1. The document defines various fluid properties and concepts, including defining fluids as substances that flow and take the shape of their container, and discussing the differences between solids and fluids.
2. It also covers fluid mechanics, which studies fluids at rest and in motion, and fluid statics, kinematics, and dynamics.
3. Additionally, the document discusses various fluid types including ideal fluids, real fluids, Newtonian fluids, and non-Newtonian fluids. It also defines key fluid properties such as density, viscosity, vapor pressure, and surface tension.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
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
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe flow
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
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
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe flow
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.
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
Hydraulic consists of the application of fluid mechanics to water flowing in an isolated environment (pipe, pump) or in an open channel (river, lake, ocean). Civil engineers are primarily concerned with open channel flow, which is governed by the interdependent interaction between the water and the channel. Applications include the design of hydraulic structures, such as sewage conduits, dams and breakwaters, the management of waterways, such as erosion protection and flood protection, and environmental management, such as prediction of the mixing and transport of pollutants in surface water.
Centre lathe, constructional features, specification, operations – taper turning methods, thread cutting methods, special attachments, machining time and power estimation. Capstan and turret lathes- tool layout – automatic lathes: semi automatic – single spindle : Swiss type, automatic screw type – multi spindle:
Centre lathe, constructional features, specification, operations – taper turning methods, thread
cutting methods, special attachments, machining time and power estimation. Capstan and turret
lathes- tool layout – automatic lathes: semi automatic – single spindle : Swiss type, automatic
screw type – multi spindle:
UNIT III SHAPER, MILLING AND GEAR CUTTING MACHINESKarthik R
Shaper - Types of operations. Drilling ,reaming, boring, Tapping. Milling operations-types of milling
cutter. Gear cutting – forming and generation principle and construction of gear milling ,hobbing
and gear shaping processes –finishing of gears.
Mechanics of chip formation, single point cutting tool, forces in machining, Types of chip, cutting
tools– nomenclature, orthogonal metal cutting, thermal aspects, cutting tool materials, tool wear,
tool life, surface finish, cutting fluids and Machinability
Law of toothed gearing – Involutes and cycloidal tooth profiles –Spur Gear terminology and
definitions –Gear tooth action – contact ratio – Interference and undercutting. Helical, Bevel, Worm, Rack and Pinion gears
Law of toothed gearing – Involutes and cycloidal tooth profiles –Spur Gear terminology and
definitions –Gear tooth action – contact ratio – Interference and undercutting. Helical, Bevel, Worm, Rack and Pinion gears
Law of toothed gearing – Involutes and cycloidal tooth profiles –Spur Gear terminology and
definitions –Gear tooth action – contact ratio – Interference and undercutting. Helical, Bevel, Worm, Rack and Pinion gears
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.
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.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
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2. DEFINE FLUID
A fluid (or) liquid, which is capable of flowing.
It has no own shape, but confirms to the shape of
the containing vessels.
A fluid is a substance that
continually deforms under an applied shear stress
Liquids are like water, milk, air, steam.
MATTER EXISTS IN TWO STATES:
solids and the fluids.
fluids state being commonly divided into the
liquid and gaseous states.
3. DIFFERENCES BETWEEN SOLIDS
AND FLUIDS
A solid is generally own shape and change in volume
under pure compressive load.
It resistance to change in shape without a change in
volume under the application of tangential forces.
The spacing and latitude of motion of molecules are
very small in solids, large in a liquid and extremely
large in gas.
The intermolecular bonds are very strong in solids,
weak in liquids and very weak in gases.
Solids are very compact and rigid. Solids materials
are steel, wood, plastics etc.
4.
5.
6. FLUID MECHANICS
Fluid mechanics is that branch of science which deals
with the behavior of fluids (liquids or gases) at rest as
well as in motion.
This branch of science deals with the static,
kinematics and dynamic aspects of fluids.
The study of fluids at rest is called fluid statics.
The study of fluids in motion, where pressure forces
are not considered, is called fluid kinematics.
The pressure forces are also considered for the fluids
in motion, that branch of science is called fluid
dynamics.
7. UNITS AND DIMENSIONS
The word dimensions are used to describe basic concepts like mass,
length, time, temperature and force. Units are the means of expressing
the value of the dimension quantitatively or numerically.
All physical quantities are measured by units.
There are two types of units:
(i). Fundamental units.
(ii). Derived units.
FUNDAMENTAL UNITS.
All physical quantities are expressed the following :
1.Length(L)
2.Mass(M)
3.Time(T)
DERIVED UNITS.
Derived units are expressed in terms of fundamental units, this are area,
velocity, pressure etc.
8. SYSTEM OF UNITS
CGS Units
The fundamental units of length, mass and time are taken as
centimeter, gram and second respectively.
FPS Units
The fundamental units of length, mass and time are taken as
feet, pound and second respectively.
MKS Units
In this system, the fundamental units of length, mass and time
are taken as meter, kilogram, and seconds respectively.
The MKS units are called as gravitational units or engineers
units.
SI Units
This system has six basic units, two supplementary units and
twenty seven derived units.
9. S.I Six Basic Units
Quantity SI Unit Dimension
Length Metre, m L
Mass Kilogram, kg M
Time Second, s T
Temperature Kelvin, K
Current Ampere, A I
Luminosity Candela Cd
10. Two Supplementary Units
One is for measuring the plane angle called
radian(rad).
Another for measuring solid angle called
stearadian(Sr).
11. Derived Units
Quantity SI Unit
Volume m3
Area m2
velocity m/s
Discharge m3 /s
acceleration m/s2
force N
Torque, energy,
work
Joule J (or) N m
power Watt W
pressure ( or stress) N/m2
density kg /m3
Dynamic viscosity N s/m2
surface tension N/m
Kinematic viscosity m2/s
12. Thermal conductivity W/mK
Specific heat J/kgK
Entropy J/K
Momentum Kg-m/s
Weight density N/m3
Frequency Hz
Angular velocity Rad/s
Angular acceleration Rad/s2
13. DIFFERENT TYPES OF FLUIDS
Basically the fluids are classified into 5 types
and these are
1. Ideal fluid
2. Real fluid
3. Newtonian fluid
4. Non-Newtonian fluid, and
5. Ideal plastic fluid
14.
15. Ideal Fluid
A fluid which is incompressed and have no viscosity falls in the category of ideal
fluid.
Ideal fluid is not found in actual practice but it is an imaginary fluid because all
the fluid that exist in the environment have some viscosity. there in no ideal fluid in
reality.
Real Fluid
A fluid which has at least some viscosity is called real fluid.
Actually all the fluids existing or present in the environment are called real fluids..
Newtonian Fluid
If a real fluid obeys the Newton's law of viscosity (i.e the shear stress is directly
proportional to the shear strain) then it is known as the Newtonian fluid.
Example: water, kerosene
Non-Newtonian Fluid
If real fluid does not obeys the Newton's law of viscosity then it is called Non-
Newtonian fluid.
Example: paint, toothpaste
Ideal Plastic Fluid
A fluid having the value of shear stress more than the yield value and shear stress
is proportional to the shear strain (velocity gradient) is known as ideal plastic fluid.
16. PROPERTIES OF FLUIDS
Density (or) Mass Density:(ρ)
Density or mass density of a fluid is defined as the ratio
of the mass of a fluid to its volume.
Thus mass per unit volume of a fluid is called density.
ρ = Mass of fluid / Volume of fluid
Its units ,kg/m3
Temperature increase with density decrease
Pressure increase with density increase
To estimate the density from characteristic gas equation
of Pv = mRT (R= 287J/kgK (or) 0.287 KJ/kg)
Water = 1000 kg/m3, Mercury = 13600 kg/m3, Air = 1.23
kg/m3, Paraffin Oil = 800 kg/m3.
(at pressure =1.013 N/m2, and Temperature = 288.15 K.)
17. Specific weight or weight density:(w)
Specific weight or weight density of a fluid is the ratio
between the weight of a fluid to its volume.
The weight per unit volume of a fluid is called Specific
weight or weight density
It various from place to place because of acceleration due
to gravity changing from place to place.
Specific weight, w = Weight of fluid / Volume of fluid
w = ρg (w=W/V = mg/V = ρg)
Its units, N/m3
Temperature increase with specific weight decrease
Pressure increase with specific weight increase
Water =9810 N/m3, Mercury = 132943 N/m3, Air =12.07
N/m3, Paraffin Oil =7851 N/m3
18. Specific Volume:(v)
Specific volume of a fluid is defined as the
volume of a fluid occupied by a unit mass or
volume per unit mass of a fluid.
v = Volume of fluid / Mass of fluid
= 1/ ρ
Its units, m3/kg
19. Specific Gravity (or) Relative Density :(S)
Specific gravity is defined as the ratio of the density
of a fluid to density of a standard fluid.
S = density of a fluid / density of a standard fluid.
Specific gravity of mercury is 13.6
20. Viscosity
Viscosity is the property of a fluid, due to cohesion and interaction between
molecules, which offers resistance to sheer deformation.
Different fluids deform at different rates under the same shear stress.
Fluid with a high viscosity such as syrup, deforms more slowly than fluid with a
low viscosity such as water.
Shear stress,
21. Viscosity is defined as the property of a fluid which offers resistance to the
movement of one layer of fluid over adjacent layer of the fluid.
When two layers of a fluid, a distance ‘dy’ apart, move one over the other at different
velocities, say u and u+du.
The viscosity together with relative velocity causes a shear stress acting between the
fluid layers.
The top layer causes a shear stress on the adjacent lower layer while the lower layer
causes a shear stress on the adjacent top layer.
