SH College, Kochi
34. Fluidity
Measure of ability to flow with ease
Reciprocal of coefficient of viscosity = 1/η
Unit : poise-1 some times called ‘rhe’
Fluidity is rarely used in engineering.
Dr. Pius Augustine, SH College, Kochi
35. Kinematic viscosity
It is the ratio between coefficient of viscosity
and density = η / ρ
Viscosity index is a measure for the change of
kinematic viscosity with temperature.
It is used to characterise lubricating oil in
the automotive industry.
CGS unit : cm2s-1 or ‘stokes’
1 m2 / s = 10,000 stokes
Dr. Pius Augustine, SH College, Kochi
38. Sphere falling through a fluid : Stokes’ law
F = 6πηav
η – coefficient of viscosity of liquid
a – radius of the sphere
v – terminal velocity attained
Using dimensional method F = K ηx ay vz
From experiments k = 2π
Dr. Pius Augustine, SH College, Kochi
39. Terminal velocity :
The constant velocity attained by a body
as it falls down through a fluid medium is
called the terminal velocity.
V = 2 a2 (ρ- σ) g
9 η
For a sphere falling through air, σ can be
neglected
Dr. Pius Augustine, SH College, Kochi
40. Terminal velocity Derivation
Wt of the body = Vρg = 4/3 πa3 ρg
Buoyant force = Vσg = 4/3 πa3 σg
ρ – density of body σ – density of
liquid
Under dynamic equilibrium
Effective wt = Viscous force
Dr. Pius Augustine, SH College, Kochi
41. Terminal velocity Derivation
Under dynamic equilibrium
Effective wt = Viscous force
4/3 πa3 (ρ- σ) g = 6πηav
V = 2 a2 (ρ- σ) g
9 η
Dr. Pius Augustine, SH College, Kochi
42. Velocity time graph for a body moving in
viscous medium.
time
velocity
Vt
Dr. Pius Augustine, SH College, Kochi
43. Note: In Biology terminal velocity is called
sedimentation velocity.
By performing experiments on
sedimentation, useful information
concerning very small particles maybe
obtained.
Dr. Pius Augustine, SH College, Kochi
44. Rain drops falling under gravity do not acquire
very high velocity. Why?
Q. Find the terminal velocity of a rain drop of radius 0.01 mm.
Given ηair = 1.8 x 10-5 SI units and density 1.2 SI units. R. D of
water is 1. take g = 10 m/s2.
Hint:
since density of air << density of water – buoyancy neglected.
Dr. Pius Augustine, SH College, Kochi
45. Viscosity vs Friction
i. Only when motion both at rest
as well as in motion
ii. Due to cohesion partly due to adhesion
iii. Viscous F α A independent of area
iv. F α dv/dx independent of relative
velocity of the surfaces
v. Depend on shape independent of shape
Dr. Pius Augustine, SH College, Kochi
46. Frictional force between solids operates
even when they do not move with
respect to each other. Do we have
viscous force acting between two layers
even if there is no relative motion?
Dr. Pius Augustine, SH College, Kochi
47. Variation of viscosity with temperature
Liquids:
Viscosity decreases with rise in temperature
For glycerine η = 46 poise at 0 oC and 3.5 poise
at 30 oC.
Gases:
Viscosity increases with rise in temperature.
Dr. Pius Augustine, SH College, Kochi
48. Liquids?
Liquids – viscosity is due to attraction
among molecules and between molecules
and solid in contact.
As temperature increases, molecular
attraction is getting weakened, hence
viscosity decrease.
Dr. Pius Augustine, SH College, Kochi
49. Gases?
Gases – molecules are farther apart and viscosity is
due to collision between fast moving molecules
with slow moving molecules. Fast molecules will
be impeded in collision.
As temperature increases, molecular activity
increases and this causes disorderly mixing of the
molecules. So viscosity increases.
Dr. Pius Augustine, SH College, Kochi
50. A man jumping
without parachute, Vterminal = 120 km/h with
parachute, Vterminal = 14 km/h
Fog formation – tiny droplets and dust
particles have small terminal velocity, and
appear to suspend in air.
Hail storm does not cause much damage as
they come with terminal velocity rather
than acceleration.
Dr. Pius Augustine, SH College, Kochi
51. Practical applications of viscosity
i. Selection of lubricant.
ii. Fountain pen ink – neither flows
down nor stuck up in the pen.
iii. Streamlining – shaping (aeroplane,
rocket)
Dr. Pius Augustine, SH College, Kochi
52. An air bubble of 1cm radius is rising
at a steady rate of 0.5 cm/s through
a liquid of density of 0.8 g/cm3.
