statics

1. In the name of Allah the Most Gracious the Most
Merciful

2. FLUID MECHANICS – I
(CE- 251)
Dr. Ammara Mubeen
ammara@nice.nust.edu.pk

3. About Fluid Mechanics-1 Course
Course Title Fluid Mechanics I
Course Code CE – 251
Credit Hours 2+1
Theory 2
Practical 1
• Course Goals: Intends to provide understanding of the fluid statics and
dynamic concepts of fluid flows.
• Course Description:
The course provide students with basic information on statics, kinematics, and
dynamics of fluids. These include the study of Properties of fluids; Fluid statics;
Translation and rotation of fluid masses; Dimensional analysis and similitude;
Fundamentals of fluid flow; Fluid resistance; Compressible flow; Ideal fluid
flow; Fluid measurements.

4. Fluid Mechanics-1 (CE-251)
 Recommended Book:
 1. J. B. Franzini and Finnemore, Fluid Mechanics with
Engineering Application, McGraw-Hill New York (Latest
Edition)
 Additional resources.
 1. F. M. White, Fluid mechanics, Mcgraw-Hill (0-07-128646-2)
 2. Monson Young, Fundamentals of Fluid Mechanics, (Latest
Edition)
 3. Douglus, Fluid Mechanics, McGraw-Hill Inc.
 4. Jack P. Fundamentals of Fluid Mechanics, McGraw-Hill Inc.
 5. Merle Potter, Mechanics of Fluid, CL- Engineering (2011)

5. Course Learning Outcomes
S.No CLO Domain
Taxonomy
Level
PLO
1 Explain the basic principles of fluid
statics.
Cognitive 2 1
2 Apply the principles of conservation
of mass, momentum and energy for
solving pipe flow problems
Cognitive 3 2
3
Demonstrate the basic principles of
both fluid statics & dynamics by
carrying out experiments
Psychomotor 3 1

6. Course Topics( Fluid Mechanics-1)
0. Introduction to Fluid Mechanics (this file)
1. Fluid Properties
2. Fluid Statics
3. Fluid Dynamics (kinematics and hydrodynamics)
4. Fluid Flow Measurements
5. Dynamics of Viscous Fluid Flow in Closed Pipe
6. Dynamics of Fluid Flow in Open Channel Flow
7. Dimensional Analysis and Hydraulic Similitude

7. FLUID MECHANICS
• Course Outline:
• 0. Introduction: Importance of course in engineering, course syllabus,
grading policy, learning outcome, advices
• 1. Fluid Properties: Solids and fluids (liquids and gases). Units and
dimensions. Physical properties of fluids; density, specific weight, specific
volume, specific gravity, surface tension, compressibility. Viscosity,
measurement of viscosity, Newton's equation of viscosity. Hydrostatics,
kinematics, hydrodynamics, hydraulics.
• 2. Fluid Statics: Pressure intensity and pressure head, pressure and
specific weight relationship, absolute and gauge pressure, measurement
of pressure, Piezo-meter, manometer. Differential manometer and Borden
gauge. Forces on Immersed Bodies: Forces on submerged planes & curved
surfaces and their applications, Drag and Lift forces, buoyancy and
floatation. Equilibrium of floating and submerged bodies.
7
7

8. FLUID MECHANICS-1 CE-251
8
• 3. Fluid Kinematics: Steady and unsteady flow, laminar and
turbulent flow, uniform and non-uniform flow. Path-line,
streamlines and stream tubes. Velocity and discharge. Control
volume, Equation of continuity for compressible and incompressible
fluids.
• 4. Fluid Dynamics:
• Different forms of energy in a flowing liquid, head, Bernoulli's
equation and its application, Energy line and Hydraulic Gradient
Line,
• Momentum Equation and its Application (Forces on pressure
conduits, reducers and bends, stationary and moving blades,
torques in rotating machines).

