This document provides information on fluid flow rates and Bernoulli's equation. It defines volume, weight, and mass flow rates and the continuity equation. Bernoulli's equation accounts for changes in elevation head, pressure head, and velocity head between points in a fluid system. The document outlines the procedure for applying Bernoulli's equation to problems and provides examples of its use. Limitations include its validity only for incompressible fluids with no added/lost energy or friction between points.
Fluid Mechanics Chapter 3. Integral relations for a control volumeAddisu Dagne Zegeye
Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
This document discusses equilibrium of particles and free body diagrams. It provides an example of drawing a free body diagram for a cylinder suspended by two cables, and using the equations of equilibrium to solve for the unknown tensions in the cables. It also discusses 3D equilibrium, giving an example problem of finding an unknown force on a particle given its position and four other forces.
Experiment NO:6 describes a compression test performed on an anisotropic wooden material to determine its compressive strength when force is applied both parallel and perpendicular to its fibers. When force was applied perpendicular to the fibers, the wooden block failed at a compressive strength of 4.7712x107 N/m2. When applied parallel to the fibers, the failure strength was lower at 1.204x107 N/m2. Detailed load-deformation data is provided in tables showing that the material can withstand over 10 times more load when compressed parallel rather than perpendicular to its fibers, as the fibers act like columns parallel to the load.
The Finite Element Method (FEM) is a numerical method to solve differential equations by dividing a system into small elements. In FEM, the region of interest is divided into elements and the differential equations are reduced to algebraic equations using approximations over each element. Two example problems, an axial rod problem and a beam problem, are used to introduce the FEM methodology. The methodology involves pre-processing to generate elements, obtaining elemental equations, assembling the equations, applying boundary conditions, solving the system of equations, and post-processing to calculate secondary quantities like stresses and strains.
1) Bernoulli's equation states that the total energy of a fluid particle remains constant as it flows through a pipe or channel. This includes the particle's potential energy, kinetic energy, and pressure energy.
2) The document provides an example calculation using Bernoulli's equation to determine the total head of water flowing through a pipe.
3) Bernoulli's equation is derived from Euler's equation for fluid motion and the conservation of energy, based on assumptions of inviscid, incompressible, steady flow along a streamline.
Fluid Mechanics Chapter 3. Integral relations for a control volumeAddisu Dagne Zegeye
Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation
Fluid Mechanics Chapter 4. Differential relations for a fluid flowAddisu Dagne Zegeye
Introduction, Acceleration field, Conservation of mass equation, Linear momentum equation, Energy equation, Boundary condition, Stream function, Vorticity and Irrotationality
This document discusses equilibrium of particles and free body diagrams. It provides an example of drawing a free body diagram for a cylinder suspended by two cables, and using the equations of equilibrium to solve for the unknown tensions in the cables. It also discusses 3D equilibrium, giving an example problem of finding an unknown force on a particle given its position and four other forces.
Experiment NO:6 describes a compression test performed on an anisotropic wooden material to determine its compressive strength when force is applied both parallel and perpendicular to its fibers. When force was applied perpendicular to the fibers, the wooden block failed at a compressive strength of 4.7712x107 N/m2. When applied parallel to the fibers, the failure strength was lower at 1.204x107 N/m2. Detailed load-deformation data is provided in tables showing that the material can withstand over 10 times more load when compressed parallel rather than perpendicular to its fibers, as the fibers act like columns parallel to the load.
The Finite Element Method (FEM) is a numerical method to solve differential equations by dividing a system into small elements. In FEM, the region of interest is divided into elements and the differential equations are reduced to algebraic equations using approximations over each element. Two example problems, an axial rod problem and a beam problem, are used to introduce the FEM methodology. The methodology involves pre-processing to generate elements, obtaining elemental equations, assembling the equations, applying boundary conditions, solving the system of equations, and post-processing to calculate secondary quantities like stresses and strains.
1) Bernoulli's equation states that the total energy of a fluid particle remains constant as it flows through a pipe or channel. This includes the particle's potential energy, kinetic energy, and pressure energy.
2) The document provides an example calculation using Bernoulli's equation to determine the total head of water flowing through a pipe.
3) Bernoulli's equation is derived from Euler's equation for fluid motion and the conservation of energy, based on assumptions of inviscid, incompressible, steady flow along a streamline.
Fluid Mechanics Chapter 5. Dimensional Analysis and SimilitudeAddisu Dagne Zegeye
Introduction, Dimensional homogeneity, Buckingham pi theorem, Non dimensionalization of basic equations, Similitude, Significance of non-dimensional numbers in fluid flows
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This document discusses the characteristic curves of turbines, which are used to study a turbine's performance under various conditions. There are three main types of characteristic curves: 1) Constant head curves, which show performance at constant head by varying speed and flow, 2) Constant speed curves, which show performance at constant speed by varying head and flow, and 3) Constant efficiency curves, which determine the zone of maximum efficiency for the turbine. The characteristic curves are provided by turbine manufacturers based on actual test data and include curves showing unit discharge, unit power, efficiency, and other parameters.
