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.
This document defines fluids and their properties. It discusses the differences between solids and fluids, and defines the various states of matter. Fluids are classified as ideal fluids, real fluids, Newtonian fluids, and non-Newtonian fluids. The key properties of fluids discussed include density, specific weight, viscosity, vapor pressure, and surface tension. Concepts such as bulk modulus, compressibility, and capillarity are also introduced. Various fluid flow measurement devices that utilize Bernoulli's equation are briefly mentioned.
This document provides an introduction to fluid mechanics. It begins with definitions of mechanics, statics, dynamics, and fluid mechanics. It then discusses different categories of fluid mechanics including fluid statics, fluid kinematics, fluid dynamics, hydrodynamics, hydraulics, gas dynamics, and aerodynamics. The document also defines what a fluid is, discusses the properties of fluids including density, specific weight, specific volume, and specific gravity. It concludes by explaining viscosity, kinematic viscosity, and Newton's law of viscosity.
This document provides an overview of fluid mechanics concepts related to flow through pipes. It discusses different types of head losses that can occur through pipes including major losses due to friction and minor losses due to fittings. It also covers topics such as hydraulic grade line, pipes in series and parallel, syphons, power transmission through pipes, flow through nozzles, and water hammer effects in pipes.
1) The document discusses fluid kinematics, which deals with the motion of fluids without considering the forces that create motion. It covers topics like velocity fields, acceleration fields, control volumes, and flow visualization techniques.
2) There are two main descriptions of fluid motion - Lagrangian, which follows individual particles, and Eulerian, which observes the flow at fixed points in space. Most practical analysis uses the Eulerian description.
3) The Reynolds Transport Theorem allows equations written for a fluid system to be applied to a fixed control volume, which is useful for analyzing forces on objects in a flow. It relates the time rate of change of an extensive property within the control volume to surface fluxes and the property accumulation.
This document provides an overview of boundary layer concepts and laminar and turbulent pipe flow. It defines boundary layer thickness, displacement thickness, and momentum thickness. It describes how boundary layers develop on surfaces and transition from laminar to turbulent. It also discusses Reynolds number effects, momentum integral estimates for flat plates, and examples calculating boundary layer thickness in air and water flow. Finally, it introduces concepts of laminar and turbulent pipe flow.
This document discusses laminar and turbulent fluid flow in pipes. It defines the Reynolds number and explains that laminar flow occurs at Re < 2000, transitional flow from 2000 to 4000, and turbulent flow over 4000. The entrance length for developing pipe flow profiles is discussed. Fully developed laminar and turbulent pipe flows are compared. Equations are provided for average velocity, shear stress at the wall, and pressure drop based on conservation of momentum and energy analyses. The Darcy friction factor is defined, and methods for calculating it for laminar and turbulent flows are explained, including the Moody chart. Types of pipe flow problems and accounting for minor losses and pipe networks are also summarized.
This document defines fluids and their properties. It discusses the differences between solids and fluids, and defines the various states of matter. Fluids are classified as ideal fluids, real fluids, Newtonian fluids, and non-Newtonian fluids. The key properties of fluids discussed include density, specific weight, viscosity, vapor pressure, and surface tension. Concepts such as bulk modulus, compressibility, and capillarity are also introduced. Various fluid flow measurement devices that utilize Bernoulli's equation are briefly mentioned.
This document provides an introduction to fluid mechanics. It begins with definitions of mechanics, statics, dynamics, and fluid mechanics. It then discusses different categories of fluid mechanics including fluid statics, fluid kinematics, fluid dynamics, hydrodynamics, hydraulics, gas dynamics, and aerodynamics. The document also defines what a fluid is, discusses the properties of fluids including density, specific weight, specific volume, and specific gravity. It concludes by explaining viscosity, kinematic viscosity, and Newton's law of viscosity.
This document provides an overview of fluid mechanics concepts related to flow through pipes. It discusses different types of head losses that can occur through pipes including major losses due to friction and minor losses due to fittings. It also covers topics such as hydraulic grade line, pipes in series and parallel, syphons, power transmission through pipes, flow through nozzles, and water hammer effects in pipes.
1) The document discusses fluid kinematics, which deals with the motion of fluids without considering the forces that create motion. It covers topics like velocity fields, acceleration fields, control volumes, and flow visualization techniques.
2) There are two main descriptions of fluid motion - Lagrangian, which follows individual particles, and Eulerian, which observes the flow at fixed points in space. Most practical analysis uses the Eulerian description.
3) The Reynolds Transport Theorem allows equations written for a fluid system to be applied to a fixed control volume, which is useful for analyzing forces on objects in a flow. It relates the time rate of change of an extensive property within the control volume to surface fluxes and the property accumulation.
This document provides an overview of boundary layer concepts and laminar and turbulent pipe flow. It defines boundary layer thickness, displacement thickness, and momentum thickness. It describes how boundary layers develop on surfaces and transition from laminar to turbulent. It also discusses Reynolds number effects, momentum integral estimates for flat plates, and examples calculating boundary layer thickness in air and water flow. Finally, it introduces concepts of laminar and turbulent pipe flow.
This document discusses laminar and turbulent fluid flow in pipes. It defines the Reynolds number and explains that laminar flow occurs at Re < 2000, transitional flow from 2000 to 4000, and turbulent flow over 4000. The entrance length for developing pipe flow profiles is discussed. Fully developed laminar and turbulent pipe flows are compared. Equations are provided for average velocity, shear stress at the wall, and pressure drop based on conservation of momentum and energy analyses. The Darcy friction factor is defined, and methods for calculating it for laminar and turbulent flows are explained, including the Moody chart. Types of pipe flow problems and accounting for minor losses and pipe networks are also summarized.
This presentation introduces concepts of hydrostatics including total pressure on immersed surfaces, center of pressure, and applications. Total pressure on a surface depends on its orientation (horizontal, vertical, inclined) and is calculated by integrating pressure over small elements. The center of pressure is the point where the total pressure force acts and can be found using the theorem of parallel axis. Examples of hydrostatics applications discussed are water pressure on structures like sluice gates, lock gates, and masonry walls. Conditions for stability of dams are also outlined.
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
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.