9. FLUID MECHANICS-1 CE-251
9
• 5. Flow Measurement: Orifices and mouthpieces, sharp-crested
weirs and notches, pitot tube and pitot static tube, venturimeter
• 6. Dimensional Analysis and Similitude: concept of dimensional
analysis, method of dimensional analysis, similitude, concept of
dimensional similarity, dimensional numbers, model analysis

10. List of Practical
No. List of Practical
1 Determining the density of water
2 Studying the distribution of pressure within static liquids to verify Pascal's Law.
3 Calibrating a Bourdon Type Gauge
4
Determining the hydrostatic thrust and location of center of pressure of a
submerged body
5 Investigating stability of ship in relation to the position of its metacenter
6 Investigating and verifying the Bernoulli's Theorem in steady flow
7 Investigating the flow characteristics of various types of flow meters
8 Investigating the reaction forces produced by change in momentum of fluid flow.
9
Determining the Coefficients of velocity, contraction and discharge of a small
orifice
10 Investigating velocities of different materials in fluids
11
Flow visualization for illustrating streamlines around solid bodies using flow
Visualization Table

11. DISTRIBUTION OF MARKS (Theory)
FLUID MECHANICS – I (CE- 251)
Distribution Contribution in Grading
Theory (67%)
Assignments/Quizzes 20% 13
Mid Semester Exam 30% 20
1 x Final Exam 50% 34

12. Practical's Assessment (1 credit hour) Marks Distribution Absolute (33%)
Lab Work (Report, Quizzes, Attendance
in Lab) 70% 23.1
Rubrics 30% 9.9
Total: 33
FLUID MECHANICS – I (CE- 251)
DISTRIBUTION OF MARKS (Practicals)
Lab Attendance: Be regular in attending Labs. Consult lab staff for your attendance record.
Attendance marks will be based on the record provided by the lab staff.

13. Points for Consideration
• Office hours: A golden time to build up your skills and excel in the
course and strengthen your engineering skills in the subject.
• Assignments: assignments are bonus points it will only benefit you if
you spend the necessary time to understand the basics and solve the
problems yourself. Keep up with the assignments, as the topics in this
course build upon each other.
• Quizzes: Focused assessment by chapter and after 4-practicals to
monitor your progress and discover your weakness in the chapter and
Practicals. Efficiently use the office hours.
• Be professional and watch the deadlines: In your professional life
dedication and keeping deadlines are your keys to success. Start
practicing it right from this institution.
13

14. • Examination Policy
• Use the additional references to be better prepared. For the
examinations.
• Examinations are closed book
• Attendance Policy
• The NUST Attendance Policy applies to this course
• The classroom doors will be closed 5 minutes after the class
start time.
• Assignment Delay Policy
• 1 day of delay will reduce your assignment grade by 1.
• 2 days delay mean -2 and so on… if assignment is delayed by one week,
it will not be graded.
Important Note:
14

15. FLUID MECHANICS – I (CE- 251)
Introduction to Fluid Mechanics and
its applications

17. FLUID MECHANICS
Fluid: Fluids are substance which area capable of flowing and
conforming the shapes of container.
Fluids can be in gas or liquid states.
Mechanics: Mechanics is the branch of science that deals with
the state of rest or motion of body under the action of forces.
Fluid Mechanics: Branch of mechanic that deals with the
response or behavior of fluid either at rest or in motion.

18. Branches of Fluid Mechanics
 Fluid Statics: It is the branch of fluid mechanics which
deals with the response/behavior of fluid when they are
at rest.
 Fluid kinematics: It deals with the response of fluid
when they are in motion without considering the energies
and forces in them.
 Fluid dynamics: It deals with the behavior of fluids when
they are in motion considering energies and forces in
them.
 Hydraulics: It is the most important and
practical/experimental branch of fluid mechanics which
deals with the behavior of water and other fluid either at
rest or in motion.

20. CANALs
Pumps and Turbines
Water Retaining Structures

21. Significance of Fluid Mechanics
 Fluid is the most abundant available substance e.g.,
air, gases, ocean, river and canal etc.
 It provides basis for other subjects e.g.,
 Public health/environmental engineering
 Hydraulic Engineering
 Irrigation Engineering
 Coastal Engineering
 Water Resources
 etc etc

22. Forms of Fluid Mechanics
Fluid
Mechanics
Fluid Statics
Fluid
Kinematics
Fluid Dynamics
Fluid
Dynamics
Computational
Fluid Dynamics
Experimental
Fluid Dynamics
Analytical
Fluid Dynamics

23. Applications of EFD
Application in research &
development
Tropic Wind Tunnel has the ability to
create
temperatures ranging from 0 to 165
degrees
Fahrenheit and simulate rain
Example of industrial application
NASA's cryogenic wind tunnel simulates flight
conditions for scale models--a critical tool in
designing airplanes.
Application in teaching
Fluid dynamics laboratory

24. Modeling (examples)
Free surface animation for ship in
regular waves
Developing flame surface (Bell et al., 2001)
Evolution of a 2D mixing layer laden with particles of Stokes
Number 0.3 with respect to the vortex time scale (C.Narayanan)

25. State of Matter
25
• 1. gas
• 2. Liquid
• 3. Solid
fluid

26. Comparison Between Liquids and Gases
 Liquids have definite volume
at any particular temperature
 Liquids have free level
surface
 Molecules of liquid are close
to each other
 Liquids have relatively more
molecular attraction
 Liquids are slightly
compressible
 Rate of diffusion of liquid is
less
 Gases do not have any
definite volume
 Gases do not have free level
surface
 Molecules of gases are far
apart
 Gases have less molecular
attraction
 Gases are highly
compressible
 Gases have higher rate of
diffusion

27. Comparison Between Liquids and Solids
Liquid conform the shape of any
container
Liquid can flow
Molecules of liquid are distinctly
apart
Liquid have relatively less
molecular attraction
Liquid are slightly compressible
Liquids cannot sustain shear
forces
 Do not conform the shape of
container
 Solids cannot flow
 Molecules of solids are very
close to each other
 Solids have more molecular
attraction
 Solids are highly
incompressible
 Solids can sustain shear

32. Conversions
Length
1m=1000mm=100cm
1ft=12inch
1m=3.281ft
1Mile=5280ft=_______km
 Time
 1day=24hours
 1 hour=60min
 1 min=60s
 Mass 1kg=0.06852 slug
 1kg=1000g
 1kg of mass is of
weight=2.204lb
 1kg mass is of weight=9.81N
 9.81N=2.204lb
 1N= 2.204/9.8 lb=0.2246lb
 Volume
 1m3=1000liters=_______cm3
 1m3=35.32ft3
Exercise: Convert the units of following.
60 miles/hour=_________ ft/s=___________m/s=____________km/hr
(1 mile=1.6093 km)
10m3/s=________liter/min=__________ft3/s=____________ in3/s
15N/m2=___________=___________N/cm2=______________lb/ft2

34. Derived Units

35. Hydraulic Structures/Subjects
Hydropower Plants
Water Supply
Systems
Water Sewerage
Designs
Irrigation and
Agriculture
Water Cycle and
Hydrology
Surface Groundwater
Resources
Metrology and
Climate Change
Laws
Laws of Hydrostatics Euler's ,Bernoulli and Energy Conservation of mass Conservation of Momentum
Fluid Mechanics Forms
Fluid Statics Fluid Kinematics Fluid Dynamics
Properties of Fluid
Density Specific Weight Specific Volume Specific Gravity Compressibility Bulk Modulus Vapor Pressure Viscosity Surface Tension

37. Physical Properties of Fluids
Density
 Specific Volume
 Specific Weight
 Specific Gravity
 Compressibility
 Viscosity
 Surface Tension
 Pressure
 Buoyancy

38. Density
• Density quantifies the
compactness of atoms.
• May vary with
temperature or pressure
• A homogenous material
has the same density
throughout
STP

39. Specific Volume
The reciprocal of the
density of a
substance is called
its specific volume.
v = V/m = ρ-1

40. Specific Weight
STP

41. Relationship between ρ and γ

42. Effect of temperature and pressure
on Specific Weight

43. Specific Gravity (Relative Density)

45. Example
A reservoir of oil has a mass of 825 kg. The
reservoir has a volume of 0.917 m3. Compute
the density, specific weight, and specific gravity
of the oil.
Solution:
3
/
900
917
.
0
825
m
kg
V
m
volume
mass
oil 




3
/
8829
81
.
9
900 m
N
x
g
V
mg
volume
weight
oil 



 

9
.
0
998
900
@



STP
w
oil
oil
SG



46. Exercises
• If the specific weight of a liquid is 52 lb/ft3, what is its density?
• If the specific weight of a liquid is 8.1 kN/m3, what is its
density?
• If the specific volume of a gas is 375 ft3/slug, what is its
specific weight lb/ft3?
• If the specific volume of a gas is 0.70 m3/kg, what is its
specific weight N/m3?
• A certain gas weighs 16.0 N/m3 at a certain temperature and
pressure. What are the values of its density, specific volume
and specific gravity relative to air weighing12.0 N/m3?
• The specific weight of glycerin is 78.6 lb/ft3. Compute its
density and specific gravity. What is its specific weight in
kN/m3?
• If a certain gasoline weighs 43 lb/ft3, what are the values of
its density, specific volume and specific gravity relative to
water at 60oF? Use appendix A.

47. Compressibility
• Compressible fluids
• Incompressible fluids
• In fluid mechanics we deal with both compressible and
incompressible fluids of either variable or constant density.
• Although there is no such thing in reality as incompressible fluid, we
use this terms where the change in density with pressure is so small
as to be negligible. This is usually the case with liquids.
• Ordinarily, we consider the liquids as incompressible.
• We may consider the gases to be incompressible when the pressure
variation is small compared with absolute pressure.

48. Compressibility

49. Compressibility

50. Compressibility (Volumetric strain)

51. Compressibility
51
• Bulk Modulus or Volume Modulus of Elasticity (Ev):
• It is defined as ratio of volumetric stress to volumetric strain
 Ev= volumetric stress/volumetric strain
 Ev=change in pressure/compressibility










1
v
dv
dp
Ev










1


d
dp
Ev

52. Ideal Fluid & Real Fluid
• Ideal Fluid:
An Ideal Fluid is usually defined as a fluid
in which there is no friction, it is in
viscid (its viscosity is zero).
Thus the internal forces at any section
within it are always normal to the
section, even during motion. So these
forces are purely pressure forces.
Although such a fluid does not exist in
reality, many fluids approximate
frictionless flow at sufficient
distances from the solid boundaries.
So we can often conveniently analyze
their behaviors by assuming an ideal
fluid.
• Real Fluid:
In real fluid, either liquid or gas,
tangential or shearing forces
always develop whenever there is
motion relative to a body, thus
creating fluid friction, because
these forces oppose the motion
of one particle past another.
These frictional forces give rise to
fluid property called viscosity.

53. The Continuum Concept of A Fluid
• In engineering problems
dealing with fluids, one generally
deals with dimensions that are
very large compared to
molecular sizes.
• The space between the
molecules is not considered and
the fluid properties (pressure,
velocity, etc.) are considered to
vary continuously in space.
• The method of considering fluid
as a continuous mass is called as
continuum principle.
• Except in dealing with rarified
gases (a gas whose pressure is
much less than atmospheric
pressure), all normal fluid
mechanics analysis deals with
fluid as a continuum.
• Materials, such as solids, liquids and
gases, are composed of molecules
separated by "empty" space. On a
macroscopic scale, materials have
cracks and discontinuities.
• However, certain physical
phenomena can be modeled
assuming the materials exist as a
continuum, meaning the matter in
the body is continuously distributed
and fills the entire region of space it
occupies.
• A continuum is a body that can be
continually sub-divided into
infinitesimal elements with
properties being those of the bulk
material.

