Viscosity, principles of fluid mechanics, turbulent flow & laminar flow

1. FLUID
MECHANICS &
HYDRODYNAMICS
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2. INTRODUCTION
The three state of matter are solid, liquid and gas
A solid maintains a fixed shape and fixed volume even if a
large external force is applied on it
The liquids and gases do not have their own shape and take
the shape of the containing vessel
Due to this reason, the liquids and gases have the ability to
flow under the action of external force, Hence liquids and
gases are called fluids
The branch of physics which deals with the study of
properties of fluids in motion is called “hydrodynamics”
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3. We seen that a solid object’s surface moves over another solid surface ,
so relative motion is opposed by the friction between the surface , its
called “solid friction”
The situation similar for fluid and gas (moving fluid)
A fluid moves in the form of layers, when a layer of fluid moves over
another layer, their relative motion is opposed by the internal friction of
the fluid, this property of fluid known as “fluid friction/viscosity”
The property of a moving fluid to oppose the relative motion between
its layers is called “viscosity of the fluid”
Viscosity  Resistance of fluid to flow  Internal friction
Viscosity is more  Greater force required for flow (Exa- Honey &
Water)
Viscosity is more  harder to move (Exa- Swimming in honey & water)
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5. CAUSE OF VISCOSITY
Viscosity is the internal friction of a fluid which opposes the motion of
one layer of fluid past another
The force of attraction between the molecules of a moving fluid
determine the viscosity of the fluid
A B
d
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6. Consider a liquid flowing steadily over a solid horizontal surface AB a
shown in fig
The layer of the liquid in contact with the surface AB is at rest because
of the adhesion forces
As we move up, the velocity of layers goes on increasing so that the
layer at the top has maximum velocity
1st layer moving faster than 2nd and another layers, so the average
speed of the molecules of the faster layer is decreased
The result is that a backward dragging force called viscous drag F is
developed which opposes the motion of the liquid
The viscous drag/ backward retarding force acts tangentially on the
layers
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7. It is found that drag between the two layers is directly proportional to
the area of the layers in contact and the velocity gradient du/dy
between them,
Where du = change in velocity, dy = perpendicular distance between
the layers
Thus when a liquid flows, a backward dragging force or viscous drag is
developed between its layers that retards the motion of the liquid
Coefficient of viscosity of a liquid is defined as the tangential force
required to maintain a unit velocity gradient between two parallel layers
each of unit area
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8.  SI Unit of ɳ is decapoise
 1 decapoise = 10 poise (Pascal.sec)
 Measured by Viscometer
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9. DISCUSSION
The viscosity of an ideal liquid is zero
The coefficient of viscosity of liquid decreases with the increase in
temperature and vice-versa
Fluid friction v/s solid friction
Solid friction arises with one solid surface moves over another surface
Fluid friction arises into one layer of a fluid moves over another layer
Similarities between fluid friction and solid friction
1. Both comes into play whenever there is a relative motion
2. Both oppose the relative motion
3. Both arises from intermolecular forces
4. Bothe depend on nature of surface
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10. Difference between fluid friction and solid friction