This document discusses flow through pipes, including:
- Laminar and turbulent flow characteristics defined by Reynolds number
- Head losses calculated using Darcy-Weisbach and minor loss equations
- Friction factors determined from Moody diagrams for laminar and turbulent flows
- Total head loss in a pipe system equals major losses in pipe sections plus minor losses from fittings
1) Compressible flow is when the density of a fluid changes during flow, such as gases. Incompressible flow assumes constant density, such as liquids.
2) Examples of compressible flow include gases through nozzles, compressors, high-speed projectiles and planes, and water hammer.
3) Bernoulli's equation relates pressure, temperature, and specific volume and only applies to steady, incompressible flow without friction losses along a single streamline.
This document provides an introduction and overview of a fluid mechanics course taught by Dr. Mohsin Siddique. It outlines the course details including goals, topics, textbook, and assessment methods. The course aims to provide an understanding of fluid statics and dynamics concepts. Key topics covered include fluid properties, fluid statics, fluid flow measurements, dimensional analysis, and fluid flow in pipes and open channels. Students will be evaluated through assignments, quizzes, a midterm exam, and a final exam. The course intends to develop skills relevant to various engineering fields involving fluid mechanics.
Unit 6 discusses losses in pipes, including major and minor losses. Major losses are due to friction and calculated using Darcy-Weisbach or Chezy's formulas. Minor losses are due to changes in pipe direction, size, or obstructions and are also calculated using specific formulas. The document also discusses equivalent pipes, pipes in series, pipes in parallel, and two and three reservoir pipe flow analysis problems. Head losses are calculated using friction and minor loss formulas, and continuity and energy equations are used to analyze pipe flows.
This document discusses various topics related to fluid mechanics including:
1. Fluid statics, hydrostatic pressure variation, and Pascal's law.
2. Different types of pressures like atmospheric pressure, gauge pressure, vacuum pressure, and absolute pressure.
3. The hydrostatic paradox and how pressure intensity is independent of the weight of fluid.
4. Different types of manometers used to measure pressure like piezometers, U-tube manometers, single column manometers, differential manometers, and inverted U-tube differential manometers.
5. How bourdon tubes and diaphragm/bellows gauges can be used to measure pressure by converting pressure differences into mechanical displacements.
1) The document discusses fluid flow through orifices and mouthpieces. It describes the theory of small orifices discharging fluid using Bernoulli's equation and defines relevant terms like coefficient of velocity and coefficient of discharge.
2) Torricelli's theorem states the velocity of a discharging jet is proportional to the square root of the head producing flow. The theoretical discharge can be calculated using the orifice area and velocity.
3) Examples are provided to demonstrate calculating coefficients of velocity, discharge, and contraction for given orifice dimensions and fluid flow values.
This document discusses dimensional analysis and its applications. It begins with an introduction to dimensions, units, fundamental and derived dimensions. It then discusses dimensional homogeneity, methods of dimensional analysis including Rayleigh's method and Buckingham's π-theorem. The document also covers model analysis, similitude, model laws, model and prototype relations. It provides examples of applying Rayleigh's method and Buckingham's π-theorem to define relationships between variables. Finally, it discusses different types of forces acting on fluids and dimensionless numbers, and provides model laws for Reynolds, Froude, Euler and Weber numbers.
When a body moves through a fluid, it experiences two forces: drag and lift. Drag acts parallel to the flow and slows the body down, while lift acts perpendicular to the flow. These forces depend on factors like the fluid's velocity and density, the body's size and shape, and its angle of attack relative to the flow. Streamlined shapes with small frontal areas experience less pressure drag than blunt bodies, which experience boundary layer separation and higher pressures on one side. The forces can be calculated using drag and lift coefficients, which vary based on the Reynolds number and other flow properties.
This chapter discusses differential analysis of fluid flow. It introduces the concepts of stream function and vorticity. The key equations derived are:
1) The differential equations of continuity, linear momentum, and mass conservation which relate the time rate of change of fluid properties like density and velocity within an infinitesimal control volume.
2) The Navier-Stokes equations which model viscous flow using Newton's laws and relate stresses to strain rates via viscosity.
3) Equations for inviscid, irrotational flow where viscosity and vorticity are neglected.
4) The stream function, a potential function whose contour lines represent streamlines, allowing 2D problems to be solved using a
Fluid properties such as density, specific volume, specific weight, specific gravity, compressibility, viscosity, and surface tension are discussed. Density is defined as the mass of a substance per unit volume. Specific volume is defined as the volume of substance per unit mass. Specific weight is the weight of substance per unit volume. Specific gravity is the ratio of density of a substance to the density of water. Compressibility refers to the change in volume of a fluid with changes in pressure. Viscosity is a measure of a fluid's resistance to shear forces and depends on factors like cohesion and molecular momentum. The falling sphere viscometer is used to measure viscosity and involves dropping a sphere in a fluid and measuring its velocity over
This document discusses fluid statics and pressure measurement. It defines concepts like absolute pressure, gauge pressure, atmospheric pressure, and Pascal's law. It describes devices used to measure pressure like manometers, piezometers, and Bourdon gauges. Specifically, it provides details on how liquid manometers and differential manometers work, including the principles, setup, and equations to calculate pressure. It also lists the advantages and limitations of using manometers for pressure measurement applications.
This document discusses key concepts in fluid dynamics, including:
(i) Fluid kinematics describes fluid motion without forces/energies, examining geometry of motion through concepts like streamlines and pathlines.
(ii) Fluids can flow steadily or unsteadily, uniformly or non-uniformly, laminarly or turbulently depending on properties of the flow and fluid.
(iii) The continuity equation states that mass flow rate remains constant for an incompressible, steady flow through a control volume according to the principle of conservation of mass.
This document discusses fluid pressure and various ways to measure it. It defines pressure as a force per unit area and explains that pressure increases linearly with depth in a static fluid. It also describes how manometers and barometers work to measure pressure differences and atmospheric pressure respectively using the hydrostatic pressure equation. Manometers use columns of liquid like mercury or water, while barometers use a mercury column to directly measure atmospheric pressure at sea level.
This document discusses boundary layer development. It begins by defining boundary layers and describing the velocity profile near a surface. As distance from the leading edge increases, the boundary layer thickness grows due to viscous forces slowing fluid particles. The boundary layer then transitions from laminar to turbulent. Turbulent boundary layers have a logarithmic velocity profile and thicker boundary layer compared to laminar. Pressure gradients and surface roughness also impact boundary layer development and transition.
