Fluid properties like density, viscosity, and specific gravity are important to characterize different fluids. Density is defined as mass per unit volume and determines whether a flow is compressible or incompressible. Viscosity measures a fluid's resistance to flow and internal friction. It is proportional to shear stress and inversely proportional to velocity gradient. Water has a viscosity of 1x10-3 N-s/m2 while air is less viscous at 1.8x10-5 N-s/m2. Specific gravity is the ratio of a fluid's density to that of water and is a dimensionless property.
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
A fluid is a state of matter in which its molecules move freely and do not bear a constant relationship in space to other molecules.
In physics, fluid flow has all kinds of aspects: steady or unsteady, compressible or incompressible, viscous or non-viscous, and rotational or irrotational to name a few. Some of these characteristics reflect properties of the liquid itself, and others focus on how the fluid is moving.
Fluids are :-
Liquid : blood, i.v. infusions)
Gas : O2 , N2O)
Vapour (transition from liquid to gas) : N2O (under compression in cylinder), volatile inhalational agents (halothane, isoflurane, etc)
Sublimate (transition from solid to gas bypassing liquid state) : Dry ice (solid CO2), iodine
Fluid dynamics, actually is the study of fluid under motion, governed with a certain set of conservation equations, wherein things are conserved, with reference to mass, momentum & energy.
If these three quantities i.e. mass, momentum & energy are solved entirely we can define any fluid flow. The conservation laws are formulated in the form of equations which we try to solve and that’s what simulation is all about. For my blogs kindly visit: https://www.learncax.com/knowledge-base/blog/by-author/ganesh-visavale
An effective reservoir management by streamline based simulation, history mat...Shusei Tanaka
The use of the streamline-based method for reservoir management is receiving increased interest in recent years because of its computational advantages and intuitive appeal for reservoir simulation, history matching and rate allocation optimization. Streamline-based method uses snapshots of flow path of convective flow. Previous studies proved its applicability for convection dominated process such as waterflooding and tracer transport. However, for a case with gas injection with strong capillarity and gravity effects, the streamline-based method tends to lose its advantages for reservoir simulation and may result in loss of accuracy and applicability for history-matching and optimization problems.
In this study, we first present the development of a 3D 3-phase black oil and compositional streamline simulator. Then, we introduce a novel approach to incorporate capillary and gravity effects via orthogonal projection method. The novel aspect of our approach is the ability to incorporate transverse effects into streamline simulation without adversely affecting its computational efficiency. We demonstrate our proposed method for various cases, including CO2 injection scenario. The streamline model is shown to be particularly effective to examine and visualize the interactions between heterogeneity which resulting impact on the vertical and areal sweep efficiencies.
Next, we apply the streamline simulator to history matching and rate optimization problems. In the conventional approach of streamline-based history matching, the objective is to match flow rate history, assuming that reservoir energy was matched already, such as pressure distribution. The proposed approach incorporates pressure information as well as production flow rates, aiming that reservoir energy are also reproduced during production rate matching.
Finally, we develop an NPV-based optimization method using streamline-based rate reallocation algorithm. The NPV is calculated along streamline and used to generate diagnostic plots of the effectiveness of wells. The rate is updated to maximize the field NPV. The proposed approach avoids the use of complex optimization tools. Instead, we emphasize the visual and the intuitive appeal of streamline methods and utilize flow diagnostic plots for optimal rate allocation.
We concluded that our proposed approach of streamline-based simulation, inversion and optimization algorithm improves computational efficiency and accuracy of the solution, which leads to a highly effective reservoir management tool that satisfies industry demands.
FMM- UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICSKarthik R
Units and dimensions- Properties of fluids- mass density, specific weight, specific volume, specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow characteristics – concept of control volume - application of continuity equation, energy equation and momentum equation.
UNIT I FLUID POWER PRINICIPLES AND HYDRAULIC PUMPS 9
Introduction to Fluid power – Advantages and Applications – Fluid power systems – Types of fluids
- Properties of fluids and selection – Basics of Hydraulics – Pascal’s Law – Principles of flow - Friction loss – Work, Power and Torqu
FMM- UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICSKarthik R
Units and dimensions- Properties of fluids- mass density, specific weight, specific volume, specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow characteristics – concept of control volume - application of continuity equation, energy equation and momentum equation.