Fluid Mechanics Chapter 2 Part II. Fluids in rigid-body motionAddisu Dagne Zegeye
1. The document discusses rigid-body motion of fluids, where fluid particles move together with no internal motion or deformation. It presents equations of motion relating pressure, acceleration, and gravity for fluids undergoing rigid-body translation or rotation.
2. Special cases are considered, including fluids at rest, where pressure only varies with height, and fluids in free fall or accelerated upward, where pressure gradients are altered by acceleration.
3. For fluids accelerating linearly, equations are derived showing pressure varies with both vertical position and horizontal displacement from the acceleration axis, forming parallel inclined surfaces of constant pressure.
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
1. The document discusses the continuity equation, which states that the flow rate of an incompressible fluid is constant at any point in a fluid system with no accumulation.
2. The formula for continuity equation is given as: ρ1A1v1 = ρ2A2v2, where ρ is density, A is cross-sectional area, and v is velocity.
3. Examples of applications include calculating water velocity changes in pipes or rivers of varying diameters, and a sample problem is worked out calculating velocities at different pipe positions.
This document contains lecture notes on fluid mechanics. It begins with an introduction to fluid mechanics, including definitions of key terms like fluid, continuum, density, and viscosity. It then covers topics in fluid statics like pressure, hydrostatic force, and buoyancy. Later sections discuss the description and analysis of fluid motion using concepts like the control volume, streamlines, and conservation equations. The document aims to explain the physics of fluid motion to undergraduate students through examples and without advanced mathematics.
This experiment aimed to determine the Reynolds number (NRe) as a function of flow rate for liquid flowing through a circular pipe. NRe was calculated for 6 trials with increasing flow rates. All trials had NRe below 2100, indicating laminar flow as observed by the smooth movement of dye in the pipe. As flow rate increased, NRe also increased but remained in the laminar flow regime. The results show that flow type depends on NRe, with laminar flow occurring at low velocities (NRe < 2100).
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.
Strength of Materials, Lecture - 1.
Introduction + Recommended Books
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
Fluid tutorial 2_ans dr.waleed. 01004444149 dr walid
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Detailed calculations are shown to determine values like mass, pressure, shear stress, drag force, velocity, and viscosity based on given variables like temperature, volume, pressure, velocity, dimensions, torque, and fluid properties.
The document defines and provides examples of non-flow processes in thermodynamics, specifically polytropic processes. It states that in a non-flow process, the change in internal energy of a fluid equals the net heat supplied minus the net work done. It then discusses polytropic processes, defining them by the equation pV^n = constant, and providing examples of indices for different types of compression processes. The document provides equations to calculate work, temperature, and pressure changes for a polytropic process on a perfect gas. It includes an example problem calculating these values.
relative acceleration diagram for a linkDr.R. SELVAM
The document describes how to determine the acceleration of a point on a rigid link. It explains that the acceleration has two components - a radial component perpendicular to the velocity and a tangential component parallel to the velocity. It provides steps to draw an acceleration diagram: 1) Draw a vector for the acceleration of point A, 2) Draw a vector parallel to the link AB for the radial component, 3) Draw a vector for the tangential component perpendicular to the radial component, and 4) Join the vectors to determine the total acceleration of point B with respect to point A.
The study aimed to determine the performance of centrifugal pumps operating individually, in series, and in parallel. Experiments were conducted to collect head-flow data for a single pump, two pumps in series, and two pumps in parallel. The data was used to calculate output power, input power, and efficiency. Operating pumps in series increased the total head able to be achieved compared to a single pump, while operating in parallel increased the total flow rate. Combining multiple pumps improves overall pumping efficiency and performance.
The document discusses fluid dynamics and Bernoulli's equation. It provides:
1) Objectives of understanding measurements of fluids in motion and applying Bernoulli's equation to calculate energy in pipes, venturi meters, and orifices.
2) An explanation of Bernoulli's equation and its components of potential, pressure, and kinetic energy.
3) Examples of applying the equation to calculate discharge in a horizontal venturi meter using measurements of pressure and height differences.
The document discusses fluid pressure and its relationship to depth. It introduces Pascal's law and how it applies to hydraulic systems. Specifically:
1) Pressure increases with depth in fluids due to the weight of the fluid above pushing down. Pascal's law states that pressure increases are equal throughout a confined fluid.
2) Hydraulic systems use this principle to multiply forces. A small force applied to a piston with a small surface area can create a much larger force when transmitted through fluid to a piston with a larger surface area.
3) An example is given of a hydraulic car lift, where 1 kg applied to a small piston creates enough pressure to lift 10 kg with a larger piston, multiplying the applied
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.
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
This document provides solutions to problems from Chapter 4 of the textbook "Fluid Mechanics: Fundamentals and Applications" by Çengel & Cimbala. The chapter covers fluid kinematics. The solutions solve problems related to defining kinematics and fluid kinematics, calculating centerline speed through a nozzle, finding stagnation points in velocity fields, comparing Lagrangian and Eulerian descriptions of fluid motion, calculating material acceleration and the rate of change of pressure following a fluid particle.