This document provides an overview of fluid kinematics, which is the study of fluid motion without considering forces. It discusses key concepts like streamlines, pathlines, and streaklines. It describes Lagrangian and Eulerian methods for describing fluid motion. It also covers various types of fluid flow such as steady/unsteady, laminar/turbulent, compressible/incompressible, and one/two/three-dimensional flow. Important topics like continuity equation, velocity, acceleration, and stream/velocity potential functions are also summarized. The document is intended to outline the syllabus and learning objectives for a course unit on fluid kinematics.
The document discusses properties of fluids and dimensional analysis. It covers 10 key properties of fluids including mass density, specific weight, specific volume, viscosity, and surface tension. It provides definitions, formulas, values and units for each property. It also discusses how properties vary with temperature and pressure. Dimensional analysis techniques like Rayleigh's method and Buckingham π-theorem are explained along with their applications. Model analysis and different types of similarities (geometric, kinematic, dynamic) are defined. Finally, the document discusses fluid statics topics like pressure measurement devices, hydrostatic forces, and buoyancy.
Dimensional analysis Similarity laws Model laws R A Shah
Rayleigh's method- Theory and Examples
Buckingham Pi Theorem- Theory and Examples
Model and Similitude
Forces on Fluid
Dimensionless Numbers
Model laws
Distorted models
This presentation introduces concepts of hydrostatics including total pressure on immersed surfaces, center of pressure, and applications. Total pressure on a surface depends on its orientation (horizontal, vertical, inclined) and is calculated by integrating pressure over small elements. The center of pressure is the point where the total pressure force acts and can be found using the theorem of parallel axis. Examples of hydrostatics applications discussed are water pressure on structures like sluice gates, lock gates, and masonry walls. Conditions for stability of dams are also outlined.
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
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.
This document discusses flow through pipes, including:
- Laminar and turbulent flow characteristics defined by Reynolds number
- Head losses calculated using Darcy-Weisbach and minor loss equations
- Friction factors determined from Moody diagrams for laminar and turbulent flows
- Total head loss in a pipe system equals major losses in pipe sections plus minor losses from fittings
1) Compressible flow is when the density of a fluid changes during flow, such as gases. Incompressible flow assumes constant density, such as liquids.
2) Examples of compressible flow include gases through nozzles, compressors, high-speed projectiles and planes, and water hammer.
3) Bernoulli's equation relates pressure, temperature, and specific volume and only applies to steady, incompressible flow without friction losses along a single streamline.
This document provides an introduction and overview of a fluid mechanics course taught by Dr. Mohsin Siddique. It outlines the course details including goals, topics, textbook, and assessment methods. The course aims to provide an understanding of fluid statics and dynamics concepts. Key topics covered include fluid properties, fluid statics, fluid flow measurements, dimensional analysis, and fluid flow in pipes and open channels. Students will be evaluated through assignments, quizzes, a midterm exam, and a final exam. The course intends to develop skills relevant to various engineering fields involving fluid mechanics.
Unit 6 discusses losses in pipes, including major and minor losses. Major losses are due to friction and calculated using Darcy-Weisbach or Chezy's formulas. Minor losses are due to changes in pipe direction, size, or obstructions and are also calculated using specific formulas. The document also discusses equivalent pipes, pipes in series, pipes in parallel, and two and three reservoir pipe flow analysis problems. Head losses are calculated using friction and minor loss formulas, and continuity and energy equations are used to analyze pipe flows.
This document discusses various topics related to fluid mechanics including:
1. Fluid statics, hydrostatic pressure variation, and Pascal's law.
2. Different types of pressures like atmospheric pressure, gauge pressure, vacuum pressure, and absolute pressure.
3. The hydrostatic paradox and how pressure intensity is independent of the weight of fluid.
4. Different types of manometers used to measure pressure like piezometers, U-tube manometers, single column manometers, differential manometers, and inverted U-tube differential manometers.
5. How bourdon tubes and diaphragm/bellows gauges can be used to measure pressure by converting pressure differences into mechanical displacements.
1) The document discusses fluid flow through orifices and mouthpieces. It describes the theory of small orifices discharging fluid using Bernoulli's equation and defines relevant terms like coefficient of velocity and coefficient of discharge.
2) Torricelli's theorem states the velocity of a discharging jet is proportional to the square root of the head producing flow. The theoretical discharge can be calculated using the orifice area and velocity.
3) Examples are provided to demonstrate calculating coefficients of velocity, discharge, and contraction for given orifice dimensions and fluid flow values.
This document discusses dimensional analysis and its applications. It begins with an introduction to dimensions, units, fundamental and derived dimensions. It then discusses dimensional homogeneity, methods of dimensional analysis including Rayleigh's method and Buckingham's π-theorem. The document also covers model analysis, similitude, model laws, model and prototype relations. It provides examples of applying Rayleigh's method and Buckingham's π-theorem to define relationships between variables. Finally, it discusses different types of forces acting on fluids and dimensionless numbers, and provides model laws for Reynolds, Froude, Euler and Weber numbers.
When a body moves through a fluid, it experiences two forces: drag and lift. Drag acts parallel to the flow and slows the body down, while lift acts perpendicular to the flow. These forces depend on factors like the fluid's velocity and density, the body's size and shape, and its angle of attack relative to the flow. Streamlined shapes with small frontal areas experience less pressure drag than blunt bodies, which experience boundary layer separation and higher pressures on one side. The forces can be calculated using drag and lift coefficients, which vary based on the Reynolds number and other flow properties.
This chapter discusses differential analysis of fluid flow. It introduces the concepts of stream function and vorticity. The key equations derived are:
1) The differential equations of continuity, linear momentum, and mass conservation which relate the time rate of change of fluid properties like density and velocity within an infinitesimal control volume.
2) The Navier-Stokes equations which model viscous flow using Newton's laws and relate stresses to strain rates via viscosity.
3) Equations for inviscid, irrotational flow where viscosity and vorticity are neglected.