FMM- UNIT I FLUID PROPERTIES AND FLOW CHARACTERISTICSKarthik R
Units and dimensions- Properties of fluids- mass density, specific weight, specific volume,
specific gravity, viscosity, compressibility, vapor pressure, surface tension and capillarity. Flow
characteristics – concept of control volume - application of continuity equation, energy
equation and momentum equation.
Unit 3 introduction to fluid mechanics as per AKTU KME101TVivek Singh Chauhan
strictly following syllabus of KME 101T of AKTU for first yr 2021
fluid properties, bernoulli's equation with proof and numericals , pumps, turbine , hydraulic lift, continuity equation
Definations related to refrigeration like refrigerating effect,TON of refrigeration,COP,vapour compression refrigeration system and vapour absorption refrigeration system,types of refrigerants and properties of refrigerants.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
2. Fluid Concept
Fluid mechanics is a division in applied
mechanics related to the behaviour of liquid
or gas which is either in rest or in motion.
The study related to a fluid in rest or
stationary is referred to fluid static,
otherwise it is referred to as fluid dynamic.
Fluid can be defined as a substance which
can deform continuously when being
subjected to shear stress at any magnitude.
In other words, it can flow continuously as
a result of shearing action. This includes
any liquid or gas.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
3. DEFINE FLUIDS
(a) Solid (b) Liquid (c) Gas
k
kk
k
Free surface
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
4. A fluid is a substance that flows under the action of
shearing forces. If a fluid is at rest, we know that the
forces on it are in balance.
A gas is a fluid that is easily compressed. It fills any
vessel in which it is contained.
A liquid is a fluid which is hard to compress. A
given mass of liquid will occupy a fixed volume,
irrespective of the size of the container.
A free surface is formed as a boundary between a
liquid and a gas above it.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
5. • Define “characteristics” of a specific fluidDefine “characteristics” of a specific fluid
•Properties expressed by basic “dimensions”Properties expressed by basic “dimensions”
– length, mass (or force), time, temperaturelength, mass (or force), time, temperature
• Dimensions quantified by basic “units”Dimensions quantified by basic “units”
We will consider systems of units, important fluidWe will consider systems of units, important fluid
properties (not all), and the dimensions associated withproperties (not all), and the dimensions associated with
those properties.those properties.A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
6. Classification of fluids
Ideal fluid and Real fluid
Newtonian fluid and Non- newtonian fluid
Compressible and incompressible fluid.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
8. IDEAL FLUID
The fluid in which there is no friction; it is INVISCID
(it’s viscosity is zero).
The internal forces at any section within it are always
normal to the section, even during motion.
So, these forces are purely pressure forces.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
This does not exist in reality, many fluids approximate frictionless
flow at sufficient distances from solid boundaries and hence we
can analyze their behavior by assuming an ideal fluid.
9. In real fluids, either liquid or gas, tangential or
shearing forces are developed always 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 a fluid property
called Viscosity.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
Real fluids
10. Non Newtonian fluids
Non Newtonian fluids are relatively uncommon in
engineering use (examples are paints, printer’s ink,
gels and emulsions, sludges and slurries, and certain
plastics).
So, we will use fluids that obey Newton’s equation of
viscosity under normal conditions.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
11. • Length = meters (m)Length = meters (m)
• Mass = kilograms (kg)Mass = kilograms (kg)
• Time = second (s)Time = second (s)
• Force = Newton (N)Force = Newton (N)
– Force required to accelerate 1 kg @ 1 m/sForce required to accelerate 1 kg @ 1 m/s22
– Acceleration due to gravity (g) = 9.81 m/sAcceleration due to gravity (g) = 9.81 m/s22
– Weight of 1 kg at earth’s surface = W = mg = 1 kg (9.81 m/sWeight of 1 kg at earth’s surface = W = mg = 1 kg (9.81 m/s22
) =) =
9.81 kg-m/s9.81 kg-m/s22
= 9.81 N= 9.81 N
• Temperature = Kelvin (Temperature = Kelvin (oo
K)K)
– 273.15273.15 oo
K = freezing point of waterK = freezing point of water
– oo
K = 273.15 +K = 273.15 + oo
CC
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
12. • Work and energy = Joule (J)Work and energy = Joule (J)
J = N*m = kg-m/sJ = N*m = kg-m/s22
* m = kg-m* m = kg-m22
/s/s22
• Power = watt (W) = J/sPower = watt (W) = J/s
• SI prefixes:SI prefixes:
G = giga = 10G = giga = 1099
c = centi = 10c = centi = 10-2-2
M = mega = 10M = mega = 1066
m = milli = 10m = milli = 10-3-3
k = kilo = 10k = kilo = 1033
µµ = micro = 10= micro = 10-6-6
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
13. • Mass per unit volume (e.g., @ 20Mass per unit volume (e.g., @ 20 oo
C, 1 atm)C, 1 atm)
– WaterWater ρρwaterwater = 1,000 kg/m= 1,000 kg/m33
(62.4 lbm/ft(62.4 lbm/ft33
))
– MercuryMercury ρρHgHg = 13,500 kg/m= 13,500 kg/m33
– AirAir ρρairair = 1.205 kg/m= 1.205 kg/m33
• Densities of gases = strong f (T,p) =compressibleDensities of gases = strong f (T,p) =compressible
• Densities of liquids are nearly constantDensities of liquids are nearly constant
(incompressible) for constant temperature(incompressible) for constant temperature
• Specific volume = 1/density = volume/massSpecific volume = 1/density = volume/mass
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
14. The density of a fluid is defined as its mass per
unit volume. It is denoted by the Greek
symbol, ρ.
ρ =
V m3
kgm-3
If the density is constant (most liquids), the flow is
incompressible.
If the density varies significantly (eg some gas flows), the
flow is compressible.
(Although gases are easy to compress, the flow may be treated
as incompressible if there are no large pressure fluctuations)
ρ water= 998 kgm-3
ρair =1.2kgm-3
kg
m
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
15. 2 kg, 4000 cm3
Wood
177 cm3
45.2 kg
;
mass m
Density
volume V
ρ= =
Lead: 11,300 kg/mLead: 11,300 kg/m33
Wood: 500 kg/mWood: 500 kg/m33
4000 cm3
Lead
Same volume
2 kg
Lead
Same mass
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
16. 4 kg
3
4 kg
;
7800 kg/m
m m
V
V
ρ
ρ
= = =
V = 5.13 x 10-4
m3V = 5.13 x 10-4
m3
What is the mass if the volume is 0.046 m3
?
3 3
(7800 kg/m )(0.046 m );m Vρ= =
m = 359 kgm = 359 kg
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
18. Ratio of fluid density to density of water @ 4o
C
3
/1000 mkg
SG
liquid
water
liquid
liquid
ρ
ρ
ρ
==
Water SGwater = 1
Mercury SGHg = 13.55
Note: SG is dimensionless and independent of system of units
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
19. Specific Gravity
STPwater
liquid
STPwater
liquid
SG
@@ γ
γ
ρ
ρ
==
A.N.KHUDAIWALA
(L.M.E) G.P.PORBANDAR
The specific gravity (or relative density) can be defined in two ways:
Definition 1: A ratio of the density of a liquid to the density of
water at standard temperature and pressure (STP)
(20°C, 1 atm), or
Definition 2: A ratio of the specific weight of a liquid to the
specific weight of water at standard temperature
and pressure (STP) (20°C, 1 atm),
Unit: dimensionless.
20. The specific gravity (or relative density) of a
material is the ratio of its density to the density of
water (1000 kg/m3
).
Steel (7800 kg/m3
) ρr = 7.80
Brass (8700 kg/m3
) ρr = 8.70
Wood (500 kg/m3
) ρr = 0.500
Steel (7800 kg/m3
) ρr = 7.80
Brass (8700 kg/m3
) ρr = 8.70
Wood (500 kg/m3
) ρr = 0.500
Examples:Examples:
3
1000 kg/m
x
r
ρ
ρ =
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
22. • Viscosity,Viscosity, µµ,, is a measure of resistance to fluid flow as ais a measure of resistance to fluid flow as a
result of intermolecular cohesion. In other words, viscosityresult of intermolecular cohesion. In other words, viscosity
can be seen as internal friction to fluid motion which cancan be seen as internal friction to fluid motion which can
then lead to energy loss.then lead to energy loss.