Calculate the co-efficient of viscosity
of the liquid. Neglect density of air.
Dr. Pius Augustine, SH College, Kochi
53. Terminal velocity = - 0.5 cm/s
(σ - ρ) = - ρ = (-0.8)
-ve sign has been taken as bubble moves upward.
Η = 2 a2 ρ g = 2 * (-0.8) 981
9 V 9 ( -0.5)
= 348.8 poise
Dr. Pius Augustine, SH College, Kochi
54. Eight rain drops of radius 1mm each
falling down with a terminal
velocity of 5cm/s coalesce to form a
bigger drop. Calculate the terminal
velocity of the bigger drop.
Dr. Pius Augustine, SH College, Kochi
55. V’ = 2 R2 (ρ - σ) g for big drop
9 η
V = 2 r2 (ρ - σ) g for small drop
9 η
Volbig = 8 * Volsmall
4/3 πR3 = 8 * 4/3 πr3
R = 2r
V’/ V = 0.22/0.12 = 20 cm/s
Dr. Pius Augustine, SH College, Kochi
56. What is the reason for floating of clouds in the sky ?
Water particles of clouds attain a terminal
velocity while moving through air. This
terminal velocity is very low and remain
suspended in the sky.
When cloud is getting denser, terminal
velocity increase and they fall freely.
Dr. Pius Augustine, SH College, Kochi
57. A small and a big air bubbles rise up through a
liquid. Which rises faster ?
Terminal velocity is directly proportional to
radius2.
Hence big air bubble rises faster.
Direction of viscous force in this case is
downward or terminal velocity is –ve.
Dr. Pius Augustine, SH College, Kochi
59. Poiseuille’s Equation
Volume of liquid flowing through a tube
per second [V] depends on
i. Coefficient of viscosity η
ii. radius of tube r
iii. Pressure gradient P/l
Dr. Pius Augustine, SH College, Kochi
60. Poiseuille’s Equation
η r and P/l
Using dimensional analysis
M0L3T-1 = [ML-1T-1]a[L]b[ML-2T-2]c
On solving, V = πPr4
8lη
Dr. Pius Augustine, SH College, Kochi
61. Essential conditions for Poiseuille’s
equation to hold good.
i. Capillary tube is horizontal ie. no
gravity effect
ii. Flow is stream line parallel to the
axis
iii. No radial flow of liquid
iv. Liquid is viscous
Dr. Pius Augustine, SH College, Kochi
62. The cylindrical layer in contact with the wall of the
capillary tube is at rest. The velocity of the liquid layers
goes on increasing as we move from the wall towared the
axis of the tube.
acceleration of liquid at any point is zero .
liquid can withstand small shearing stress.
These conditions are realized in actual
practice if the capillary tube is of fine bore
and the liquid flows with small velocity.
Dr. Pius Augustine, SH College, Kochi
63. Calculate the mass of water flowing in
10 min. through a tube of radius 1 cm,
one meter in length and there is a
constant pressure head of 20 cm of
water. η = 0.009 cgs unit.
Dr. Pius Augustine, SH College, Kochi
64. V = πPr4 P = hdg = 20 *1*980
8lη
= 3.14 * 20 *1*980 *14
8 * 100 * 0.009
= 8.56 * 103 cm3 per second
Volume collected in 600 seconds = 8.56 * 103*
600
Mass of water collected = Volume * density(1
for water)
= 5.136 * 106 g.Dr. Pius Augustine, SH College, Kochi
65. Application of viscosity
Knowledge of viscous drag is used to determine the molecular
mass using centrifuges in biological and medical labs.
High viscous liquids as buffers in trains.
For damping the motion of certain instruments
Proper shaping – streamlining (aeroplanes, ship hulls, rockets)
In the study of circulation of blood. – variation in η of blood
will talk about the efficiency of the person.
Production and transportation of oils
Quality of ink
Variation in η with temperature helps in identifying the best
lubricant for a particular machine.
Dr. Pius Augustine, SH College, Kochi
66. Application of viscosity
Knowledge of viscous drag is used to determine the
molecular mass using centrifuges in biological
and medical labs.
High viscous liquids as buffers in trains.
For damping the motion of certain instruments
Production and transportation of oils
Dr. Pius Augustine, SH College, Kochi
68. Application of viscosity
Proper shaping – streamlining (aeroplanes, ship hulls,
rockets)
In the study of circulation of blood. – variation in η of
blood will talk about the efficiency of the person.