This shear stress is proportional to the rate of change of velocity with respect to y.
22. Dynamic Viscosity (µ):
Its defined as the Shear stress(τ), required causing
unit rate of shear deformation(du/dy).
µ = τ /(du/dy).
Its units, N-s/m2 (or) kg/m-s (or) poise
Kinematic Viscosity (ν):
Its defined as the ratio of dynamic viscosity to mass
density.
Its units, m2/s (or) stoke
24. VAPORIZATION:
• A change from the liquid state to the gaseous state is known as
vaporization.
VAPOUR PRESSURE:
• The liquid is kept in closed vessel.
• The vaporization take place, the molecules escapes from the free
surface of the liquid.
• This vapour molecules occupies the space b/w free liquid surface
and the top of the vessel.
• These accumulated vapours exert a pressure on the liquid surface.
• This pressure is called the vapour pressure of the liquid.
• Water vapour pressure is 2337N/m2 at 200C, but 101325N/m2 at
1000C.
25. SURFACE TENSION
Surface tension is defined as the tensile force acting on the surface of a
liquid in contact with a gas or on the surface between two immiscible
liquids such that the contact surface behaves like a membrane under
tension.
Due to molecules attraction, liquids have properties of cohesion and
adhesion.
Cohesion is due to the force of attraction b/w molecular of same liquid.
This force is very small.
Adhesion is due to the force of attraction b/w the molecules of two
different liquid.
The molecules of the liquid and molecules of solid surface
26.
27. BULK MODULUS
It define as the ratio of change in pressure to the rate of
change of volume is called as bulk modulus of the material.
Bulk modulus (K) = (change in pressure) /
(volumetric strain)
K = -(dp/(dV/V))
Volumetric strain is the change in volume divided by the
original volume. (dV/V)
Negative sign for dV indicates the volume decreases as
pressure increases.
K = dp/(dρ/ρ) [dV/V = - dρ/ρ]
Typical values of Bulk Modulus:
• K = 2.05 x 109 N/m2 for water
• K = 1.62 x 109 N/m2 for oil.
28. COMPRESSIBILITY
The compressibility of a fluid is the reduction of the volume of the
fluid due to an external pressure acting on it.
A compressible fluid will reduce (or) change in volume in the
presence of external pressure.
Compressibility is the reciprocal of the bulk modulus of elasticity, K
which is defined as the ratio of compressive stress to volumetric
strain.
Compressibility is given by = 1/K
Its unit in N/m2
In nature all the fluids are compressible. Gases are highly
compressible but liquid s are not highly compressible.
Relationship b/w bulk modulus (K) and Pressure(P) for a gas
The relationship b/w bulk modulus of elasticity(K) and Pressure for
a gas for two different processes of compression are as:
(i). Isothermal process.
(ii). Isentropic (or) adiabatic process.
29. CAPILLARITY
Capillarity is defined as a phenomenon of rise or fall of a
liquid surface relative to the adjacent general level of liquid in
a small tube, when the tube is held vertically in the liquid
Capillarity occurs because of intermolecular forces b/w the
liquid and surrounding solid surface. And due to pressure of
cohesion and adhesion which cause the liquid work against
gravity
It is expressed in terms of cm or mm of liquid.
Its value depends upon the specific weight of the liquid,
diameter of the tube and surface tension of the liquid.
30. CAPILLARY RISE
If the glass tube is inserted vertically in a liquid, say water. The liquid
will rise in the tube above the level of the liquid surface is known as
capillary rise
σ = Surface tension of liquid.
θ = Angle of contact b/w liquid and glass tube.
The Weight of liquid of height h in the tube = (Area of tube x h) x ρ x g
= (π/4 x d2 x h) x ρ x g ------------------------- (i)
Vertical component of the surface tensile force = (σ x Circumference) x cos θ
= σ x πd x cos θ ------------------------------- (ii)
Equating equation (i) & (ii)
(π/4 x d2 x h) x ρ x g = σ x πd x cos θ
h = σ x πd x cos θ / (π/4 x d2) x ρ x g
h = 4 σ cos θ / ρ x g x d
31. CAPILLARY DEPRESSION
If the glass tube is dipped vertically in a liquid, say mercury. The level of
mercury in the tube will be lower than the general level of the outside
liquid.
Two forces are acting on the mercury inside the tube.
First one is due to surface tension acting in the down ward direction
and equal to σ x πd x cos θ --------- (i)
Second force is due to hydrostatic force acting upward and is equal to
intensity of pressure at a depth ‘h’ x Area
= p x (π/4 x d2 ) = ρg x h x (π/4 x d2 ) -------------- (ii)
• Equating equation (i) & (ii)
• σ x πd x cos θ = ρ x g x h x (π/4 x d2 )
• h = 4 σ cos θ / ρ x g x d