The document provides information on applying Bernoulli's equation and the conservation of mass and energy principles to solve fluid mechanics problems involving pipe flow. It discusses key concepts like:
- Bernoulli's equation relating pressure, velocity, and height.
- How to derive and apply the continuity equation to relate flow rate, velocity, and pipe cross-sectional area.
- The conservation of energy principle and different forms of energy (pressure, potential, kinetic).
- How to set up and solve example problems involving pipe flow and components like nozzles, valves, and changes in pipe diameter or elevation using Bernoulli's equation and accounting for friction losses.
The document discusses different types of flow measurement techniques. It covers topics like the Pitot tube, which measures static and stagnation pressure to determine flow velocity. It also discusses common obstruction flowmeters like the orifice meter, Venturi meter, and nozzle meter that use a constriction to measure flow rate based on pressure differences. Examples are provided to demonstrate calculations of flow rate and pressure drop using equations that depend on parameters like diameter ratio, discharge coefficient, and fluid properties.
This document discusses fluid mechanics concepts including Newton's second law applied to fluid flows and the Bernoulli equation. It provides examples of using the Bernoulli equation to solve problems involving fluid flow, pressure, velocity, and height. The examples calculate pressure differences, flow rates, and maximum jet heights. The document also briefly introduces flowrate measurement using a Pitot tube.
Fluid MechanicsVortex flow and impulse momentumMohsin Siddique
1. The momentum equation relates the total force on a fluid system to the rate of change of momentum as fluid flows through a control volume.
2. Forces can be resolved into components in different directions for multi-dimensional flows. The total force is equal to the sum of pressure, body, and reaction forces.
3. Examples of applying the momentum equation include calculating forces on a pipe bend, nozzle, jet impact, and curved vane due to changing fluid momentum. Setting up coordinate systems aligned with the flow is important for resolving forces into components.
1) The document discusses methods for calculating the friction factor f in turbulent pipe flow.
2) It provides equations from Swamee-Jain, Haaland, and Churchill that can be used to explicitly calculate f based on parameters like Reynolds number, relative roughness, and pipe diameter.
3) The example problem calculates f for water flowing in a ductile iron pipe, finding f=0.038 using Moody's diagram and the relative roughness of the pipe material.
This document discusses fluid dynamics and flow through pipes. It defines types of flow such as steady, uniform, laminar and turbulent. It also defines concepts like discharge, mass flow rate, and the continuity equation. Examples are provided to demonstrate how to use the continuity equation to calculate velocities and flow rates at different points in pipes with changes in diameter or branches.
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
The document discusses different types of flow measurement techniques. It covers topics like the Pitot tube, which measures static and stagnation pressure to determine flow velocity. It also discusses common obstruction flowmeters like the orifice meter, Venturi meter, and nozzle meter that use a constriction to measure flow rate based on pressure differences. Examples are provided to demonstrate calculations of flow rate and pressure drop using equations that depend on parameters like diameter ratio, discharge coefficient, and fluid properties.
This document discusses fluid mechanics concepts including Newton's second law applied to fluid flows and the Bernoulli equation. It provides examples of using the Bernoulli equation to solve problems involving fluid flow, pressure, velocity, and height. The examples calculate pressure differences, flow rates, and maximum jet heights. The document also briefly introduces flowrate measurement using a Pitot tube.
Fluid MechanicsVortex flow and impulse momentumMohsin Siddique
1. The momentum equation relates the total force on a fluid system to the rate of change of momentum as fluid flows through a control volume.
2. Forces can be resolved into components in different directions for multi-dimensional flows. The total force is equal to the sum of pressure, body, and reaction forces.
3. Examples of applying the momentum equation include calculating forces on a pipe bend, nozzle, jet impact, and curved vane due to changing fluid momentum. Setting up coordinate systems aligned with the flow is important for resolving forces into components.
1) The document discusses methods for calculating the friction factor f in turbulent pipe flow.
2) It provides equations from Swamee-Jain, Haaland, and Churchill that can be used to explicitly calculate f based on parameters like Reynolds number, relative roughness, and pipe diameter.