This document provides an overview of the content that will be covered in a gas turbines course. The course objectives are to explain the function, types, thermodynamic principles, design considerations, protection/control, operation, and common problems of gas turbine systems. The content includes introductions to fluid mechanics/thermodynamics principles, the different types and components of gas turbines, auxiliary systems, and operation/maintenance. Key concepts like viscosity, density, specific heat, internal energy, enthalpy, and Bernoulli's theorem are defined.
This document discusses fluid flow and provides information on several topics:
1) It describes laminar and turbulent flow, and introduces the Reynolds number which determines the transition between these two flow regimes.
2) It discusses mass balances and the continuity equation which states that the rate of mass input equals the rate of mass output in steady state flow.
3) It derives the overall energy balance equation based on the first law of thermodynamics and describes how to apply this to steady state flow systems.
4) It introduces the mechanical energy balance equation which is useful for analyzing flowing liquids and accounts for kinetic energy, potential energy, and frictional losses.
Fluid Mechanics Chapter 5. Dimensional Analysis and SimilitudeAddisu Dagne Zegeye
Introduction, Dimensional homogeneity, Buckingham pi theorem, Non dimensionalization of basic equations, Similitude, Significance of non-dimensional numbers in fluid flows
- The document discusses one-dimensional finite element analysis.
- It describes the derivation of shape functions for linear one-dimensional elements like a bar element. Shape functions define the variation of displacement within the element.
- The stiffness matrix, which represents the element's resistance to deformation, is also derived for a basic linear bar element. It is shown to be symmetric and its properties are discussed.
- Examples are provided to demonstrate calculating displacements at points within a one-dimensional element using the shape functions.
This document discusses the characteristic curves of turbines, which are used to study a turbine's performance under various conditions. There are three main types of characteristic curves: 1) Constant head curves, which show performance at constant head by varying speed and flow, 2) Constant speed curves, which show performance at constant speed by varying head and flow, and 3) Constant efficiency curves, which determine the zone of maximum efficiency for the turbine. The characteristic curves are provided by turbine manufacturers based on actual test data and include curves showing unit discharge, unit power, efficiency, and other parameters.
Fluid Mechanics Chapter 2 Part II. Fluids in rigid-body motionAddisu Dagne Zegeye
1. The document discusses rigid-body motion of fluids, where fluid particles move together with no internal motion or deformation. It presents equations of motion relating pressure, acceleration, and gravity for fluids undergoing rigid-body translation or rotation.
2. Special cases are considered, including fluids at rest, where pressure only varies with height, and fluids in free fall or accelerated upward, where pressure gradients are altered by acceleration.
3. For fluids accelerating linearly, equations are derived showing pressure varies with both vertical position and horizontal displacement from the acceleration axis, forming parallel inclined surfaces of constant pressure.
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
1. The document discusses the continuity equation, which states that the flow rate of an incompressible fluid is constant at any point in a fluid system with no accumulation.
2. The formula for continuity equation is given as: ρ1A1v1 = ρ2A2v2, where ρ is density, A is cross-sectional area, and v is velocity.
3. Examples of applications include calculating water velocity changes in pipes or rivers of varying diameters, and a sample problem is worked out calculating velocities at different pipe positions.
This document contains lecture notes on fluid mechanics. It begins with an introduction to fluid mechanics, including definitions of key terms like fluid, continuum, density, and viscosity. It then covers topics in fluid statics like pressure, hydrostatic force, and buoyancy. Later sections discuss the description and analysis of fluid motion using concepts like the control volume, streamlines, and conservation equations. The document aims to explain the physics of fluid motion to undergraduate students through examples and without advanced mathematics.
This experiment aimed to determine the Reynolds number (NRe) as a function of flow rate for liquid flowing through a circular pipe. NRe was calculated for 6 trials with increasing flow rates. All trials had NRe below 2100, indicating laminar flow as observed by the smooth movement of dye in the pipe. As flow rate increased, NRe also increased but remained in the laminar flow regime. The results show that flow type depends on NRe, with laminar flow occurring at low velocities (NRe < 2100).
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.
Strength of Materials, Lecture - 1.
Introduction + Recommended Books
Mehran University of Engineering and Technology.
Department of Mechanical Engineering.
Fluid tutorial 2_ans dr.waleed. 01004444149 dr walid
This document contains 11 multi-step physics problems involving fluid mechanics concepts like pressure, viscosity, density, and fluid flow. The problems are solved with relevant equations for ideal gases, compressible fluids, laminar flow, and viscometry. Detailed calculations are shown to determine values like mass, pressure, shear stress, drag force, velocity, and viscosity based on given variables like temperature, volume, pressure, velocity, dimensions, torque, and fluid properties.