• Different fluids deform at different rates under the sameDifferent fluids deform at different rates under the same
shear stress. The ease with which a fluid pours is anshear stress. The ease with which a fluid pours is an
indication of its viscosity. Fluid with a high viscosity such asindication of its viscosity. Fluid with a high viscosity such as
syrup deforms more slowly than fluid with a low viscositysyrup deforms more slowly than fluid with a low viscosity
such as water. The viscosity is also known as dynamicsuch as water. The viscosity is also known as dynamic
viscosity.viscosity.
Units:Units: N.s/m2 or kg/m/sN.s/m2 or kg/m/s
Typical values:Typical values:
Water = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/sWater = 1.14x10-3 kg/m/s; Air = 1.78x10-5 kg/m/s
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
23. • Proportionality constant = dynamic (absolute)Proportionality constant = dynamic (absolute)
viscosityviscosity
• Newton’s Law of ViscosityNewton’s Law of Viscosity
• ViscosityViscosity
• UnitsUnits
• Water (@ 20Water (@ 20oo
C):C): µµ = 1= 1xx1010-3-3
N-s/mN-s/m22
• Air (@ 20Air (@ 20oo
C):C): µµ = 1.8= 1.8xx1010-5-5
N-s/mN-s/m22
• Kinematic viscosityKinematic viscosity
V
V+d
v
dy
dV
µτ =
dydV /
τ
µ =
2
2
//
/
m
sN
msm
mN ⋅
=
ρ
µ
ν =
Kinematic viscosity: m2
/s
1 poise = 0.1 N-s/m2
1 centipoises = 10-2
poise = 10-3
N-s/m2
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
24. Viscosity
From Newton’s equation of viscosity we have,
µ = τ / (dU/dY)
This is known as Coefficient of viscosity, the
absolute viscosity, the dynamic viscosity or simply
the viscosity of fluid.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
The distinction between solids and fluid lies in the
manner in which each can resist SHEARING
STRESS.
Further distinction among various kinds of fluids
and solids is as:
25. Viscosity
In case of solids, shear stress depends on magnitude
of deformation but according to Newton’s equation of
viscosity the shear stress is proportional to time rate
of (angular) deformation.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
A fluid for which absolute viscosity does not change with rate
of deformation is called NEWTONIAN FLUID.
The slope of this line is “Absolute Viscosity”
A fluid for which absolute viscosity changes with rate of
deformation is called NON-NEWTONIAN FLUID.
26. Viscosity
Kinematic Viscosity = Absolute Viscosity / Density
ν = µ / ƿ
Is called so because force is not involved, the only
dimensions being length and time, as in Kinematics.
UNITS:
In BG: ft2
/sec
In S.I: m2
/s
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
In Metric system it had units
cm2
/s, also known as
STOKE(St).
Name given after Sir George Stoke, an
English Physicist and pioneering investigator
of viscosity.
-6 2
27. Kinematic viscosity, ν
A.N.KHUDAIWALA
(L.M.E) G.P.PORBANDAR
Definition: is the ratio of the viscosity to the density;
• will be found to be important in cases in which significant viscous and
gravitational forces exist.
Units: m2
/s
Typical values:
Water = 1.14x10-6 m2/s; Air = 1.46x10-5 m2/s;
In general,
viscosity of liquids with temperature, whereas
viscosity of gases with in temperature.
ρµ=ν /
28. Viscosity
DISTINCTION BETWEEN µ & ν :
µ of most fluids is virtually INDEPENDENT of
pressures encountered ordinarily in engineering work.
ν of gases varies strongly with pressure because of
change in density.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
29. Example 1.2
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:
A.N.KHUDAIWALA
(L.M.E) G.P.PORBANDAR
3
/900
917.0
825
mkg
m
volume
mass
oil ==
∀
==ρ
3
oil m/N882981.9x900g
mg
volume
weight
==ρ=
∀
==γ
9.0
998
900
@
===
STPw
oil
oilSG
ρ
ρ
30. Surface Tension
Surface tension coefficient s can be defined as the intensity of
intermolecular traction per unit length along the free surface of a
fluid, and its SI unit is N/m.
The surface tension effect is caused by unbalanced cohesion
forces at fluid surfaces which produce a downward resultant force
which can physically seen as a membrane.
The coefficient is inversely proportional to temperature and is
also dependent on the type of the solid interface.
For example, a drop of water on a glass surface will have a
different coefficient from the similar amount of water on a wood
surface.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
31. Surface Tension
The effect may be becoming significant for small fluid system such
as liquid level in a capillary, as depicted in Fig. 1.6, where it will
decide whether the interaction form by the fluid and the solid
surface is wetted or non-wetted.
