Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
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
Topics:
1. Introduction to Fluid Dynamics
2. Surface and Body Forces
3. Equations of Motion
- Reynold’s Equation
- Navier-Stokes Equation
- Euler’s Equation
- Bernoulli’s Equation
- Bernoulli’s Equation for Real Fluid
4. Applications of Bernoulli’s Equation
5. The Momentum Equation
6. Application of Momentum Equations
- Force exerted by flowing fluid on pipe bend
- Force exerted by the nozzle on the water
7. Measurement of Flow Rate
a). Venturimeter
b). Orifice Meter
c). Pitot Tube
8. Measurement of Flow Rate in Open Channels
a) Notches
b) Weirs
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
Properties of Fluids, Fluid Static, Buoyancy and Dimensional AnalysisSatish Taji
The presentation includes a brief view of the basic properties of a fluid, fluid statics, Pascal's law, hydrostatic law, fluid classification, pressure measurement devices (manometers and mechanical gauges), hydrostatic forces on different surfaces, buoyancy and metacentric height, and dimensional analysis.
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.
hi, I am sujon I just completed graduate at International University of Business Agriculture and Technology in Bangladesh Department of Mechanical Engineering
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
Properties of Fluids, Fluid Static, Buoyancy and Dimensional AnalysisSatish Taji
The presentation includes a brief view of the basic properties of a fluid, fluid statics, Pascal's law, hydrostatic law, fluid classification, pressure measurement devices (manometers and mechanical gauges), hydrostatic forces on different surfaces, buoyancy and metacentric height, and dimensional analysis.
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.
hi, I am sujon I just completed graduate at International University of Business Agriculture and Technology in Bangladesh Department of Mechanical Engineering
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
This presentation contains the Fluid flow chapter of Pharmaceutical engineering. This chapter include the definition of flow of fluid, Reynolds number, Bernollis therom, Manometers, Fluid flow measuring equipment's and applications.
Fluid Mechanics introduction for UG students
Fluid properties
Reynolds experiment
Manometer
Orificemeter
Venturimeter
Pitot tube
Rotameter
Current flow meter
FMM Unit 1. Define the expression for Reynold's numberpptxMohan313217
A horizontal pipe line is 40m long is connected to a water tank at one end and discharges freely into the Atmosphere at the other end. For the first 25m of its length from the tank, the pipe is 150mm diameter and its diameter is suddenly enlarged to 300mm. The height of water level in the tank is 8m above the Centre of the pipe. Considering all losses of head which is occurring, determine the rate of flow. Take f=0.01 for both sections of the pipe.
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.
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.
Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
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.
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.
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.
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.
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/
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
1. UNIT 1 INTRODUCTION
CE6451 FLUID MECHANICS &
MACHINERY
BY
Dr. A. Asha
Professor/Mechanical Engineering
Kamaraj College of Engineering & Technology, Virudhunagar
2. INTRODUCTION TO FLUID MECHANICS
• Fluid mechanics is the branch of science which deals with the
behaviour of fluids at rest and in motion
• Fluid mechanics is classified as
Fluid statics
Fluid dynamics is classified as
a. Fluid kinematics
b. Fluid kinetics
3. PROPERTIES OF FLUIDS
• Density or Mass density (ρ) : It is defined as the ration of the mass of the fluid
to the volume of the fluid
𝜌 =
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑓𝑙𝑢𝑖𝑑
𝜌 of water = 1000 kgm /m3
units : kgm /m3
• Specific weight or weight density (w) : It is defined as the weight of the fluid
volume of the fluid
w=
𝑤𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
=
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑 ×𝑎𝑐𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
w = 𝜌 ×g
units : N/m3 w of water = 9810 N/m3
4. PROPERTIES OF FLUIDS
• Specific volume : It is defined as the reciprocal of density of the fluid
specific volume =
𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
𝑚𝑎𝑠𝑠 𝑜𝑓 𝑡ℎ𝑒 𝑓𝑙𝑢𝑖𝑑
Units : m3/ kgm
• Specific gravity (S): It is defined as the ratio of the density of the liquid
to the density of water (OR) it is defined as the ratio of the weight
density of the liquid to the weight density of water.
S =
𝜌 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑
𝜌 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
(OR)
𝑤 𝑜𝑓 𝑙𝑖𝑞𝑢𝑖𝑑
𝑤 𝑜𝑓 𝑤𝑎𝑡𝑒𝑟
5. PROPERTIES OF FLUIDS
• Viscosity : It is defined as the property of the fluid which offers resistance to the
movement of one layer of the fluid over another adjacent layer of the fluid.
• Newtons law of viscosity (µ) : It states that the shear stress (τ) on a fluid element
layer is directly proportional to the rate of shear strain. The constant of
proportionality is called the co-efficient of viscosity. Mathematically
τ = 𝜇
𝑑𝑢
𝑑𝑦
Units of dynamic viscosity = Ns/m2 , poise
1 poise = 0.1 Ns/m2
• Kinematic viscosity (ϒ)
ϒ=
𝜇
𝜌
It is defined as the ratio of dynamic viscosity of the
fluid to the density of the fluid.
Units of kinematic viscosity = m2 /s , stokes
I stoke = 1 cm2/s
6. PROPERTIES OF FLUIDS
• Compressibility and Bulk modulus :
Compressibility is defined as the reciprocal of bulk modulus.
Bulk modulus (K) is defined as the ratio of compressive stress to volumetric strain
K =
𝑰𝒏𝒄𝒓𝒆𝒂𝒔𝒆 𝒐𝒇 𝒑𝒓𝒆𝒔𝒔𝒖𝒓𝒆
−𝒅𝒗/𝒗
Surface Tension (σ) = Surface tension is defined as the force acting on the surface
of a liquid in contact with a gas or on the surface between two immiscible fluids
such that the contact surface behaves like a membrane under tension.