The document defines and provides examples of non-flow processes in thermodynamics, specifically polytropic processes. It states that in a non-flow process, the change in internal energy of a fluid equals the net heat supplied minus the net work done. It then discusses polytropic processes, defining them by the equation pV^n = constant, and providing examples of indices for different types of compression processes. The document provides equations to calculate work, temperature, and pressure changes for a polytropic process on a perfect gas. It includes an example problem calculating these values.
relative acceleration diagram for a linkDr.R. SELVAM
The document describes how to determine the acceleration of a point on a rigid link. It explains that the acceleration has two components - a radial component perpendicular to the velocity and a tangential component parallel to the velocity. It provides steps to draw an acceleration diagram: 1) Draw a vector for the acceleration of point A, 2) Draw a vector parallel to the link AB for the radial component, 3) Draw a vector for the tangential component perpendicular to the radial component, and 4) Join the vectors to determine the total acceleration of point B with respect to point A.
The study aimed to determine the performance of centrifugal pumps operating individually, in series, and in parallel. Experiments were conducted to collect head-flow data for a single pump, two pumps in series, and two pumps in parallel. The data was used to calculate output power, input power, and efficiency. Operating pumps in series increased the total head able to be achieved compared to a single pump, while operating in parallel increased the total flow rate. Combining multiple pumps improves overall pumping efficiency and performance.
The document discusses fluid dynamics and Bernoulli's equation. It provides:
1) Objectives of understanding measurements of fluids in motion and applying Bernoulli's equation to calculate energy in pipes, venturi meters, and orifices.
2) An explanation of Bernoulli's equation and its components of potential, pressure, and kinetic energy.
3) Examples of applying the equation to calculate discharge in a horizontal venturi meter using measurements of pressure and height differences.
The document discusses fluid pressure and its relationship to depth. It introduces Pascal's law and how it applies to hydraulic systems. Specifically:
1) Pressure increases with depth in fluids due to the weight of the fluid above pushing down. Pascal's law states that pressure increases are equal throughout a confined fluid.
2) Hydraulic systems use this principle to multiply forces. A small force applied to a piston with a small surface area can create a much larger force when transmitted through fluid to a piston with a larger surface area.
3) An example is given of a hydraulic car lift, where 1 kg applied to a small piston creates enough pressure to lift 10 kg with a larger piston, multiplying the applied
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.
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
This document provides solutions to problems from Chapter 4 of the textbook "Fluid Mechanics: Fundamentals and Applications" by Çengel & Cimbala. The chapter covers fluid kinematics. The solutions solve problems related to defining kinematics and fluid kinematics, calculating centerline speed through a nozzle, finding stagnation points in velocity fields, comparing Lagrangian and Eulerian descriptions of fluid motion, calculating material acceleration and the rate of change of pressure following a fluid particle.
This document provides an overview of the content that will be covered in a gas turbines course. The course objectives are to explain the function, types, thermodynamic principles, design considerations, protection/control, operation, and common problems of gas turbine systems. The content includes introductions to fluid mechanics/thermodynamics principles, the different types and components of gas turbines, auxiliary systems, and operation/maintenance. Key concepts like viscosity, density, specific heat, internal energy, enthalpy, and Bernoulli's theorem are defined.
This document discusses fluid flow and provides information on several topics:
1) It describes laminar and turbulent flow, and introduces the Reynolds number which determines the transition between these two flow regimes.
2) It discusses mass balances and the continuity equation which states that the rate of mass input equals the rate of mass output in steady state flow.
3) It derives the overall energy balance equation based on the first law of thermodynamics and describes how to apply this to steady state flow systems.
4) It introduces the mechanical energy balance equation which is useful for analyzing flowing liquids and accounts for kinetic energy, potential energy, and frictional losses.
The document discusses the fundamental principles of fluid mechanics - conservation of mass, energy, and momentum - and how they are applied to derive equations for open channel flow. It specifically covers the continuity, energy, and momentum equations. The energy equation relates changes in energy within a control volume, while the momentum equation relates the overall forces on the control volume boundaries. The document also discusses topics like specific energy, critical flow, hydraulic jumps, and how these concepts are used to analyze channel transitions and design channel flows.
This document discusses the key differences between equilibrium and rate in mass transfer operations. It explains that equilibrium sets the maximum amount that can be transferred, while rate depends on driving force, area, and resistance. Various mass transfer processes are modeled depending on if they reach equilibrium (distillation) or involve diffusion (membranes). Rate equations and ways to increase rate are presented. Phase diagrams for single and multiple component systems are also covered, including lines, points, and how to read information from them. Gibbs phase rule and its application to distillation with two components and phases is explained.
1) This document discusses heat, work, and the first law of thermodynamics. It defines heat and work as the two ways energy can transfer across the boundary of a closed system, with heat transferring due to a temperature difference and work occurring from a force acting through a distance.
2) The first law of thermodynamics states that the change in a system's internal energy is equal to the net heat transferred to the system plus the net work done by the system. This is illustrated with examples of processes involving only heat transfer, where the energy change equals the net heat.