If the adhesion of fluid molecules to the adjacent solid surface is
stronger than the intermolecular cohesion, the fluid is said to wet
on the surface. Otherwise, it is a non-wetted interaction.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
32. Surface Tension
The pressure inside a drop of fluid can be calculated using a free-body
diagram of a spherical shape of radius R cut in half, as shown in Fig. 1.7,
and the force developed around the edge of the cut sphere is 2πRσ.
This force must be balance with the difference between the internal
pressure pi and the external pressure pe acting on the circular area of the
cut. Thus,
2πRσ = ∆pπR2
∆p = pi –pe =
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
2σ
R
33. Properties of Fluids
Density = ρ (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 = γ (Heaviness of fluid)
weight per unit volume γ = ρg
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 = ρf / ρw SG of Hg = 13.55
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
36. Differences between adhesive &
Cohesive
A distinction is usually made between an
adhesive force, which acts to hold two
separate bodies together (or to stick one
body to another) and a cohesive force,
which acts to hold together the like or
unlike atoms, ions, or molecules of a
single body.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
37. Capillarity
Rise and fall of liquid in a capillary tube is caused by surface tension.
Capillarity depends on the relative magnitudes of the cohesion of the liquid to
walls of the containing vessel.
When the adhesive forces between liquid and solid are larger than the liquid's
cohesive forces, the meniscus in a small diameter tube will tend to be concave
If adhesive forces are smaller than cohesive forces the meniscus will tend to be
convex, for example mercury in glass.
water
mercury
concave
convex
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
38. Compressibility of Liquids
Compressibility is the change in volume due to
change in pressure.
The compressibility of liquid is inversely related to its
volume modulus of elasticity (also known as bulk
modulus).
Eν = - ν(dp/dν) = - (ν/dν)dp
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
Where; ν = Specific Volume.
(ν/dν) = Dimensionless
ratio
39. Compressibility of Liquids
In most engineering problems, the bulk modulus at
or near atmospheric pressure is one of the interest.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
The BULK MODULUS is a property of fluid.
And for liquids, is a function of temperature and
pressure.
Eν is directly related to temperature. It
minimum compressibility at this
temperature.
40. Compressibility of Liquids
We often specify applied pressures in terms of
absolute terms, because atmospheric pressure varies.
Absolute pressure is the actual pressure on fluid
relative to absolute zero.
The standard atmospheric pressure at sea level is
about 14.7 psia or 101.3 kn/m2
abs or 1013 mb.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
41. • Different behavior of liquids and gases to an increase of pressure.
Bulk modulus and the compressibility modulus
FLUID. Pressure
V
V
P
∆
∆
Β −=
The pressure due to a fluid pressing in on an object tends to compress the object.
The ratio of the increase in pressure ΔP to the fractional decrease in volume -
(ΔV/V) is called the bulk modulus.
Liquids and solids are relatively incompressible, they have large values of B.
On the other way, the density of liquid and solids is relatively constant with
pressure changes
Gases are easily compressed and the values of B are strongly dependent on
pressure changes. The density of gases depends strongly of pressure changes,
besides of changes in temperature.
The compressibility modulus is the
reciprocal of bulk modulus (1/B)
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
42. Vapour Pressure
Vapour pressure is the partial pressure produced by fluid vapour
in an open or a closed container, which reaches its saturated
condition or the transfer of fluid molecules is at equilibrium along
its free surface.
In a closed container, the vapour pressure is solely dependent on
temperature. In a saturated condition, any further reduction in
temperature or atmospheric pressure below its dew point will
lead to the formation of water droplets.
On the other hand, boiling occurs when the absolute fluid
pressure is reduced until it is lower than the vapour pressure of
the fluid at that temperature.
For a network of pipes, the pressure at a point can be lower than
the vapour pressure, for example, at the suction section of a
pump. Otherwise, vapour bubbles will start to form and this
phenomenon is termed as cavitation.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR
43. Basic Unit System & Units
Derived Units
There are many derived units all obtained from combination of the above
primary units. Those most used are shown in the table below:
The SI system consists of six primary units, from which
all quantities may be described but in fluid mechanics we
are generally only interested in the top four units from this
table.
A.N.KHUDAIWALA (L.M.E) G.P.PORBANDAR