1. the force of friction between two layers of fluid depends upon the
area of contact and the velocity gradient between the layers. However
the frictional force between the surface of two solids is independent of
the area of the contact and of the relative velocity
2. the viscosity of a liquid decreases with the increase in temperature
whereas the solid friction is independent of the temperature
3. in case of solid friction, heat is generated at the surface between
the solids. When a fluid moves over a solid, heat is generated within the
fluid and not at the interface of the solid and the fluid
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11. IMPORTANCE OF VISCOSITY
1. Viscosity of air/liquid is used in providing damping torque in
measuring instruments
2. The viscosity of blood depends upon the concentration of red cells.
Therefore, viscosity of blood can be used to detect blood cell deficiency
3. Oil used as a lubricant should have proper value of viscosity
4. The viscosity of oil helps in applying brakes
5. Blood circulation through arteries depends upon the viscosity of
blood
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12. APPLICATION OF VISCOSITY
1. Knowledge of viscosity and its variation with temperature help us to
select a suitable lubricant for a given machine
2.viscosity of organic liquid such as proteins and cellulose help us to
calculate their molecular weight and determine their shape
3. the knowledge of viscosity helps in studying the circulation of blood
through arteries and veins
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13. MCQs
1. How can you measure viscosity?
a) See how quickly it can spread down an incline
b) Use a viscometer
c) See how easy or difficult it is to stir or otherwise manipulate the
material
d) All of these answers are methods to measure viscosity
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14. 2. Which of the following is a definition of viscosity?
a) Resistance to flow of the material
b) Thickness of the material
c) The amount of force required to deform the material
d) All of these answers are correct
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15. 3. Which of the following is the most viscous?
a) Pudding
b) Milk
c) Water
d) Applesauce
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16. 4. Unit of viscosity
a) Pascle.s
b) Decapoise
c) Poice
d) All of above
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17. 5. which force is exerted at the most bottom layer of the fluid?
a) Buoyancy force
b) Rotational force
c) Adherence force
d) None of above
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18. 6. Temperature increase then viscosity is __________?
a) Decrease
b) Increase
c) Equal
d) Zero
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19. PROPERTIES OF WATER
1. Buoyancy
2. Hydrostatic Pressure
3. Cohesion
4. Adhesion
5. Surface Tension
6. Hydrodynamics
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20. 1. Buoyancy
Upward force of water acting on a body that creates an apparent
decrease in the weight of a body while immersed .
Definition. Buoyancy is the upward force that works opposite to gravity.
Properties. Archimedes’ principle states that an immersed body
experiences upward thrust equal to the volume of liquid displaced
Specific gravity and density
Difference in size and shape
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21. COB
Center of buoyancy, rather than
center of gravity, affects the
body in an aquatic environment
Definition. The center of
buoyancy is the reference point
of an immersed object on which
buoyant (vertical) forces of fluid
predictably act.
Properties. Vertical forces that
do not intersect the center of
buoyancy create rotational
motion.
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22. Buoyant force
When a body is partially or wholly immersed in a fluid , it displaces a
certain amount of fluid. The displaced fluid exerts an upward force on
the body, called buoyant force (Fb)
The upward force acting on a body partially or wholly immersed in a
fluid is called buoyant force. It is also known as upward thrust or
buoyancy
The resultant force is then directed up. Thus we find that when body is
immersed in a fluid, the force of gravity (W=mg) acts downward while
the buoyant force Fb exerted by the fluid acts upward
The relative magnitudes of W and Fb will decide whether the body will
sink or float in the fluid
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23. Archimedes’ Principle (Law of
floatation)
When a body is partially or wholly immersed in a liquid, the buoyant
force acting on the body is equal to the weight of the liquid displaced
by the body
Buoyancy force, Fb = weight of the liquid displaced by the body
= Mass of the liquid displaced by the body × g
= ( p1 V1) × g
Fb = p1 g V1
Where –
◦ p1 = density of liquid ,
◦ V1 = volume of the liquid displaced by the body
◦ g = acceleration due to gravity,
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25. Law of floatation
We have seen above that the body will float in a liquid if Fb=W Or
Fb>W.
Therefore, law of floatation may be stated as under : a body will float in
a liquid if the buoyant force acting on the body is equal to or greater
than the weight of the body , Fb > W
A body will float in a liquid if the density of the body is less than or
equal to the density of the liquid
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26. 2. Hydrostatic Pressure
Definition. Hydrostatic pressure is the pressure exerted on immersed
objects.
Properties :- Pascal’s law states that the pressure exerted by fluid on
an immersed object is equal on all surfaces of the object. As the
density of water and depth of immersion increase, so does hydrostatic
pressure.
Clinical Significance
Increased pressure reduces or limits effusion, assists venous return,
induces bradycardia and centralizes peripheral blood flow.
The proportionality of depth and pressure allows patients to perform
exercise more easily when closer to the surface.
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28. 3. Cohesion
Tendency of water molecules to
adhere to each other.
Water is attracted to water.
Directly proportional to
VISCOSITY.
Sig: contributes to resistance
when moving through water.
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29. 4. Adhesion
Tendency of water molecules to
adhere to molecules of other
substances.
Water is attracted to other
materials.
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30. 5. Surface Tension
Definition. The surface of a fluid acts as a membrane
under tension. Surface tension is measured as force
per unit length.
Properties :- The attraction of surface molecules is
parallel to the surface. The resistive force of surface
tension changes proportionally to the size of the
object moving through the fluid surface.
Clinical Significance
An extremity that moves through the surface
performs more work than if kept under water.
Using equipment at the surface of the water
increases the resistance.
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31. 6. Hydrodynamics
Definition. Hydromechanics comprise the physical properties and
characteristics of fluid in motion.
Components of Flow Motion
Laminar / streamline/ steady flow - Movement where all molecules
move parallel to each other, typically slow movement.
Turbulent flow - Movement where molecules do not move parallel to
each other, typically faster movements.
Drag - The cumulative effects of turbulence and fluid viscosity acting on
an object in motion.
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32. Types of liquid flow
1. STREAMLINE FLOW
If all the liquid particles that pass any given point follow the same path at the
same speed.
Exa:- liquid flowing through pipe
The flowing liquid will have a certain velocity V1 at a, a velocity V2 at b and so
on so…
If with the passage of time, the velocity of whatever liquid particle happens to
be at a is still V1, that at b is still V2, then the flow is said to be steady or
streamline flow
Every particle starting at a will follow the same path abc, its called streamline
It’s a special case of streamline or steady flow in which the liquid flows as a
series of parallel layers and on one layer crosses another layer. Thus smooth
streamline flow is known as laminar flow
a-V1 b-V2 c-V3
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33. 2. TURBULENT FLOW
The flow of liquid is said to be turbulent flow or disorderly flow if the speed
and direction of the liquid particles passing any point change with time
Fig shows the turbulent flow of a liquid moving through a narrow construction
Generally, turbulent flow occurs in liquid moving at a high speeds
When the velocity of the liquid is small, the flow is laminar / steady
However, if the velocity of liquid exceeds certain limiting value called critical
velocity, the steady flow changes into turbulent flow.
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36. 1. During the water and string excitement,
the factor keeping the water bonded to the
string was the concept of ________.
a) A. Cohesion
b)B. Surface tension
c) C. Capillary action
d)D. Adhesion
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37. 2. This image specifically demonstrates one
example of how ________________ is beneficial to
living organisms.
a) A. Adhesion
b)B. Surface tension
c) C. Specific heat
d)D. Both a and d
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38. 3. The buoyancy force is equal to the weight of
the fluid displaced by the body.
a) A. True
b) B. False
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39. 4. Low of floatation also known as
a) Archimedes principal
b) Pascal’s law
c) Newton’s law
d) None of above
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40. 5. Hydrostatic pressure is depends on ______
a) Archimedes principal
b) Pascal’s law
c) Newton’s law
d) None of above
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41. 6. ___________is the reference point of an
immersed object on which buoyant (vertical)
forces of fluid
a) The center of buoyancy
b) The center of Gravity
c) The center of line
d) All of above
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42. 7. Viscosity is directly proportional to _____?
a) Cohesion
b) Adhesion
c) Surface tension
d) All of above
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43. 8. Surface tension is measured as ________?
a) Force per unit weight
b) Force per unit length
c) Force per unit height
d) All of above
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44. 9. Movement of all molecules in parallel to each
other known as _____?
a) Turbulent flow
b) Streamline flow
c) Steady flow
d) B & c both
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45. 10. The cumulative effects of turbulence and fluid
viscosity acting on an object in motion
a) Stream line flow
b) Turbulent flow
c) Drag
d) All of above
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