54. Viscosity
The viscosity of a fluid is a measure of its resistance to shear or
angular deformation.
It is the property of a fluid by mixture of which it offers
resistance to deformation under the influence of shear forces. It
depends upon the cohesion and molecular momentum
exchange between fluid layers.
It can also be defined as internal resist offered by fluid to flow.
It is denoted by μ.
It is also termed as coefficient of viscosity or absolute viscosity or
dynamic viscosity or molecular viscosity.

55. Factor affecting viscosity
• 1. Cohesion
• 2. Molecular momentum
• 1. Cohesion: It is the attraction between molecules of fluid. More
the molecular attraction (cohesion) more is the viscosity (resistance
to flow) of fluid.
• It is dominant in liquids.
• 2. Molecular momentum: Molecules in any fluid change their
position with time and is known as molecular activity. It is dominant
in gases

56. Kinematic Viscosity
 It is ratio of absolute viscosity and density of fluid.
 It is denoted by (nu)


 

57. Effect of temperature on viscosity
For Liquids:
In case of liquids, cohesion (molecular
attraction is dominant). Therefore, if the
temperature of liquid is increased, its
cohesion and hence viscosity will
decrease.
For Gases:
In gases momentum exchange is
dominant. Therefore, if the temperature
of gases is increases, its momentum
exchange will increase and hence viscosity
will increase.
T
1


T



59. Newton’s Equation of Viscosity
59
• Consider a fluid element sheared in one plane by a single shear stress ( )
as in Figure. The shear strain angle ( ) will continuously grow with time
as long as the stress is maintained, the upper surface moving at speed
larger than the lower.
t


 


Eq. 1
Figure: shear stress causes continuous shear deformation in a fluid: (a). a fluid element straining at
a rate of (b). Newtonian shear stress distribution in a shear layer near a wall.
u

 /

60. Newton’s Equation of Viscosity
60
• From geometry of Figure we see that
• In the limit of infinitesimal changes, this becomes a relating between
shear strain rate and velocity gradient
• Substituting Eq. 2 into Eq. 1
• Introducing coefficient of proportionality (µ)
• Where µ is called constant of coefficient of viscosity/ absolute
viscosity/dynamics viscosity
y
t
u



 
tan Eq. 2
y
u
t 



 
 
tan
if
Eq. 2
y
u


  Eq. 3
y
u



 
Eq. 4

61. Newton’s Equation of Viscosity
61
• The above equation is called as Newton’s equation of viscosity.
• The equation shows that the shearing stress is directly proportional
to the velocity gradient and it is known as Netwon’s law of velocity.
• In the above equation
• du/dy= velocity gradient or rate of change of deformation
• μ = absolute viscosity
• τ=shear stress
dy
du

 

62. Dimensional Analysis of Viscosity
62
• Viscosity
• This expression is used to write
fundamental unit of viscosity
 Kinematic Viscosity
2
2
)
/
(
L
FT
T
L
L
FL
U
y
A
F





T
L
L
M
LT
M
2
3






LT
M
MLT
F
L
T
MLT


 


 2
2
2


63. Unit of Viscosity
63
• Viscosity
Widely used unit is Poise =0.1N.s/m2
 Kinematic Viscosity
Widely used unit is Stoke=10-4m2/s
LT
M /


T
L /
2


SI BG CGS
N-s/m2 Lb-s/ft2 Dyne-s/cm2
(Poise, P)
Kg/(m-s) Slug/(ft-s) g/(cm-s)
SI BG CGS
m2/s ft2/s cm2/s
(stoke)

71. Shear Stress ~ Velocity gradient curve
71
• Ideal Fluid: The fluid which does not offer resistance to flow
• Newtownian Fluid: Fluid which obey Newtown’s law of viscosity
slope of curve ( )is constant
For example water, air, alcohol, glycerol etc.
• Non-Newtonian fluid: Fluid which does not obey Newtown’s Law of
viscosity
slope of curve ( )changing continuously
For example Flubber (Slime) , Ketchup, soap solutions, jam, emulsions
etc.
dy
du


0
0 

 

dy
du


dy
du /
~

dy
du /
~


72. Shear Stress ~ Velocity gradient curve
72
• Ideal Solid: solid which can never be deformed under the action of
force
• Real solid: solid which can be deformed under action of forces
• Ideal Plastic: These are substances which offer resistance to shear
forces without deformation upon a certain extent but if the load is
further increased then they deform
• Real Plastic: These are substances in which there is deformation
with the application of force and it increases with increase in
applied load.
0

dy
du

75. Exercises
• Exercise 2.11.2: To what temperature must the fuel oil with the
higher specific gravity in fig. A.2 be heated in order that its
kinematic viscosity may be reduced to three times that of water
at 40°F?
• Exercise 2.11.3: Compare the ratio of the absolute viscosities of
air and water at 70°F with the ratio of their kinematic viscosities
at the same temperature and 14.7 psia.
• Exercise 2.11.6: A liquid has an absolute viscosity of 3.2 x 10-4 lb
sec/ft2. It weighs 56 lb/ft3. What are its absolute and kinematic
viscosities in SI units?

82. Exercises
• Sample Problem 2.10: Water at 10°C stands in
a clean glass tube of 2 mm diameter at height
of 35 mm. What is the true static height?
• Exercise 2.12.1: Tap water at 68°F stands in a
glass tube of 0.32 inch diameter at a height of
4.50 inch. What is the true static height?
• Exercise 2.12.2: Distilled water at 20°C stands
in a glass tube of 6.0 mm diameter at a height
of 180 mm. What is the true static height?

83. Exercises
• Exercise 2.12.3: Use Eq. (2.12) to compute the
capillary depression of mercury at 68°F ( θ =
140°) to be expected in a 0.05 inch diameter
tube.
• Exercise 2.12.4: Compute the capillary rise in
mm of pure water at 10°C expected in an 0.8
mm diameter tube.

84. NUST Institute of Civil Engineering/Ammara
Mubeen

85. NUST Institute of Civil Engineering/Ammara
Mubeen

86. Sample Problem 2.3
• At a depth of 8 km in the ocean the pressure is 81.8
MPa. Assume that the specific weight of seawater at
surface is 10.05 kN/m3 and that the average volume
modulus is 2.34 x 109 N/m2 for that pressure range.
a. What will be the change in specific volume between
that at the surface and at that depth?
b. What will be the specific volume at that depth?
c. What will be the specific weight at that depth?

87. Exercises
2.5.2) At normal atmospheric condition, approximately what pressure in psi
must be applied to water to reduce its volume by 2%?
2.5.3) Water in hydraulic press is subjected to pressure of 4500 psia at 68
degree F. If initial pressure is 15 psia, approximately what will be the
percentage decrease in the specific volume?
2.5.4) At normal atmospheric conditions, approximately what pressure in
MPa must be applied to water to reduce its volume by 3%?
2.5.5) A rigid cylinder, inside diameter 15 mm, contains a column of water 500
mm long. What will the column length be if a force of 2 kN is applied to its
end by frictionless plunger? Assume no leakage

88. Sample Problem 2.4
• A vessel contains 85 l of water at 10 degree C and
atmospheric pressure. If the water is heated to 70
degree C, what will be the percentage change in its
volume.?
• What weight of water must be removed to maintain
the volume at its original value.

89. Exercises
• 2.6.1
• Use Fig. 2.1 to find the approximate specific weight of water in
lb/ft3 under the following conditions: (a) at a temperature of 60
degree C under 101.3 kPa abs pressure, (b) at60 degree C under
a pressure of 13.79 MPa abs.
• 2.6.3
• A vessel contains 5 ft3 of water at 40 degree F and atmospheric
pressure. If the water is heated to 80 degree F, what will be the
percentage change in its volume.? What weight of water must be
removed to maintain the volume at its original value?

90. NUST Institute of Civil Engineering/Ammara
Mubeen

91. NUST Institute of Civil Engineering/Ammara
Mubeen