Units : N/m
For liquid droplet h=
𝟒𝝈
𝒅
For soap bubble h=
𝟖𝝈
𝒅
Capillarity : It is defined as the phenomenon of rise or fall of a liquid surface in a
small tube relative to the adjacent general level of liquid when the tube is held
vertically in the liquid. The rise of the liquid surface is capillary rise while the fall in
the liquid surface is known as capillary depression
For capillary rise h=
𝟒𝝈
𝝆𝒈𝒅
For capillary depression
h=
𝟒𝝈𝒄𝒐𝒔𝜽
𝝆𝒈𝒅
Where θ = angle of contact between liquid and glass tube.
7. TYPES OF FLUIDS
• Ideal fluid : A fluid which is incompressible and is having no viscosity
is known as ideal fluid. Ideal fluid is an imaginary fluid
• Real fluid : A fluid which possess viscosity is known as real fluid. All
fluids in practice are known as real fluid
• Newtonian fluids : a real fluid in which the shear stress is directly
proportional to the rate of shear strain is called as Newtonian fluid
• Non – Newtonian fluid : a real fluid in which the shear stress is not
proportional to the rate of shear strain is known as non Newtonian
fluid
• Ideal plastic fluid : A fluid in which shear stress is more than the yield
value and shear stress is proportional to the rate of shear strain is
known as ideal plastic fluid
8. TYPES OF FLOW
• Steady flow : a steady flow is a flow in which the fluid characteristics
like pressure, density, etc does not vary with respect to time
• Un steady flow : a unsteady flow is a flow in which the fluid
characteristics like pressure, density, etc vary with respect to time
• Uniform flow : A flow in which the velocity at any given time does not
change with respect to distance
• Non uniform flow : A flow in which the velocity at any given time
change with respect to distance
• Compressible flow : The flow in which the density of the fluid changes
from point to point ρ≠ 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡,
• Incompressible flow : The flow in which the density of the fluid do not
change from point to point ρ = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
9. RATE OF FLOW (OR) DISCHARGE
• It is defined as the quantity of a fluid flowing per second through a
section of a pipe or a channel. For an incompressible fluid the rate of
flow or discharge is expressed as the volume of the fluid flowing
across the section per second.
• For incompressible fluids (Q) = A × V
Where A = Cross sectional area of the pipe
V = average velocity of fluid across the section
10. CONTINUITY EQUATION
• The equation is based on the law of conservation of mass
• It states that for a fluid flowing through the pipe at all the cross section the quantity of the fluid
per second is a constant.
• Consider two cross sections of a pipe as shown in the fig
Let V1 be the velocity at cross section 1-1 Let V2 be the velocity at cross section 2-2
Let A1 be the velocity at cross section 1-1 Let A2 be the velocity at cross section 2-2
According to the law of conservation of mass
Rate of flow at section 1-1 = Rate of flow at section 2-2
𝝆 𝟏 𝑨 𝟏 𝑽 𝟏 = 𝝆 𝟐 𝑨 𝟐 𝑽 𝟐
this is the general expression for both compressible and incompressible fluids
For incompressible fluid the above equation is 𝑨 𝟏 𝑽 𝟏 = 𝑨 𝟐 𝑽 𝟐 because density is constant
1
1
2
2
11. BERNOULLIS THEOREM
• It states that in a steady, ideal flow of an incompressible fluid the total energy at any
point of the fluid is constant. The total energy consists of pressure energy, kinetic
energy and datum energy. Thus mathematically bernoullis equation is written as
𝒑
𝝆𝒈
+
𝒗 𝟐
𝟐𝒈
+ 𝒛 = 𝑪𝒐𝒏𝒔𝒕𝒂𝒏𝒕
𝒑
𝝆𝒈
= Pressure energy
𝒗 𝟐
𝟐𝒈
= Kinetic energy
Z = datum energy
• Assumptions of Bernoulli's equation :
1. The fluid is ideal
2. The flow is steady
3. The flow is incompressible
4. The flow is irrotational
13. APPLICATIONS OF BERNOULLIS EQUATION
• Venturimeter
• Orificemeter
• Pitot tube
Venturimeter :
The venturimeter is a device which is used to measure the rate of flow through a closed pipe
It consists of 3 parts
(a) A short converging part
(b) Throat
(c) Diverging part
Theoretical discharge
Cd =
𝑸 𝒂𝒄𝒕𝒖𝒂𝒍
𝑸 𝑻𝒉𝒆𝒐𝒓𝒆𝒕𝒊𝒄𝒂𝒍
a1 = area of the pipe a2 = area of the throat
h= x
𝒔 𝒎
𝒔 𝒇
− 𝟏 𝒔 𝒎 = specific gravity of manometric fluid for mercury = 13.6
𝒔 𝒇 = 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐠𝐫𝐚𝐯𝐢𝐭𝐲 𝐨𝐟 𝐰𝐚𝐭𝐞𝐫 for water = 1
14. ORIFICEMETER
• It is a device used for measuring the rate of flow of a fluid through a
pipe. It consists of a flat circular plate which has a circular sharp
edged hole called as orifice which is concentric to the pipe
15. DISCHARGE OF ORIFICEMETER
• Let a1 = area of the pipe a0 = area of the orifice
• Actual discharge
h= x
𝒔 𝒎
𝒔 𝒇
− 𝟏
𝒔 𝒎 = specific gravity of manometric fluid for mercury = 13.6
𝒔 𝒇 = 𝐬𝐩𝐞𝐜𝐢𝐟𝐢𝐜 𝐠𝐫𝐚𝐯𝐢𝐭𝐲 𝐨𝐟 𝐰𝐚𝐭𝐞𝐫 for water = 1