3) Different types of thermodynamic processes are examined, including isobaric, isochoric, isothermal, and poly
The document discusses three equations commonly used in fluid mechanics - the mass, Bernoulli, and energy equations. It provides an overview of the conservation of mass principle and defines relevant terms like mass flow rate. It then discusses various forms of mechanical energy and energy conversion efficiencies. Finally, it outlines how the Bernoulli equation is derived from Newton's second law and how the energy equation is developed and applied to fluid mechanics problems.
1) The document discusses heat, work, and the first law of thermodynamics. It defines heat and work as the two types of energy transfer across boundaries of closed systems.
2) The first law of thermodynamics, also called the law of conservation of energy, states that the total energy of a system remains constant, with increases in internal energy equal to net heat and work transfers.
3) Specific examples are provided to illustrate the first law for closed systems undergoing various processes like heating, cooling, and adiabatic changes with and without work. Formulas are derived for calculating internal energy changes based on the first law.
lab 4 requermenrt.pdf
MECH202 – Fluid Mechanics – 2015 Lab 4
Fluid Friction Loss
Introduction
In this experiment you will investigate the relationship between head loss due to fluid friction and
velocity for flow of water through both smooth and rough pipes. To do this you will:
1) Express the mathematical relationship between head loss and flow velocity
2) Compare measured and calculated head losses
3) Estimate unknown pipe roughness
Background
When a fluid is flowing through a pipe, it experiences some resistance due to shear stresses, which
converts some of its energy into unwanted heat. Energy loss through friction is referred to as “head
loss due to friction” and is a function of the; pipe length, pipe diameter, mean flow velocity,
properties of the fluid and roughness of the pipe (the later only being a factor for turbulent flows),
but is independent of pressure under with which the water flows. Mathematically, for a turbulent
flow, this can be expressed as:
hL=f
L
D
V
2
2 g
(Eq.1)
where
hL = Head loss due to friction (m)
f = Friction factor
L = Length of pipe (m)
V = Average flow velocity (m/s)
g = Gravitational acceleration (m/s^2)
Friction head losses in straight pipes of different sizes can be investigated over a wide range of
Reynolds' numbers to cover the laminar, transitional, and turbulent flow regimes in smooth pipes. A
further test pipe is artificially roughened and, at the higher Reynolds' numbers, shows a clear
departure from typical smooth bore pipe characteristics.
Experiment 4: Fluid Friction Loss
The head loss and flow velocity can also be expressed as:
1) hL∝V −whe n flow islaminar
2) hL∝V
n
−whe n flow isturbulent
where hL is the head loss due to friction and V is the fluid velocity. These two types of flow are
seperated by a trasition phase where no definite relationship between hL and V exist. Graphs
of hL −V and log (hL) − log (V ) are shown in Figure 1,
Figure 1. Relationship between hL ( expressed by h) and V ( expressed by u ) ;
as well as log (hL) and log ( V )
Experiment 4: Fluid Friction Loss
Experimental Apparatus
In Figure 2, the fluid friction apparatus is shown on the right while the Hydraulic bench that
supplies the water to the fluid friction apparatus is shown on the left. The flow rate that the
hydraulic bench provides can be measured by measuring the time required to collect a known
volume.
Figure 2. Experimental Apparatus
Experimental Procedure
1) Prime the pipe network with water by running the system until no air appears to be discharging
from the fluid friction apparatus.
2) Open and close the appropriate valves to obtain water flow through the required test pipe, the four
lowest pipes of the fluid friction apparatus will be used for this experiment. From the bottom to the
top, these are; the rough pipe with large diameter and then smooth pipes with three successively
smaller diameters.
3) Measure head loss ...
1) This document discusses isentropic flow, including governing equations, stagnation relations, effects of area variation, nozzles, diffusers, and the effect of back pressure.
2) Key concepts covered are stagnation temperature, pressure and properties, how Mach number relates stagnation and static quantities, and how pressure and area change with Mach number in converging and diverging ducts.
3) Examples provided include calculating stagnation properties from flow conditions and sketching the steady flow adiabatic ellipse.
This document discusses Bernoulli's equation and its significance. It provides background on Bernoulli's principle, derives the general Bernoulli's equation, and discusses its different forms. Several applications of Bernoulli's equation are described, including in pumps, ejectors, carburetors, siphons, and pilot tubes. Limitations due to fluid viscosity are also noted. In conclusion, the equation is valid for fluid flow as it obeys the conservation of energy principle.
The document describes an experiment measuring fluid flow rate. Students measured the volume and time it took for water to pass through a volumetric tank. They then calculated the flow rate, mass flow rate, and weight flow rate. The results showed the relationship between flow rate and time, as well as the slopes between flow rate and mass/weight flow rate. Factors that impact flow rate like viscosity, temperature, and pipe characteristics were also discussed.
This document describes procedures for measuring fluid viscosity. Key points:
- The experiment aims to calibrate a capillary tube system and measure viscosities of Newtonian and non-Newtonian fluids like water and peach juice.
- Equipment includes a capillary tube, sensors, timers and containers to pass fluids through the tube and measure flow properties.
- Calculations are provided to determine viscosity based on measurements of fluid flow rate and pressure using equations that apply to laminar flow.
- Viscosity is an intrinsic property but can vary for non-Newtonian fluids based on applied shear stress.
This document provides information on various topics related to chemical reaction engineering:
- It discusses types of reactors, how materials behave within reactors, and how to process and interpret data from chemical reactors.
- It explains the concepts of reversible and irreversible reactions, and the three ways a species may lose its chemical identity: decomposition, combination, and isomerization.
- Rate of reaction is discussed, including how it can be expressed as the rate of disappearance of reactants or formation of products.
- Other topics covered include mass/energy balances, Laplace transforms, psychrometric charts, pump curves, and pipe friction tables.
This document discusses methods for solving fluid flow problems. It outlines two essential equations: [1] the equation of continuity, which states that the inflow equals the outflow in steady flow through a control volume, and [2] the Bernoulli equation, which relates pressure, velocity, and elevation along a streamline based on the principle of conservation of energy. Common applications where these equations are used include pipes, rivers, and overall processes. The procedure for solving flow problems involves choosing a datum plane, noting where velocity, pressure, and other variables are known or to be assumed, and applying the continuity and Bernoulli equations.
This study examines the behavior of buried pipelines subjected to external pressure from surrounding soil and internal pressure from carried gas. A 3D finite element model of the pipeline was created in ABAQUS. The pipeline was analyzed under external pressure only and under both external and internal pressures. Two parameters were used to determine onset of buckling: total energy and axial strain. For external pressure only, buckling began around 0.32 seconds as seen in fluctuating total energy and decreasing axial strain plots. For both pressures, buckling began around 0.44 seconds. The internal pressure delayed buckling compared to external pressure alone.
On Absorption Practice, Methods and Theory: An Empirical Example JosephLehmann4
- The document summarizes an experiment on absorption processes using a countercurrent gas-liquid absorption tower.
- Key findings include developing relationships between liquid flow rate, vapor flow rate, and pressure drop. Generalized correlations were constructed from these relationships.
- Absorption of CO2 from air into water was also studied. Data showed decreasing CO2 removal over time as the water became saturated.
International Journal of Engineering Research and DevelopmentIJERD Editor
Electrical, Electronics and Computer Engineering,
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Numerical Calculation of Solid-Liquid two-Phase Flow Inside a Small Sewage Pumptheijes
Based on a mixture multiphase flow model,theRNG k–εturbulencemodelandfrozen rotor method were used to perform a numerical simulation of steady flow in the internal flow field of a sewage pump that transports solid and liquid phase flows. Resultsof the study indicate that the degree of wear on the front and the back of the blade suction surface from different densities of solid particles shows a completely opposite influencing trend. With the increase of delivered solid-phase density, the isobaric equilibrium position moves to the leading edge point of the blade, but the solid-phase isoconcentration point on the blade pressure surface and suction surface basically remains unchanged. The difference between hydraulic lift and water lift indelivering solid- and liquid-phase flows shows a rising trend with the increase of working flow
This chapter discusses four key equations in fluid mechanics - the mass, Bernoulli, momentum, and energy equations. The mass equation expresses conservation of mass, while the Bernoulli equation concerns conservation of kinetic, potential, and flow energies in regions of negligible viscous forces. The energy equation expresses conservation of energy. Examples are provided to demonstrate how to apply the Bernoulli equation to problems involving water spraying and water discharge from a tank.
Strategies for Effective Upskilling is a presentation by Chinwendu Peace in a Your Skill Boost Masterclass organisation by the Excellence Foundation for South Sudan on 08th and 09th June 2024 from 1 PM to 3 PM on each day.
Executive Directors Chat Leveraging AI for Diversity, Equity, and InclusionTechSoup
Let’s explore the intersection of technology and equity in the final session of our DEI series. Discover how AI tools, like ChatGPT, can be used to support and enhance your nonprofit's DEI initiatives. Participants will gain insights into practical AI applications and get tips for leveraging technology to advance their DEI goals.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
How to Manage Your Lost Opportunities in Odoo 17 CRMCeline George
Odoo 17 CRM allows us to track why we lose sales opportunities with "Lost Reasons." This helps analyze our sales process and identify areas for improvement. Here's how to configure lost reasons in Odoo 17 CRM
How to Fix the Import Error in the Odoo 17Celine George
An import error occurs when a program fails to import a module or library, disrupting its execution. In languages like Python, this issue arises when the specified module cannot be found or accessed, hindering the program's functionality. Resolving import errors is crucial for maintaining smooth software operation and uninterrupted development processes.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2. Chapter Objectives
• Define volume flow rate, weight flow rate, and mass flow rate and their
units.
• Define steady flow and the principle of continuity.
• Write the continuity equation, and use it to relate the volume flow rate, area,
and velocity of flow between two points in a fluid flow system.
• Describe five types of commercially available pipe and tubing: steel pipe,
ductile iron pipe, steel tubing, copper tubing, and plastic pipe and tubing.
• Specify the desired size of pipe or tubing for carrying a given flow rate of
fluid at a specified velocity.
3. Fluid Flow Rate and the
Continuity Equation
Types of flowrate equation
4. • The quantity of fluid flowing in a system per unit time can be expressed
by the following three different terms:
• Q The volume flow rate is the volume of fluid flowing past a section per
unit time.
• W The weight flow rate is the weight of fluid flowing past a section per
unit time.
• M The mass flow rate is the mass of fluid flowing past a section per
unit time.
5. • The weight flow rate W is related to Q by
• where γ is the specific weight of the fluid. The units of W are then
• The mass flow rate M is related to Q by
6. • The units of M are then
• Table 6.1 shows the flow rates.
• Useful conversions are
7. • The most fundamental of these three terms is the volume flow rate Q,
which is calculated from
• where A is the area of the section and ν is the average velocity of
flow. The units of Q can be derived as follows, using SI units for
illustration:
10. Example 3.2
• Given a flow rate of water is 6000 L/min, find its weight flow rate and
convert it to kN/h.
11. • The method of calculating the velocity
of flow of a fluid in a closed pipe
system depends on the principle of
continuity.
• Fig 3.1 shows the portion of a fluid
distribution system showing variations in
velocity, pressure, and elevation.
• This can be expressed in terms of the
mass flow rate as
• As M=ρAv, we have
• Equation (6.1) is a mathematical
statement of the principle of continuity
and is called the continuity equation.
• It is used to relate the fluid density, flow
area, and velocity of flow at two
sections of the system in which there is
steady flow.
• It is valid for all fluids, whether gas or
liquid.
(3.1)
12. Fig 3.1 The portion of a fluid distribution system
13. • If the fluid in the pipe in Fig. 3.1 is a liquid that can be considered
incompressible, then the terms ρ1 and ρ2 is the same.
• Since Q = Av,
• Equation (6.2) is the continuity equation as applied to liquids only; it
states that for steady flow the volume flow rate is the same at any
section.
(3.2)
14. Example 3.3
In Fig. 3.1 the inside diameters of the pipe at sections 1 and 2 are 50 mm
and 100 mm, respectively. Water at is flowing with an average velocity
of 8 m/s at section 1. Calculate the following:
(a) Velocity at section 2
(b) Volume flow rate
(c) Weight flow rate
(d) Mass flow rate
16. Then the velocity at section 2 is
Notice that for steady flow of a liquid, as the flow area
increases, the velocity decreases.
This is independent of pressure and elevation.
17. (b) Volume flow rate Q.
From Table 3.1, Q = vA. Because of the principle of
continuity we could use the conditions either at section 1
or at section 2 to calculate Q. At section 1 we have
18. (c) Weight flow rate W.
From Table 3.1, W = γQ. At 70°C, the specific weight of
water is 9.59kN/m3. Then the weight flow rate is
19. (d) Mass flow rate M.
From Table 3.1, M = ρQ. At the density of water is
978 kg/m3. Then the mass flow rate is
20. Example 3.4
At one section in an air distribution system, air at 101.35 kPa and 310.9
K has an average velocity of 6.096 m/s and the duct is 7.5 x10-3 m2. At
another section, the duct is round with a diameter of 0.457 m, and the
velocity is measured to be 4.57 m/s. calculate:
a. The density of the air in the round section
b. The weight flowrate of air in . At 101.35 kPa and 310.9 kPa, the
density of air is 1.134 kg/m3 and the specific weight is 11.14 N/m3.
22. • In physics you learned that energy can be neither created nor
destroyed, but it can be transformed from one form into another.
• This is a statement of the law of conservation of energy.
• Fig 3.2 shows the element of a fluid in a pipe.
23. • There are three forms of energy that are always
considered when analyzing a pipe flow problem.
1. Potential Energy. Due to its elevation, the potential energy
of the element relative to some reference level is
where w is the weight of the element.
(3.3)
24. 2. Kinetic Energy. Due to its velocity, the kinetic energy of the
element is
3. Flow Energy. Sometimes called pressure energy or flow
work, this represents the amount of work necessary to
move the element of fluid across a certain section against
the pressure p. Flow energy is abbreviated FE and is
calculated from
(3.5)
(3.4)
25. • Equation (3.5) can be derived as follows.
• The work done is
where V is the volume of the element. The weight of the
element w is
where γ is the specific weight of the fluid. Then, the volume
of the element is
26. • And we have Eq. (3.5)
• Fig 3.3 shows the flow energy.
27. • The total amount of energy of these three forms
possessed by the element of fluid is the sum E,
• Each of these terms is expressed in units of energy,
which are Newton-meters (Nm) in the SI unit system
and foot-pounds (ft-lb) in the U.S. Customary
System.
28. • Fig 3.3 shows the fluid elements used in Bernoulli’s
equation.
29. • At section 1 and 2, the total energy is
• If no energy is added to the fluid or lost between sections 1
and 2, then the principle of conservation of energy requires
that
30. • The weight of the element w is common to all terms
and can be divided out.
• The equation then becomes
• This is referred to as Bernoulli’s equation.
3.6
32. • Each term in Bernoulli’s equation, Eq. (3.6), resulted
from dividing an expression for energy by the weight
of an element of the fluid.
• Each term in Bernoulli’s equation is one form of
the energy possessed by the fluid per unit
weight of fluid flowing in the system.
• The units for each term are “energy per unit weight.”
In the SI system the units are Nm/N and in the U.S.
Customary System the units are lb.ft/lb.
33. • Specifically,
• Fig 3.4 shows the pressure head, elevation head,
velocity head, and total head.
34.
35. • In Fig. 3.4 you can see that the velocity head at
section 2 will be less than that at section 1. This can
be shown by the continuity equation,
• In summary,
• Bernoulli’s equation accounts for the changes in
elevation head, pressure head, and velocity
head between two points in a fluid flow system.
It is assumed that there are no energy losses or
additions between the two points, so the total
head remains constant.
37. • Although Bernoulli’s equation is applicable to a large
number of practical problems, there are several limitations
that must be understood to apply it properly.
1. It is valid only for incompressible fluids because the
specific weight of the fluid is assumed to be the same at the
two sections of interest.
2. There can be no mechanical devices between the two
sections of interest that would add energy to or remove
energy from the system, because the equation states that
the total energy in the fluid is constant.
38. 3. There can be no heat transferred into or out of the
fluid.
4. There can be no energy lost due to friction.
• In reality no system satisfies all these restrictions.
• However, there are many systems for which only a
negligible error will result when Bernoulli’s equation
is used.
• Also, the use of this equation may allow a fast
estimate of a result when that is all that is required.
40. • Below is the procedure for applying bernoulli’s equation:
1. Decide which items are known and what is to be found.
2. Decide which two sections in the system will be used when writing
Bernoulli’s equation. One section is chosen for which much data is
known. The second is usually the section at which something is to
be calculated.
3. Write Bernoulli’s equation for the two selected sections in the
system. It is important that the equation is written in the
direction of flow. That is, the flow must proceed from the section
on the left side of the equation to that on the right side.
4. Be explicit when labeling the subscripts for the pressure head,
elevation head, and velocity head terms in Bernoulli’s equation.
You should note where the reference points are on a sketch of
the system.
41. 5. Simplify the equation, if possible, by canceling terms that
are zero or those that are equal on both sides of the
equation.
6. Solve the equation algebraically for the desired term.
7. Substitute known quantities and calculate the result, being
careful to use consistent units throughout the calculation.
42. In Fig. 3.4, water at 10°C is flowing from section 1 to section
2. At section 1, which is 25 mm in diameter, the gage
pressure is 345 kPa and the velocity of flow is 3.0 m/s.
Section 2, which is 50 mm in diameter, is 2.0 m above section
1. Assuming there are no energy losses in the system,
calculate the pressure p2.
List the items that are known from the problem statement
before looking at the next panel.
Example 3.5
43.
44. The pressure p2 is to be found. In other words, we are asked
to calculate the pressure at section 2, which is different from
the pressure at section 1 because there is a change in
elevation and flow area between the two sections.
We are going to use Bernoulli’s equation to solve the
problem. Which two sections should be used when writing
the equation?
45. Now write Bernoulli’s equation.
The three terms on the left refer to section 1 and the
three on the right refer to section 2.
46. The final solution for p2 should be
The continuity equation is used to find v2:
This is found from
(3.7)
47. Now substitute the known values into Eq. (3.7).
The details of the solution are
48. The pressure p2 is a gage pressure because it was
computed relative to p1, which was also a gage pressure.
In later problem solutions, we will assume the pressures
to be gage unless otherwise stated.
49. Tanks, Reservoirs and Nozzles Exposed to the Atmosphere
• When the fluid at a reference point is exposed to the
atmosphere, the pressure is zero and the pressure head
term can be cancelled from Bernoulli’s equation.
• Fig 3.5 shows the siphon.
50. • The tank from which the fluid is being drawn can be assumed to
be quite large compared to the size of the flow area inside the
pipe.
• The velocity head at the surface of a tank or reservoir is
considered to be zero and it can be cancelled from Bernoulli’s
equation.
• When the two points of reference for Bernoulli’s equation are
both inside a pipe of the same size, the velocity head terms on
both sides of the equation are equal and can be cancelled.
• When the two points of reference for Bernoulli’s equation are
both at the same elevation, the elevation head terms z1 and z2
are equal and can be cancelled.
51. Example 3.6
• For the siphon in Figure 3.6, the
distance X = 5 m and Y = 1 m.
calculate:
a. the volume flowrate of water
through the nozzle.
b. the pressure at point A.