4) The stream function, a potential function whose contour lines represent streamlines, allowing 2D problems to be solved using a
Fluid properties such as density, specific volume, specific weight, specific gravity, compressibility, viscosity, and surface tension are discussed. Density is defined as the mass of a substance per unit volume. Specific volume is defined as the volume of substance per unit mass. Specific weight is the weight of substance per unit volume. Specific gravity is the ratio of density of a substance to the density of water. Compressibility refers to the change in volume of a fluid with changes in pressure. Viscosity is a measure of a fluid's resistance to shear forces and depends on factors like cohesion and molecular momentum. The falling sphere viscometer is used to measure viscosity and involves dropping a sphere in a fluid and measuring its velocity over
This document discusses fluid statics and pressure measurement. It defines concepts like absolute pressure, gauge pressure, atmospheric pressure, and Pascal's law. It describes devices used to measure pressure like manometers, piezometers, and Bourdon gauges. Specifically, it provides details on how liquid manometers and differential manometers work, including the principles, setup, and equations to calculate pressure. It also lists the advantages and limitations of using manometers for pressure measurement applications.
This document discusses key concepts in fluid dynamics, including:
(i) Fluid kinematics describes fluid motion without forces/energies, examining geometry of motion through concepts like streamlines and pathlines.
(ii) Fluids can flow steadily or unsteadily, uniformly or non-uniformly, laminarly or turbulently depending on properties of the flow and fluid.
(iii) The continuity equation states that mass flow rate remains constant for an incompressible, steady flow through a control volume according to the principle of conservation of mass.
This document discusses fluid pressure and various ways to measure it. It defines pressure as a force per unit area and explains that pressure increases linearly with depth in a static fluid. It also describes how manometers and barometers work to measure pressure differences and atmospheric pressure respectively using the hydrostatic pressure equation. Manometers use columns of liquid like mercury or water, while barometers use a mercury column to directly measure atmospheric pressure at sea level.
This document discusses boundary layer development. It begins by defining boundary layers and describing the velocity profile near a surface. As distance from the leading edge increases, the boundary layer thickness grows due to viscous forces slowing fluid particles. The boundary layer then transitions from laminar to turbulent. Turbulent boundary layers have a logarithmic velocity profile and thicker boundary layer compared to laminar. Pressure gradients and surface roughness also impact boundary layer development and transition.
This document provides an overview of fluid kinematics, which is the study of fluid motion without considering forces. It discusses key concepts like streamlines, pathlines, and streaklines. It describes Lagrangian and Eulerian methods for describing fluid motion. It also covers various types of fluid flow such as steady/unsteady, laminar/turbulent, compressible/incompressible, and one/two/three-dimensional flow. Important topics like continuity equation, velocity, acceleration, and stream/velocity potential functions are also summarized. The document is intended to outline the syllabus and learning objectives for a course unit on fluid kinematics.
The document discusses properties of fluids and dimensional analysis. It covers 10 key properties of fluids including mass density, specific weight, specific volume, viscosity, and surface tension. It provides definitions, formulas, values and units for each property. It also discusses how properties vary with temperature and pressure. Dimensional analysis techniques like Rayleigh's method and Buckingham π-theorem are explained along with their applications. Model analysis and different types of similarities (geometric, kinematic, dynamic) are defined. Finally, the document discusses fluid statics topics like pressure measurement devices, hydrostatic forces, and buoyancy.
Dimensional analysis Similarity laws Model laws R A Shah
Rayleigh's method- Theory and Examples
Buckingham Pi Theorem- Theory and Examples
Model and Similitude
Forces on Fluid
Dimensionless Numbers
Model laws
Distorted models
The document discusses physical hydraulic model testing of structures. It provides an outline for a one-day training on the topic. The training will cover:
- What hydraulic structures are and why physical testing is conducted
- The hydraulic design procedure and testing options
- Conducting a SWOT analysis of physical model testing
It will also cover the theoretical background of physical modeling, including similitude laws and dimensionless numbers. A practical exercise on computing model dimensions is included. The training will conclude with a case study of physical model testing conducted for the Diamer Basha Dam project in Pakistan.
This document contains information about a fluid mechanics course taught by Dr. Yaser H. Alahmadi, including recommended textbooks, the course outline, definitions of key fluid mechanics terms like fluid and viscosity, basic fluid properties, the no-slip condition, and an example problem calculating fluid velocity. It provides essential concepts and information needed to understand fluid mechanics.
008a (PPT) Dim Analysis & Similitude.pdfhappycocoman
This document discusses dimensional analysis and similitude. It defines dimensional analysis as the study of relations between physical quantities based on their units and dimensions. Dimensional analysis involves identifying the base quantities like length, mass, time that physical quantities are measured in. Dimensional analysis is useful for checking equations for dimensional homogeneity and developing scaling laws. The document discusses Rayleigh's and Buckingham π theorem methods of dimensional analysis. It also discusses the three types of similitude required for model analysis: geometric, kinematic and dynamic similitude. Finally, it defines several common dimensionless numbers like Reynolds number, Froude number, Euler number, Weber number and Mach number in terms of dominant forces.
This document provides an introduction to fluid mechanics. It outlines key learning outcomes, including understanding basic fluid mechanics concepts and applications. It defines fluids and gives examples. Key fluid properties like density, viscosity, pressure and compressibility are explained. Different types of fluids and flows are classified, including viscous and inviscid, internal and external, incompressible and compressible, steady and unsteady, and natural and forced flows. Dimensional analysis and units are also covered. Tables of contents and illustrations are included to aid understanding of the topic.
Dimensional analysis is a mathematical technique used to solve engineering problems by studying dimensions. It relies on the principle that dimensionally homogeneous equations will have identical powers of fundamental dimensions (mass, length, time, etc.) on both sides. There are two main methods: Rayleigh's method determines relationships between variables based on dimensional homogeneity. Buckingham's π-theorem determines the minimum number of dimensionless groups needed to describe a phenomenon with multiple variables. Model analysis uses scaled models and dimensional analysis to predict the performance of full-scale structures before being built. Complete similitude between a model and prototype, including geometric, kinematic, and dynamic similarity, allows test results from the model to accurately represent the prototype.
Similitude and Dimensional Analysis -Hydraulics engineering Civil Zone
This document discusses similitude and dimensional analysis for model testing in hydraulic engineering. It introduces key concepts like similitude, prototype, model, geometric similarity, kinematic similarity, dynamic similarity, dimensionless numbers, and model laws. Reynolds model law is described in detail, which states that the Reynolds number must be equal between the model and prototype for problems dominated by viscous forces, such as pipe flow. An example problem demonstrates how to calculate the velocity and flow rate in a hydraulic model based on given prototype parameters and Reynolds model law.
This document provides information about a fluid mechanics course taught by Dr. Muhammad Uzair at NED University of Engineering & Technology. The course objectives are to impart theoretical knowledge of fluid statics and dynamics and enable students to analyze and solve engineering problems. The course learning outcomes include being able to define fluid mechanics concepts, apply equations to solve problems, and analyze dimensional analysis and experimental work problems. The course will cover topics such as fluid properties, fluid statics, fluid dynamics, and dimensional analysis over its contents. Student learning will be assessed through exams, assignments, reports, and quizzes.
This document discusses dimensional analysis and dimensionless numbers that are important in fluid mechanics. It defines Reynolds number, Froude number, Euler number, Weber number, and Mach number. It explains how dimensional analysis can help reduce the number of variables in experimental investigations. It also discusses similitude and the different types of model testing including undistorted and distorted models. The key uses and advantages of model testing are outlined.
001a (PPT) Introduction & Properties of fluids.pdfhappycocoman
1. The document provides information about Dr. Vijay G. S., a professor in the Department of Mechanical and Manufacturing Engineering at Manipal. It includes his contact information and office location.
2. The document then discusses fundamental concepts in fluid mechanics, including definitions of fluids, fluid statics, kinematics, and dynamics. It also explains properties such as density, viscosity, and compressibility.
3. The document presents preliminary concepts relevant to fluid mechanics, such as scalar and vector quantities, units of measurement, Newton's laws of motion, and other key terms. It also discusses different systems of units used in fluid mechanics.
- Dimensional analysis is a technique used to determine the relationship between variables in a physical phenomenon based on their dimensions and units.
- It allows reducing the number of variables needed to describe a phenomenon through the use of dimensionless parameters known as π terms.
- Lord Rayleigh and Buckingham developed systematic methods for dimensional analysis. Buckingham's π-method involves identifying all variables, their dimensions, and grouping them into as many dimensionless π terms as needed to describe the phenomenon.
multiphase flow modeling and simulation ,Pouriya Niknam , UNIFIPouriya Niknam
This document discusses modeling and simulation of multiphase flows using computational fluid dynamics (CFD). It begins with definitions of multiphase flow and discusses important types including bubbly, droplet, particle-laden, and annular flows. The document then provides tips on multiphase simulation including choosing appropriate modeling approaches such as Lagrangian, Eulerian, or volume of fluid methods depending on the problem. It concludes with discussions of challenges such as convergence difficulties and appropriate solver settings and techniques to address these challenges.
This document discusses rheology methods for analyzing the mechanical properties of materials. It begins with an introduction to rheology, defining it as the study of flow and deformation of materials. Important variables in rheological analysis are then outlined, including shear stress, shear rate, strain, and viscosity. Three main methods of rheological measurement are described: melt index instruments, rotational rheometers, and capillary rheometers. Rotational rheometers measure viscosity using different plate and cylinder geometries under varying shear rates and temperatures. Capillary rheometers examine processing behavior by forcing material through a die. The document concludes that rheology is a useful characterization tool for understanding structure-property relationships in materials development.
This document provides information about a fluid mechanics course. It includes the course instructor's contact information and recommended textbooks. It then introduces key concepts in fluid mechanics, defining it as the study of fluids at rest or in motion. It discusses the distinction between solids and fluids, and between gases and liquids. It also outlines several application areas of fluid mechanics in fields like biomechanics, household systems, mechanical engineering, and civil engineering.
This document provides an introduction to fluid mechanics for chemical engineers. It defines a fluid and discusses the continuum hypothesis. It describes key fluid properties like density, pressure, viscosity, surface tension and vapor pressure. It also classifies fluid motions as steady or unsteady, uniform or non-uniform, viscous or inviscid, compressible or incompressible, and laminar or turbulent. The document provides examples of areas where fluid mechanics is applied, like process units, pipelines, fluid machinery and environmental applications.
Fluid mechanics is the study of fluids either at rest or in motion. There are two main types of fluids: liquids and gases. Liquids have strong cohesive forces that allow them to retain their shape, while gases have negligible cohesive forces and are free to expand. Fluid properties include density, viscosity, and other thermodynamic properties. Viscosity describes a fluid's resistance to flow and is dependent on factors like temperature. Reynolds number is used to characterize different flow regimes from laminar to turbulent. Fluid mechanics has many applications in fields like engineering, biology, and meteorology.
This document provides an overview of the course "Fluid Mechanics for MEC154" which covers various topics in fluid mechanics including Newtonian and non-Newtonian flows, Pascal's law, manometry, buoyancy, steady and pulsatile flows, and more. Key concepts in fluid mechanics such as viscosity, Newtonian and non-Newtonian fluids, and the differences between liquids and gases are explained. Examples of fluid mechanics applications in areas like medical equipment, internal body flows, and manufacturing are also presented.
Experiment 2
Group E
Introduction
Abstract:
Introduction
Apparatus Explanation:
The experiment is performed on an apparatus that consists of an aluminum alloy pipe that is connected to a diffuser to the suction eye of a centrifugal fan.
To measure the distribution of static pressure, 14 taps are connected to manometers placed along the pipe. (Tap number 14 reads the static pressure)
A Pitot tube is placed at the end of the pipe to measure stagnation pressure. (Tap number 19 reads the stagnation pressure)
The discharge opening down the stream can be adjusted from 0% to 100% open, also the speed of the fan can be adjusted too.
Motivation
Objective:
A Pitot tube and a manometer were used for in this experiment to measure the radial velocity profile of an air flow inside a pipe.
Using a Pitot tube and manometer to determine the velocity profile.
Determine boundary layer thickness along the wall of the pipe.
Investigate the axial pressure distribution along the pipe
Background
The no-slip condition states that the velocity of the fluid is equal to the velocity of the solid boundary which the fluid is in direct contact with a solid boundary.
As the fluid moves down stream the flow become fully developed where the velocity profile does not change with axial position, unlike with the fluid enters the pipe.
When the fluid enters the pipe it passes through the entrance region which is the distance between the fluid entrance till it becomes a fully developed flow.
The velocity profile has different shapes depending on whether the flow is laminar or turbulent.
Background
The speed of the flow can be calculated by the knowledge of the static and the stagnation pressure in a derived equation from the Bernoulli equation.
A Pitot tube is a device that measures the stagnation pressure of the flow.
The Manometer is used to measure pressure difference by the difference in high appearing on its tubes.
By the use of these two equations the equation that will be very useful for this lab is:
Manometer
Background
The Pitot tube was invented in 1732 by a French Engineer called Henri Pitot (1695-1771).
Due to design weakness the device was not effective and did was not used a lot.
But in 1856 improvements where made to the tube by another French Engineer called Henry Darcy with the assistance of Henri Bazin.
Those improvements brought the Pitot tube to large scale uses.
Application
This experiment provides the knowledge of measuring the velocity of a flow and the boundary layer thickness a long a the wall of the pipe.
This knowledge would be beneficial to calculate the speed of a fluid inside a pipe not just that but learning another method of calculating the speed of a moving object be the velocity of the flow surrounding it.
That method is already used in calculating the speed of aircraft as we can see the use of Pitot tubes on them, and it can be applied on cars or any other object.
Application
Procedure:
Turn on the motor and se ...
Similar to Properties of Fluids, Fluid Static, Buoyancy and Dimensional Analysis (20)
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Properties of Fluids, Fluid Static, Buoyancy and Dimensional Analysis
1. Unit No. 1
Properties of Fluids
and
Dimensional Analysis
Prepared By :
Prof. S. G.Taji
Department of Civil Engineering
Sanjivani College of Engineering
Kopargaon
2. Fluid : - Tendency to flow
Ideal Fluids
(Viscosity, Surface
Tension & it is
incompressible)
Real Fluids
(Viscosity, Surface
Tension and possess
Compressibility)
o. 1
3. Fluid Mechanics : - Branch of science
that deals with behaviour of fluid at
rest as well as in motion.
Fluid Statics
(Study of fluids at
rest)
Fluid Kinematics
(Study of fluids in
motion without
considering the
forces causing the
motion)
Fluid Dynamics
(Study of fluids in
motion with
consideration of
the forces causing
the motion)
Prepared By : Prof S. G. Taji
4. Properties of Fluids
• Definition
• Formula :
• Value and units : density of water is 1 gm/cm3 or 1000 kg/m3
Mass Density
• Definition
• Formula :
• Value and units : w for water = 9810 N/m3, 9.81 kN/m3,
1000 kgf/m3 or 981 dynes/cm3
Specific Weight
or
Weight Density
• Definition
• Formula :
• Units : m3/N or m3/kgf or cm3/dynes
Specific
Volume
Prepared By : Prof S. G. Taji
5. Properties of Fluids
• Definition
• Formula :
• Units : Dimensionless / No Unit
Specific Gravity
• Definition
• Formula / Derivation :
• Units : kg.f-sec/m2 or dyne-sec/cm2 or N.s/m2
• 1 N.s/m2 = 10 poise
• Dynamic Viscosity :
• Kinematic Viscosity :
• Newtons Law of Viscosity
Viscosity
Fluid Newton’s law
of viscosity
Newtonian fluidsobey refer
Fluid Newton’s law
of viscosity
Non- Newtonian
fluids
Do not obey
Prepared By : Prof S. G. Taji
6. Properties of Fluids
• Variation of Viscosity with Temperature : Viscosity
of liquids decreses with increase in temperature while viscosity
of gases increases with increase in temperature.
• Cohesive Forces
• Molecular Momentum Transfer
Prepared By : Prof S. G. Taji
7. Properties of Fluids
• Relation between viscosity and temperature :
1. For liqiuds :
μ = viscosity of liquid at t oC in poise. For water : μo = 1.79*10^-3 poise
μo = viscosity of liquid at 0 oC in poise. α = 0.03368
α , β = constants for liquids/gases. β = 0.000221
2. For Gases :
For air : μo = 0.000017 poise
α = 5.6*10^-8
β = 0.1189*10^-9
Prepared By : Prof S. G. Taji
8. Properties of Fluids
• Types of Fluids : Thixotrophic
Bingham plastic : resist a small shear stress but flow easily under large shear
stresses, e.g. sewage sludge, toothpaste, and jellies.
Pseudo plastic : most non-Newtonian fluids fall under this group. Viscosity
decreases with increasing velocity gradient, e.g. colloidal
substances like clay, milk, and cement.
Dilatants : viscosity decreases with increasing velocity gradient, e.g.
quicksand.
Thixotrophic : non-linear relationship between the shear stress and the rate
of angular deformation, beyond an initial yeild stress
Prepared By : Prof S. G. Taji
9. Properties of Fluids
• Thermodynamic properties : Effect of T & P on L and G
• Gas Equation : p = ρ*R*T or p/v = R*T
• Universal gas equation : p = ρ*R*T = p = (m/v)*R*T
pv = m*R*T
Where, ρ = density of gas
R = Gas constant = 29.3 kgf-m/kg-k (MKS)
= 29.3 9.81 Nm/kg-k = 287 J/kg-k (SI)
T = Absolute temp in k , Tabs = 273.15 + t oC
V = Specific Volume = 1/ ρ
m = n * M , ( m = mas of gas in kg)
n = number of moles in a volume of a gas ( 1 mole = 6.02*10^23 things – Avagadros no.)
M = mas of gas molecules / mas of hydrogen atom
Isothermal Process : p/ ρ = constant
Adiabatic Process : p/ ρ^k = constant (k = ratio of specific heat of
a gas at constant temp. and constant volume.)
Prepared By : Prof S. G. Taji
10. Properties of Fluids
• Defination
• Formula : 1 / Bulk Modulus (K)Compressibility
• Definition
• Formula :
• Effect of T & P : dp K and T K (liquids)
• T P K (gases)
• Isothermal Process : p = K
• Adiabatic process : K = pk
Bulk Modulus
• Definition
• Formula : 1. Liquid Droplet : p = 4σ/d
• 2. Hollow Bubble : p = 8σ/d
• 3. Liquid Jet : p = 2σ/d
• Units : N/cm2
Surface
Tension
Prepared By : Prof S. G. Taji
12. Dimensional Analysis
• Method of Dimensions.
• Mathematical Technique used in research work for design and
conducting model tests.
• Deals with the dimensions of physical quantities involved in the
phenomenon.
• All physical quantities are measured by comparison with respect to
an arbitrarily fixed value.
• Length L, Mass M and Time T are three fixed dimensions which are
of importance in fluid mechanics.
• These fixed dimensions are called as Fundamental Dimensions or
Fundamental Quantities.
• The quantities those are derived from these fundamental
quantities are known as Secondary or Derived Quantities. They
possess more than one fundamental dimensions.
Prepared By : Prof S. G. Taji
14. Dimensional Analysis
• Dimensional Homogenity : It means the dimensions of each term
in an equation on both sides are equal.
• Dimensions of L.H.S = Dimensions of R.H.S
Methodsof Dimensional
Analysis
Rayleigh’s
Method
Bckingham’s
π-Theorem
Prepared By : Prof S. G. Taji
15. Rayleigh’s Method
• To define relationship among the variables.
• This method is used for determining the expression for a variable
which depends upon maximum three or four variables only.
• Thus the expression is obtained for dependent vriable.
19. Buckingham’s π -Theorem
Method of Selecting Repeating Variables :
1. The dependent variable should not be selected as repeating
variable.
2. Repeating variables selected should not form a dimensionless
group.
3. Repeating variables togethes must have same number of
fundamental dimensions.
4. No two repeating variables should have same dimensions.
5. Repeating variables should be selected from each of the
following properties
i. Geometric Property : Length, height, width, area.
ii. Flow Property : Velocity, Acceleration, Discharge.
iii. Fluid Property : Mass density, Viscosity, Surface tension.
Prepared By : Prof S. G. Taji
23. Model Analysis
• For predicting the performance of the hydraulic
structures (such as dams, spillways etc.) or hydraulic
machines (such as turbines, pumps etc.) before
actually constructing or manufacturing, models of the
structures or machines are made and tests are
conducted on them to obtain the desired information.
• Model is a small replica of the actual structure or
machine.
• The actual structure or machine is called as Prototype.
• Models can be smaller or larger than the Prototype.
• Model Analysis is actually an experimental method of
finding solutions of complex flow problems.
Prepared By : Prof S. G. Taji
24. Model Analysis
• Advantages of Dimensional and Modal Analysis :
1. Performance of the hydraulic structure or hydraulic machine
can be easily predicted, in advance from its model.
2. With the help of D.A, a relationship between the variables
influencing a flow problem in terms of dimensionless
parameters is obtained. This relationship helps in conducting
tests on the models.
3. Merits of alternative designs can be predicted with the help
of model testing. The most and safe design is finally
adopted.
4. The tests performed on the models can be utilized for
obtaining useful information about the performance of the
prototypes.
• This can be obtained only if similarity exists between the
model and prototype. Prepared By : Prof S. G. Taji
25. Similitude or Similarities
Similitude is defined as the similarity between the model
and prototype in every aspect, which means that the
model and prototype have similar properties.
Types of Similarities:
1. Geometric Similarity : Length, Breadth, Depth, Diameter,
Area, Volume etc.
2. Kinematic Similarity : Velocity, Acceleration etc.,
3. Dynamic Similarity : Time, Discharge, Force, Pressure
Intensity, Torque, Power
Prepared By : Prof S. G. Taji
26. Similitude or Similarities
1. Geometric Similarity : The geometric similarity is said to
be exist between the model and prototype if the ratio of
all corresponding linear dimensions in the model and
prototype are equal.
Prepared By : Prof S. G. Taji
27. Similitude or Similarities
2. Kinematic Similarity : The kinematic similarity is said to be
exist between model and prototype if the ratios of
velocity and acceleration at corresponding points in the
model and at the corresponding points in the prototype
are the same.
Prepared By : Prof S. G. Taji
28. Similitude or Similarities
3. Dynamic Similarity : The dynamic similarity is said to be
exist between model & prototype if the ratios of
corresponding forces acting at the corresponding points
are Equal.
• It means for dynamic similarity between the model and
prototype, the dimensionless numbers should be same
for model and prototype.
Prepared By : Prof S. G. Taji
29. Types of Forces Acting on Moving Fluid
1. Inertia Force (Fi) : It is the product of mass and acceleration
of the flowing fluid and acts in the direction opposite to the
direction of acceleration.
• It always exists in the fluid flow problems.
2. Viscous Force (Fv) : It is equal to the product of shear stress
due to viscosity and surface area of the flow.
3. Gravity Force (Fg) : It is equal to the product of mass and
acceleration due to gravity of the flowing fluid.
4. Pressure Force (Fp) : It is equal to the product of pressure
intensity and cross sectional area of flowing fluid.
5. Surface Tension Force (Fs) : It is equal to the product of
surface tension and length of surface of the flowing.
6. Elastic Force (Fe) : It is equal to the product of elastic stress
and area of the flowing fluid.
Prepared By : Prof S. G. Taji
30. Dimensionless Numbers
• Dimensionless numbers are obtained by dividing the
inertia force by viscous force or gravity force or pressure
force or surface tension force or elastic force.
Prepared By : Prof S. G. Taji
31. Model Laws
• The laws on which the models are designed for dynamic similarity
are called model laws or laws of similarity.
1. Reynold’s Model Law : Model law in which models are based on
Reynold’s number.
Models based on Reynolds’s Number includes:
a) Pipe Flow.
b) Resistance experienced by Sub-marines, airplanes, fully
immersed bodies.
2. Froude Model Law : Model law in which models are based on
Froude’s number.
Froude Model Law is applied in the following fluid flow problems:
a) Free Surface Flows such as Flow over spillways, Weirs, Sluices,
Channels etc.
b) Flow of jet from an orifice or nozzle.
c) Where waves are likely to formed on surface.
Prepared By : Prof S. G. Taji
32. Reynold’s Model Law
• If the viscous forces are predominant, the models are designed for
dynamic similarity based on Reynold’s number.
Prepared By : Prof S. G. Taji
33. Froude Model Law
• If the gravity force is predominant, the models are designed for
dynamic similarity based on Froude number.
Prepared By : Prof S. G. Taji
34. Summary
• 10 properties of fluids with numerical.
• Effect of temperature and pressure on all the properties
of fluids.
• Rheological diagram and types of fluids.
• Fundamental and secondary quantities.
• Dimensional Homogeneity.
• Rayleigh’s method and Buckingham's π – theorem.
• Model Analysis and 3 types of similarities.
• 5 types of forces and 5 dimensionless numbers.
• 2 model laws and scale ratio of different quantities.
• Near about 30 formulae's.
Prepared By : Prof S. G. Taji
35. Unit No. 2
Fluid Statics
And
Buoyancy
Prepared By : Prof S. G. Taji
36. Fluid Pressure at a point
• Consider a small area dA in large mass of a fluid.
•
•
• Force or Pressure force F = p*A
• Units : kgf/m2 and kgf/cm2 (MKS)
N/m2 or N/mm2 (SI)
• N/m2 = Pa (Pascal)
• 1 kPa = 1000 N/m2
• 1 bar = 100 kPa = 10^5 N/m2
Prepared By : Prof S. G. Taji
37. Pascal’s Law
• It states that pressure or intensity of pressure at a point in a
static fluid is equal in all directions.
• Resolving forces in x-direction
• Resolving forces in y-direction
• Equating both we get
40. Relationship between Pressure
• Absolute Pressure : Pressure measured with reference to absolute
zero pressure.
• Gauge Pressure : Pressure measured w.r. to atmospheric pressure.
It is always above the atmospheric pressure.
• Vacuum Pressure : Pressure measured below the atmospheric
pressure.
Prepared By : Prof S. G. Taji
42. Measurement of Pressure
• Piezometer : Simplest form of manometer used for
measuring gauge pressures. It consist of a vertical tube
open at one end and attached to a container at the
other end. It measures the pressure of a liquid in a
container.
• The rise of liquid gives the pressure head at that point.
43. Measurement of Pressure
• U-tube Manometer : Consist of a glass tube bent in U-shape,
one end of which is connected to a point at which pressure is
to be measured and other end open to the atmosphere.
Prepared By : Prof S. G. Taji
44. Measurement of Pressure
• U-tube Manometer : Consist of a glass tube bent in U-shape,
one end of which is connected to a point at which pressure is
to be measured and other end open to the atmosphere.
Prepared By : Prof S. G. Taji
45. Measurement of Pressure
• Single column Manometer : Modified form of a U-tube
manometer in which a reservoir, having a large cross-
sectional area (@100 times) as compared to the area of
the tube is connected to one of the limbs of the
manometer.
• Due to large cross-sectional area of the reservoir, for any
variation in pressure, the change in the liquid level in the
reservoir will be very small which may be neglected and
hence the pressure is given by the height of the liquid in
the other limb.
• The other limb may be vertical or inclined.
1. Vertical single column manometer
2. Inclined single column manometer
Prepared By : Prof S. G. Taji
49. Measurement of Pressure
• Differential Manometers: Devices used for measuring
the difference of pressure between two points in a pipe
or in two different pipes.
• It consist of a U-tube, containing heavy liquid, whose
two ends are connected to the points whose difference
of pressure is to be determined.
Prepared By : Prof S. G. Taji
56. Hydrostatic Forces
• Hydrostatic force : Force exerted by a static fluid on any
object submerged in it.
• This means that there will be no relative movement
between adjacent fluid layers.
• Therefore the velocity gradient will be equal to zero.
• Shear stress between two adjacent layers will also be
equal to zero.
• Only a force can be exerted by a fluid on the surrounding
walls and base which is called as hydrostatic force.
• Hence in hydrostatic force analysis we should know
about
1. Total Pressure Force.
2. Centre of Pressure.
Prepared By : Prof S. G. Taji
57. Hydrostatic Forces
• Total Pressure Force : Force exerted by a static fluid on a
surface either plane or curved when the fluid comes in
contact with the surfaces.
• Always acts normal to the surface.
• Centre of Pressure : The point of application of the total
pressure force on the surface is known as centre of
pressure.
• The four cases of submerged surfaces on which total
pressure force and center of pressure is to be
determined are as follows :
1. Vertical plane surfaces
2. Horizontal plane surfaces
3. Inclined plane surfaces
4. Curved surfaces Prepared By : Prof S. G. Taji
64. Buoyancy or Force of Buoyancy
• When any object is immersed in liquid, the liquid exert some
force on that object.
• The vertical force exerted by the liquid is called as Buoyancy
or Force of Buoyancy.
• This force of buoyancy is equal to the weight of the liquid
displaced by the body.
• For equilibrium condition, weight of the body is equal to the
force exerted by the liquid.
• Centre of Buoyancy : It is the point through which force of
buoyancy acts.
• It will act at the center of gravity of weight of liquid displaced
by the body.
66. Meta centre and Metacentric Height
• Meta centre : It is defined as a point with respect to which a
body oscillates in a liquid, when a body is tilted through a
small angle.
• It can also be defined as the intersecting point between
neutral axis line of the body and line of action of force of
buoyancy.
• Metacentric Height : Distance between the meta centre and
center of gravity is known as metacentric height.
67. Stability of submerged and floating
body
• Stability of submerged body is determined by the position of
centre of buoyancy with respect to centre of gravity.
• When centre of buoyancy is above centre of gravity, then the
submerged body remains in stable equilibrium.
• When centre of buoyancy is below centre of gravity, then the
submerged body remains in unstable equilibrium.
Prepared By : Prof S. G. Taji
68. Stability of submerged and floating
body
• Stability of floating body is determined by the position of
meta centre with respect to centre of gravity.
• When meta centre is above centre of gravity, then the body
remains in stable equilibrium.
• When meta centre is below centre of gravity, then the body
remains in unstable equilibrium.
Prepared By : Prof S. G. Taji
71. Summary
• Pascal’s law and Hydrostatic law.
• Relationship between different pressures.
• Pressure measurement devices.
• 4 cases of total pressure and centre of pressure.
• Buoyancy and centre of buoyancy.
• Meta centre and Metacentric height.
• Stability of submerged and floating bodies.
• Analytical and Experimental determination of
meta-centric height.
• Near about 12 derivations.
Prepared By : Prof S. G. Taji