Quality of ink
Variation in η with temperature helps in identifying
the best lubricant for a particular machine.
Dr. Pius Augustine, SH College, Kochi
69. 2T vs 4T oils
A 2T Oil is designed to lubricate the engine
components, mix-up with the fuel completely,
burn and go out in the exhaust. A 4T Oil is not
designed to do so. As a result, when a 4T Oil is
put into in a 2T Engine, it causes spark-plug
fouling, exhaust port blockage, smoke emissions
etc.
Dr. Pius Augustine, SH College, Kochi
70. Q. In scooters more viscous mobile oil
is used in summer than in winter.
Why?
Q. Why do machine parts get jammed
in winter?
Dr. Pius Augustine, SH College, Kochi
71. Parachute and Drogue
An umbrella like collapsible device.
Produce drag when pulled through fluid.
For slowing down while dropping a man or goods
through air.
If it is used under water or at high speeds
in air it is called drogue
Dr. Pius Augustine, SH College, Kochi
73. Equation of continuity.
Fundamental equation of
fluid flow.
Extension of law of
conservation mass.
a1, v1 and a2 , v2 are area
and velocity respectively
at sections C and D
C
D
Since liquid is
incompressible
Mass of liquid crossing any
section per second is const.
Dr. Pius Augustine, SH College, Kochi
74. Equation of continuity.
Since liquid is incompressible
Mass of liquid crossing any
section per second is const.
a1v1 ρ = a2v2 ρ
av = constant
If the fluid is compressible
a1v1 ρ1 = a2v2 ρ2 or avρ = constant
C
D
Dr. Pius Augustine, SH College, Kochi
75. The product ‘av’ is the volume
flow rate dV/dt (rate at which
volume crosses a section of
the tube)
av = dV/dt
Dr. Pius Augustine, SH College, Kochi
76. Q. Deep water runs slow. Comment
Q. Air in the atmosphere is nearly
incompressible. Use this fact to
explain why particularly fast moving
winds are found in mountain
passes.
Dr. Pius Augustine, SH College, Kochi
77. A 20.0 litre bucket can be filled with water using
a water hose 3.00 cm in diameter in 2 minutes.
Calculate the speed with which the water leaves
the hose.
1 lit ~ 1m3.
Volume of water flowing/sec = 20/2x 60
Volume of water flowing/second = area x velocity.
velocity?
Dr. Pius Augustine, SH College, Kochi
78. Q. As part of a lubricating system for heavy
machinery, oil of density 850 kg/m3 is
pumped through a cylindrical pipe of
diameter 8.0 cm at a rate of 9.5 litres per
second. i) What is the speed of the oil? Ii)
What is the mass flow rate? C) If the pipe
diameter is reduced to 4.0 cm, what are the
new values of the speed and volume flow
rate? Assume that oil is incompressible.
Dr. Pius Augustine, SH College, Kochi
79. Why do the fire fighters attach brass jets
at the ends of water pipes?
av = constant.
As ‘a’ decreases, velocity
increases.
So water is able to reach the place
of fire.
Dr. Pius Augustine, SH College, Kochi
80. When the water tap is closed
with our fingers jets of water
gush through the space between
fingers with high speed. Why?
Dr. Pius Augustine, SH College, Kochi
81. Water is slowly coming out from a
vertical pipe. As the water
descends after coming out, its area
of cross – section reduces. Explain.
Dr. Pius Augustine, SH College, Kochi
82. While watering a distant plant, a
gardener partially closes the exit
hole of the pipe by putting his
finger on it. Explain why this
results in the water stream going
to a larger distance.
Dr. Pius Augustine, SH College, Kochi
83. Energy of fluid in steady flow - 3 Kinds
Kinetic energy = ½ mv2
Kinetic energy per unit mass = ½ v2
Kinetic energy / unit volume = ½ ρv2
1. Kinetic Energy
Dr. Pius Augustine, SH College, Kochi
84. Energy of fluid in steady flow - 3 Kinds
Potential energy = mgh
Potential energy / unit mass = gh
Potential energy / unit volume = ρgh
2. Potential Energy
Dr. Pius Augustine, SH College, Kochi
85. Energy of fluid in steady flow - 3 Kinds
Pressure energy = PV
Pressure energy /unit mass = P/ρ
Pressure energy / unit volume = P
3. Pressure Energy
Dr. Pius Augustine, SH College, Kochi
86. Energy of fluid in steady flow - 3 Kinds
i. kinetic energy = ½ mv2
Kinetic energy per unit mass = ½ v2
Kinetic energy / unit volume = ½ ρv2
ii. Potential energy = mgh
Potential energy / unit mass = gh
Potential energy / unit volume = ρgh
iii. Pressure energy = PV
Pressure energy /unit mass = P/ρ
Pressure energy / unit volume = P
Dr. Pius Augustine, SH College, Kochi
87. Pressure energy
The energy possessed by a fluid by virtue of
its pressure is called its pressure energy.
A fluid under pressure can do work and
possess energy called pressure energy.
Dr. Pius Augustine, SH College, Kochi
88. Pressure energy
Let A be the area of cross section of the piston.
Force acting on the piston = PA
Work done = PA x = PV
This is equivalent to the energy
contained in a volume V of the liquid
on account of its pressure called pressure energy.
x
P0 + P
P0
Dr. Pius Augustine, SH College, Kochi
90. Different forms of Bernoulli’s eqn. (practice derivation –
according to the figure you are plotting….)
Total energy = constant
PV + mgh + ½ mv2 = constant
Total energy of unit mass of fluid = constant
P/ρ + gh + ½ v2 = constant
Total energy of unit vol of fluid = constant
P + ρgh + ½ ρv2 = constant
static pressure + dynamic pressure = constant
Total pressure head = constant
P/ρg + h + v2 /2g = constant
Press head + gravitnal head +vel head= const.
Dr. Pius Augustine, SH College, Kochi
91. Corrections to be applied?
Bernoulli’s equation is derived based on certain assumptions
i. Fluid is non-viscous?
ii. Velocity of the fluid particles at different points is the same
iii. No loss of energy
Assumptions are not absolutely correct.
Velocity of the fluid is maximum along the axis and
decreases towards the walls of the tube
Part of KE is converted into heat.
Dr. Pius Augustine, SH College, Kochi
92. Q. Water flows through a tube of variable cross
section. Area of cross-section at A and B are 4
mm2 and 2 mm2 respectively. 1 cc of water enters
per second through A. Find i) the speed of water
at A, ii) the speed of water at B and iii) the
pressure difference PA-PB in the following three
cases.
Case 1. tube is horizontal
Case 2 tube is vertical (with A upwards) with
separation between A and B is 15/16 cm
Case 3 Tube is vertical (with B upwards and water
enters B at the rate of 1 cm2/s – note speed
decreases as the water falls down)
Dr. Pius Augustine, SH College, Kochi
93. Ideal fluid?
A fluid that is incompressible
(density can not be changed)
and has no internal
friction(viscosity) is ideal fluid.
Dr. Pius Augustine, SH College, Kochi
94. Applications of Bernoulli’s theorm
i. Venturimeter
ii. Pitot tube
iii.Atomiser
iv.Dynamic uplift
v. Carburettor
vi.Bunsen’s burner
Dr. Pius Augustine, SH College, Kochi
95. When a sphere or cylinder moves in still air while
spinning about an axis perpendicular to the
direction of its motion, its curved path is more
curved .
Ball drags air forward.
Relative velocity of air w.r.t ball is different for the
two diametrically opposite points, which cause
difference in pressure.
Ball turns towards the region of low pressure.
96. A spinning cricket ball takes a
curved path. Comment
Dr. Pius Augustine, SH College, Kochi
97. Why bullets are made cylindrical and not
spherical ?
Fired bullet spirals along the grooves in the
barrel and comes out spinning about its
axis.
Cylinder – direction of motion is parallel to
its spin axis. So the pressure on the sides
remains uniform throughout and will not
deviate from its straight path.
Dr. Pius Augustine, SH College, Kochi
99. Air foil
• Any surface designed in such a way as to
obtain reacting force from the air through
which it moves is known as air foil
• Generally used for wings of aeroplane
• Upper surface is slightly convex and lower
slightly concave.
• Air splits at the leading edge and meets at
the trailing edge simultaneously.
• Upper side velocity of air is more, which
causes reduction in pressure.
• Resulting uplift is called dynamic uplift.
Dr. Pius Augustine, SH College, Kochi
103. Venturimeter
It is a gauge used for measuring the rate of steady
flow of a fluid, based on Bernoullis eqn.
(fixed horizontally, PE cancels )
P1 + ½ ρv1
2 = P2 + ½ ρv2
2
P1 – P2 = ½ ρ(v2
2 – v1
2 )
P1 – P2 = hρg manometer
hρg = ½ ρ(v2
2 – v1
2 )
In actual practice ,
manometer tube
contains mercury.
hρ'g = ½ ρ(v2
2 – v1
2 )
ρ' - density of mercury.