3) The example problem calculates f for water flowing in a ductile iron pipe, finding f=0.038 using Moody's diagram and the relative roughness of the pipe material.
This document discusses fluid dynamics and flow through pipes. It defines types of flow such as steady, uniform, laminar and turbulent. It also defines concepts like discharge, mass flow rate, and the continuity equation. Examples are provided to demonstrate how to use the continuity equation to calculate velocities and flow rates at different points in pipes with changes in diameter or branches.
Head losses
Major Losses
Minor Losses
Definition • Dimensional Analysis • Types • Darcy Weisbech Equation • Major Losses • Minor Losses • Causes Head Losses
3. • Head loss is loss of energy per unit weight. • Head = Energy of Fluid / Weight • Head losses can be – Kinetic Head – Potential Head – Pressure Head 6/10/2015 4Danial Gondal Head Loss
4. • Kinetic Head – K.H. = kinetic energy / Weight = v² /2g • Potential Head – P.H = Potential Energy / Weight = mgz /mg = z • Pressure Head – P.H = P/ ρ g 6/10/2015 5
5. • (P/ ρ g) + (v² /2g ) + (z) = constant • (FL-2F-1L3LT-2L-1T2) + (L2T-2L1T2)+(L) = constant • (L) + (L) + (L) = constant • As L represent height so it is dimensionally L. 6/10/2015 6 Dimensional Analysis
6. • However the equation (P/ ρ g) + (v² /2g ) + (z) = constant Is valid for Bernoulli's Inviscid flow case. As we are studying viscous flow so (P1/ ρ g) + (v1² /2g ) + (z1) = EGL1(Energy Grade Line At point 1) (P2/ ρ g) + (v2² /2g ) + (z2) = EGL2(Energy Grade Line At point 2) 6/10/2015 7 Head Loss
7. • For Inviscid Flow EGL1 - EGL2= 0 • For Viscous Flow EGL1 - EGL2= Hf 6/10/2015 8 Head Loss
8. MAJOR LOSSES IN PIPES
9. •Friction loss is the loss of energy or “head” that occurs in pipe flow due to viscous effects generated by the surface of the pipe. • Friction Loss is considered as a "major loss" •In mechanical systems such as internal combustion engines, it refers to the power lost overcoming the friction between two moving surfaces. •This energy drop is dependent on the wall shear stress (τ) between the fluid and pipe surface. 6/10/2015 10 Friction Loss
10. •The shear stress of a flow is also dependent on whether the flow is turbulent or laminar. •For turbulent flow, the pressure drop is dependent on the roughness of the surface. •In laminar flow, the roughness effects of the wall are negligible because, in turbulent flow, a thin viscous layer is formed near the pipe surface that causes a loss in energy, while in laminar flow, this viscous layer is non-existent. 6/10/2015 11 Friction Loss
11. Frictional head losses are losses due to shear stress on the pipe walls. The general equation for head loss due to friction is the Darcy-Weisbach equation, which is where f = Darcy-Weisbach friction factor, L = length of pipe, D = pipe diameter, and V = cross sectional average flow velocity.
PLEASE NOTE THIS IS PART-1
By Referring or said Learning This Presentation You Can Clear Your Basics Fundamental Doubts about Fluid Mechanics. In this Presentation You Will Learn about Fluid Pressure, Pressure at Point, Pascal's Law, Types Of Pressure and Pressure Measurements.
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
Fluid MechanicsLosses in pipes dynamics of viscous flowsMohsin Siddique
This document discusses fluid flow in pipes. It defines the Reynolds number and explains laminar and turbulent flow regimes. It also covers the Darcy-Weisbach equation for calculating head losses due to pipe friction. The friction factor is determined using Moody diagrams based on Reynolds number and relative pipe roughness. Examples are provided to calculate friction factor, head loss, and flow rate for different pipe flow conditions.
This lab report describes an experiment to determine the viscosity of ethanol using an Ostwald viscometer. Water and ethanol were measured in the viscometer and their densities were calculated. The time taken for water and ethanol to flow through the viscometer was recorded. Using the measured densities and flow times along with the known viscosity of water, the viscosity of ethanol was calculated to be 1.867 N.s/m2 based on the formula that relates viscosity to density and flow time.
This document summarizes the key properties and classifications of fluids studied in fluid mechanics. It defines a fluid, and distinguishes fluids from solids based on their ability to deform under stress. The document outlines the main branches of fluid mechanics - hydrostatics, kinematics, and dynamics. It then describes important fluid properties like density, specific weight, specific gravity, viscosity, and surface tension. Finally, it classifies fluids as ideal, real, Newtonian, non-Newtonian, and ideal plastic fluids, and discusses the concepts of capillary action and surface tension.
Pipe Flow Friction factor in fluid mechanicsUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process. ,education ,chemical engineerin ,chemical engineering ,fluid mechanics ,heat transfer ,chemical process principles ,macdonald ,kfc ,mazeo ,chemicals ,engineers ,cv formatin ,law ,laptop.
This document describes the working principle and experimental setup for calibrating a venturimeter. A venturimeter consists of an inlet section followed by a converging section, cylindrical throat, and gradually diverging cone. It works by creating a pressure difference between the inlet and throat sections due to an increase in flow velocity at the throat. This pressure difference is measured to determine the flow rate. The experiment involves taking pressure and flow rate measurements at the inlet and throat sections using a manometer and collecting water over time. The data is then used to calculate discharge coefficients and Reynolds numbers to calibrate the venturimeter.
This document summarizes different types of fluid flow, including:
- Steady and unsteady flow
- Laminar and turbulent flow
- Compressible and incompressible flow
- One, two, and three dimensional flows
It defines each type of flow and provides examples to explain the differences between steady and unsteady flow, laminar and turbulent flow, and compressible and incompressible flow.
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 describes an experiment to verify Bernoulli's theorem. Bernoulli's theorem states that for an inviscid, incompressible fluid flowing steadily through a closed passage, the total energy at any point remains constant. The experiment involves measuring the pressure, velocity, and elevation at different points in a diverging duct carrying water. Observations are recorded and used to plot the total energy line, which should be horizontal according to Bernoulli's theorem. The results support the theorem by showing the total energy remains constant despite changes in pressure, velocity, and elevation along the duct.
History of Venturi meter, Introduction, Construction, Working Principle, Types of Venturi meter, Limitations & Precautions
, Characteristics of Venturi-meter, Applications of Venturi-meter
, Advantages & Disadvantages.
Overview:
Clemens Herschel (March 23, 1842 – March 1, 1930) was an American hydraulic engineer. He is best known for developing the Venturi-meter, which was the first large-scale, accurate device for measuring water flow.
A Venturi-meter is a device used for measuring the rate of flow of a fluid flowing through a pipe.
It is used to calculate the velocity of fluids running through a pipeline.
The fluid may be a liquid or a gas.
By reducing the cross-section area of flow passage, a pressure difference is created and the measurement of pressure difference enables the determination of discharge through pipe.
1. This document describes various types of ideal fluid flow, including uniform flow, source/sink flow, vortex flow, and combinations of different flows.
2. Special cases of flow geometry allow the stream function ψ to be related to the distance n along a path between streamlines by ψ = wn. Examples include uniform flow in the x-direction and uniform flow from a line source.
3. Combining different flow types allows modeling of more complex scenarios. A doublet represents a close source-sink pair, and combining it with uniform flow models flow around a cylinder.
The document provides information about a water pump system including a filter, valve, elbows, and pipe. It gives values for flow rate, pressure, pipe diameter and length, loss coefficients, and asks questions about:
1) Determining the filter's loss coefficient
2) Calculating the flow rate if the valve is fully open and the filter's coefficient is given
3) Calculating the percentage change in flow rate between the two scenarios
4) Drawing the total energy line and hydraulic grade line for the system.
This document discusses formulas related to fluid flow in pipes. It lists the names of group members and describes the major losses due to friction and minor losses due to entrance/exit, changes in cross-section, valves, bends, and elbows. It then summarizes Darcy's formula for head loss due to friction and provides the variables in Chezy's formula for velocity of flow in an open channel.
This document discusses fluid flow in pipes under pressure. It presents equations to describe laminar and turbulent flow. For laminar flow, the Hagen-Poiseuille equation gives the relationship between pressure drop and flow rate. For turbulent flow, the velocity profile consists of a thin viscous sublayer near the wall and a fully turbulent center zone. Equations are derived to describe velocity profiles in both the sublayer and center zone based on viscosity and turbulence effects. Pipes are classified as smooth or rough depending on roughness size compared to the sublayer thickness.
This document discusses basic thermodynamics concepts. It begins by defining a perfect gas and stating Boyle's Law and Charles' Law, which describe the relationships between pressure, volume, and temperature in gases. It then defines specific heat capacity at constant volume (Cv) as the amount of heat required to raise the temperature of a gas by 1 degree Celsius while keeping its volume constant. The document provides equations relating heat transfer, temperature change, and internal energy for a constant volume process involving a perfect gas. It explains that for such a process, no work is done since the piston cannot move during constant volume heating or cooling.
Fluid Mechanic Lab - Reynold's Number ExperimentMuhammadSRaniYah
1. The document summarizes an experiment conducted by Muhammad Sulaimon Rasul to determine different types of fluid flow (laminar, transitional, turbulent) using Reynolds apparatus.
2. The experiment measured the volume of water and time taken to fill a graduated cylinder for different flow rates. This was used to calculate Reynolds number to identify flow type.
3. All results showed Reynolds numbers less than 2000, indicating laminar flow for all trials according to the theoretical boundaries between flow types.
This document discusses hydroelectric power generation and the components involved. It begins by outlining the objectives of understanding the vocabulary, workings, configurations, and components of hydroelectric power plants. It then discusses various methods for measuring water flow rates, including basic, refined, and sophisticated methods. The document goes on to explain the principles of hydroelectric power generation using Bernoulli's equation. It describes intake structures, penstocks, turbines, tailraces, and categorizes different types of power plants. Finally, it discusses the components involved in hydroelectric systems and different types of turbines, including impulse and reaction turbines.
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.
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
Fluid MechanicsLosses in pipes dynamics of viscous flowsMohsin Siddique
This document discusses fluid flow in pipes. It defines the Reynolds number and explains laminar and turbulent flow regimes. It also covers the Darcy-Weisbach equation for calculating head losses due to pipe friction. The friction factor is determined using Moody diagrams based on Reynolds number and relative pipe roughness. Examples are provided to calculate friction factor, head loss, and flow rate for different pipe flow conditions.
This lab report describes an experiment to determine the viscosity of ethanol using an Ostwald viscometer. Water and ethanol were measured in the viscometer and their densities were calculated. The time taken for water and ethanol to flow through the viscometer was recorded. Using the measured densities and flow times along with the known viscosity of water, the viscosity of ethanol was calculated to be 1.867 N.s/m2 based on the formula that relates viscosity to density and flow time.
This document summarizes the key properties and classifications of fluids studied in fluid mechanics. It defines a fluid, and distinguishes fluids from solids based on their ability to deform under stress. The document outlines the main branches of fluid mechanics - hydrostatics, kinematics, and dynamics. It then describes important fluid properties like density, specific weight, specific gravity, viscosity, and surface tension. Finally, it classifies fluids as ideal, real, Newtonian, non-Newtonian, and ideal plastic fluids, and discusses the concepts of capillary action and surface tension.
Pipe Flow Friction factor in fluid mechanicsUsman Shah
This slide will explain you the chemical engineering terms .Al about the basics of this slide are explain in it. The basics of fluid mechanics, heat transfer, chemical engineering thermodynamics, fluid motions, newtonian fluids, are explain in this process. ,education ,chemical engineerin ,chemical engineering ,fluid mechanics ,heat transfer ,chemical process principles ,macdonald ,kfc ,mazeo ,chemicals ,engineers ,cv formatin ,law ,laptop.
This document describes the working principle and experimental setup for calibrating a venturimeter. A venturimeter consists of an inlet section followed by a converging section, cylindrical throat, and gradually diverging cone. It works by creating a pressure difference between the inlet and throat sections due to an increase in flow velocity at the throat. This pressure difference is measured to determine the flow rate. The experiment involves taking pressure and flow rate measurements at the inlet and throat sections using a manometer and collecting water over time. The data is then used to calculate discharge coefficients and Reynolds numbers to calibrate the venturimeter.
This document summarizes different types of fluid flow, including:
- Steady and unsteady flow
- Laminar and turbulent flow
- Compressible and incompressible flow
- One, two, and three dimensional flows
It defines each type of flow and provides examples to explain the differences between steady and unsteady flow, laminar and turbulent flow, and compressible and incompressible flow.
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 describes an experiment to verify Bernoulli's theorem. Bernoulli's theorem states that for an inviscid, incompressible fluid flowing steadily through a closed passage, the total energy at any point remains constant. The experiment involves measuring the pressure, velocity, and elevation at different points in a diverging duct carrying water. Observations are recorded and used to plot the total energy line, which should be horizontal according to Bernoulli's theorem. The results support the theorem by showing the total energy remains constant despite changes in pressure, velocity, and elevation along the duct.
History of Venturi meter, Introduction, Construction, Working Principle, Types of Venturi meter, Limitations & Precautions
, Characteristics of Venturi-meter, Applications of Venturi-meter
, Advantages & Disadvantages.
Overview:
Clemens Herschel (March 23, 1842 – March 1, 1930) was an American hydraulic engineer. He is best known for developing the Venturi-meter, which was the first large-scale, accurate device for measuring water flow.
A Venturi-meter is a device used for measuring the rate of flow of a fluid flowing through a pipe.
It is used to calculate the velocity of fluids running through a pipeline.
The fluid may be a liquid or a gas.
By reducing the cross-section area of flow passage, a pressure difference is created and the measurement of pressure difference enables the determination of discharge through pipe.
1. This document describes various types of ideal fluid flow, including uniform flow, source/sink flow, vortex flow, and combinations of different flows.
2. Special cases of flow geometry allow the stream function ψ to be related to the distance n along a path between streamlines by ψ = wn. Examples include uniform flow in the x-direction and uniform flow from a line source.
3. Combining different flow types allows modeling of more complex scenarios. A doublet represents a close source-sink pair, and combining it with uniform flow models flow around a cylinder.
The document provides information about a water pump system including a filter, valve, elbows, and pipe. It gives values for flow rate, pressure, pipe diameter and length, loss coefficients, and asks questions about:
1) Determining the filter's loss coefficient
2) Calculating the flow rate if the valve is fully open and the filter's coefficient is given
3) Calculating the percentage change in flow rate between the two scenarios
4) Drawing the total energy line and hydraulic grade line for the system.
This document discusses formulas related to fluid flow in pipes. It lists the names of group members and describes the major losses due to friction and minor losses due to entrance/exit, changes in cross-section, valves, bends, and elbows. It then summarizes Darcy's formula for head loss due to friction and provides the variables in Chezy's formula for velocity of flow in an open channel.
This document discusses fluid flow in pipes under pressure. It presents equations to describe laminar and turbulent flow. For laminar flow, the Hagen-Poiseuille equation gives the relationship between pressure drop and flow rate. For turbulent flow, the velocity profile consists of a thin viscous sublayer near the wall and a fully turbulent center zone. Equations are derived to describe velocity profiles in both the sublayer and center zone based on viscosity and turbulence effects. Pipes are classified as smooth or rough depending on roughness size compared to the sublayer thickness.
This document discusses basic thermodynamics concepts. It begins by defining a perfect gas and stating Boyle's Law and Charles' Law, which describe the relationships between pressure, volume, and temperature in gases. It then defines specific heat capacity at constant volume (Cv) as the amount of heat required to raise the temperature of a gas by 1 degree Celsius while keeping its volume constant. The document provides equations relating heat transfer, temperature change, and internal energy for a constant volume process involving a perfect gas. It explains that for such a process, no work is done since the piston cannot move during constant volume heating or cooling.
Fluid Mechanic Lab - Reynold's Number ExperimentMuhammadSRaniYah
1. The document summarizes an experiment conducted by Muhammad Sulaimon Rasul to determine different types of fluid flow (laminar, transitional, turbulent) using Reynolds apparatus.
2. The experiment measured the volume of water and time taken to fill a graduated cylinder for different flow rates. This was used to calculate Reynolds number to identify flow type.
3. All results showed Reynolds numbers less than 2000, indicating laminar flow for all trials according to the theoretical boundaries between flow types.
This document discusses hydroelectric power generation and the components involved. It begins by outlining the objectives of understanding the vocabulary, workings, configurations, and components of hydroelectric power plants. It then discusses various methods for measuring water flow rates, including basic, refined, and sophisticated methods. The document goes on to explain the principles of hydroelectric power generation using Bernoulli's equation. It describes intake structures, penstocks, turbines, tailraces, and categorizes different types of power plants. Finally, it discusses the components involved in hydroelectric systems and different types of turbines, including impulse and reaction turbines.
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 fluid mechanics concepts related to energy conversion. It covers bulk fluid properties like density and pressure. It introduces concepts like streamlines and stream tubes and uses the continuity equation. It derives Bernoulli's equation for steady, inviscid flow by applying conservation of energy. Bernoulli's equation relates pressure, elevation, and velocity along a streamline. Examples are provided to illustrate applying concepts like Bernoulli's equation and the Venturi effect. The objectives are to understand fluid properties, derive conservation equations, analyze viscous effects, and determine forces on immersed bodies.
8. fm 9 flow in pipes major loses co 3 copyZaza Eureka
This document provides an overview of fluid mechanics concepts related to flow in pipes over 3 weeks. It discusses laminar and turbulent flow, identifies the types of flow using the Reynolds number, and explains major and minor losses for flow in pipes. The key points are:
- There are two types of flow - internal (in pipes) and external (over bodies). Internal flow examples include water pipes, blood flow, and HVAC systems.
- Flow can be laminar, turbulent, or in transition as determined by the Reynolds number. The continuity, Bernoulli, and momentum equations govern pipe flow.
- Major losses are pressure/head losses due solely to pipe friction. They can be calculated using the Darcy-
This document summarizes different types of hydroelectric power plants and turbines. It describes impulse and reaction turbines, including Pelton, Francis, and Kaplan turbines. It provides diagrams of hydroelectric and pump storage plants. Key concepts covered include gross and net heads, discharge, water power, brake power, efficiency, and speed. Fundamental equations for hydroelectric systems are given. Common terms are defined. Sample problems demonstrate calculations for hydroelectric plant design and performance analysis.
The document summarizes hydroelectric power, including its history, types, components, working principles, and the case study of the Hirakund Dam in India. Hydropower harnesses the kinetic energy of flowing water to generate electricity. It has been used for over 2000 years and provides renewable, large-scale power. The document describes various types of hydro plants and components like dams, reservoirs, turbines and generators. It also discusses advantages like no emissions but disadvantages like ecosystem disruption.
This document discusses laminar and turbulent flow in pipes. It defines the critical Reynolds number that distinguishes between the two flow regimes. For non-circular pipes, it introduces the hydraulic diameter to characterize the pipe geometry. The document then covers topics such as the developing flow region, fully developed flow profiles and pressure drop, the friction factor, minor losses, pipe networks, and pump selection.
- The document presents solutions to exercises involving calculating probabilities of molecules from historical events mixing uniformly in fluids (oceans, atmosphere)
- It is calculated that there is nearly 100% probability that a cup of water drunk or breath of air inhaled will contain molecules from water dumped in oceans centuries ago or air exhaled in a historical greeting
- Volume calculations and probabilistic methods are used, taking into account numbers of molecules in relevant volumes and the tiny probabilities of a molecule originating from the historical events
Here are the key steps to solve this problem:
1) Use Bernoulli's equation between points 1 and 2:
P1/γ + V12/2g + Z1 = P2/γ + V22/2g + Z2 + HL
2) Given: P1 = 200 kPa, Q = 30 L/sec, HL = 20 kPa
3) Use continuity equation: A1V1 = A2V2
4) