This document defines fluid properties and concepts in fluid mechanics. It discusses:
1. The definition of a fluid as a substance that flows and takes the shape of its container. Fluids exist in liquid and gas states.
2. The differences between solids and fluids, where fluids have no definite shape and can be compressed.
3. An overview of fluid mechanics, including fluid statics, kinematics, and dynamics which consider pressure forces.
4. Fundamental concepts like density, viscosity, vapor pressure, and surface tension. It also discusses classification of fluids and fluid properties.
5. Applications of Bernoulli's equation like venturi meters, orifice meters, and pitot tubes which
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.
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.
This is related to properties of fluids in Fluid mechanics basically helpful for the Mechanical Engineering students.Most of the part is covered in this regarding the basic properties of fluids and about the meaning of fluid.
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
Fluid Mechanics,Application,Properties,Priciples And Its Importance In Petrol...Hafeezullah Jakhrani
This is very important to get knowledge about fluid mechanics.
History of fluid mechanics
Principle of Archimedes
Pascal`s concept
Applications
Bernoulli`s principle
Properties
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.
This is related to properties of fluids in Fluid mechanics basically helpful for the Mechanical Engineering students.Most of the part is covered in this regarding the basic properties of fluids and about the meaning of fluid.
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
Fluid Mechanics,Application,Properties,Priciples And Its Importance In Petrol...Hafeezullah Jakhrani
This is very important to get knowledge about fluid mechanics.
History of fluid mechanics
Principle of Archimedes
Pascal`s concept
Applications
Bernoulli`s principle
Properties
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.
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.
Fluid mechanics is a science in study the fluid of liquids and gases in the cases of silence and movement and the forces acting on them can be divided materials found in nature into two branches.
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
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tool life, surface finish, cutting fluids and Machinability
Law of toothed gearing – Involutes and cycloidal tooth profiles –Spur Gear terminology and
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Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
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.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
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.
TECHNICAL TRAINING MANUAL GENERAL FAMILIARIZATION COURSEDuvanRamosGarzon1
AIRCRAFT GENERAL
The Single Aisle is the most advanced family aircraft in service today, with fly-by-wire flight controls.
The A318, A319, A320 and A321 are twin-engine subsonic medium range aircraft.
The family offers a choice of engines
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.
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.
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.
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/
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
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 in-compressed 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