Dr. Pius Augustine, SH College, Kochi
104. Venturimeter
hρg = ½ ρ(v2
2 – v1
2 )
From equation of continuity, a1v1 = a2v2 = V
volume of liquid crossing per second
v1 = V/a1 and v2= V/a2
Substitute and solve,
V = a1a2 √2 √g √h
(a1
2
- a2
2)1/2
V α √h Dr. Pius Augustine, SH College, Kochi
105. Atomiser or Scent sprayer
Air is blown past the
mouth of this tube at a
high speed by pressing,
creates a low pressure.
Dr. Pius Augustine, SH College, Kochi
106. Velocity of Efflux:
The average flow rate of material emitted
into the atmosphere from a source such as
a smokestack. This is the average speed of
gas out of the top of a smokestack.
Dr. Pius Augustine, SH College, Kochi
108. Torricelli’s theorm - law of efflux
The velocity of efflux of a liquid through an
orifice is equal to that which a body would
attain in falling freely from the free surface
of the liquid to the orifice.
P + ρg (h + h’ ) + 0 = P + ρg h’ + ½ ρv2
ρg h =½ ρv2
V = √ 2gh
Dr. Pius Augustine, SH College, Kochi
110. Pitot Tube
It is a device used for measuring the velocity of
flow and hence the rate of flow at any depth in a
flowing liquid.
Apply Bernoulli’s theorem at openings a and b
PE cancels, and velocity at ‘a’ is zero as flow
stopped.
P1 + ½ ρ x 02 = P2 + ½ ρv2
P1 – P2 = ½ ρv2
hρg = ½ ρv2
Rate of flow = av = a √(2gh)
V = √(2gh)
Dr. Pius Augustine, SH College, Kochi
111. Pitot-Static tubes, which are also
called Prandtl tubes, are used on aircraft as
speedometers. ...
The pitot-static tube is mounted on the
aircraft, or in a wind tunnel , so that the
center tube is always pointed in the
direction of the flow and the outside holes
are perpendicular to the center tube.
Dr. Pius Augustine, SH College, Kochi
112. Ping pong ball in blown air
Dr. Pius Augustine, SH College, Kochi
113. A light ping pong ball can be balanced on a continuous
stream of water or air coming out of a jet in vertically
upward direction. Explain
Fluid speed is same on all sides of ball.
So same pressure on all sides of ball.
If the ball is displaced towards left, fluid
will have greater speed on right and less
speed on left.
Bernoulli’s theorm, pressure will be
lesser on right side .
So ball will be displaced to right – eqbm.
Dr. Pius Augustine, SH College, Kochi
115. Bunsen burner
Gas comes out of the nozzle with high
velocity causes reduction in pressure
in the stem.
Air from atmosphere rushes into the
burner.
Mixture of gas and air burns at the top.
Dr. Pius Augustine, SH College, Kochi
116. A few other examples
Ping pong ball kept on a stream of
water
Blowing off roofs
Near a fast moving train
Two moving parallel ships etc.
Dr. Pius Augustine, SH College, Kochi
117. Explain the working of
Carburettor – Bernoulli’s
principle
Dr. Pius Augustine, SH College, Kochi
118. A gypsy car has got a canvas top. When the
car runs at high speed, the top bulges out.
Explain.
Dr. Pius Augustine, SH College, Kochi
119. Q. To keep a piece of paper horizontal,
you should blow over, not under it.
Why?
When blown, velocity becomes high,
and pressure low above the paper.
High pressure in the lower side push
the paper to low pressure region.
Dr. Pius Augustine, SH College, Kochi
120. Q. Why does flag flutter, when strong
winds are blowing on a certain day?
With the fluctuations in the velocity of
air on either side of the flag, pressure
will change, which makes it flutter.
Dr. Pius Augustine, SH College, Kochi
121. For my youtube videos: please visit -
SH vision youtube channel
or
xray diffraction series
SH Vision
Dr. Pius Augustine, SH College, KochiDr. Pius Augustine, SH College, Kochi
122. 122
Appeal: Please Contribute to Prime Minister’s or Chief
Minister’s fund in the fight against COVID-19
Dr. Pius Augustine, Dept of Physics, Sacred Heart College, Thevara
we will
overcome
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Dr. Pius Augustine, Asst. Professor, Sacred Heart College, Thevara, Kochi.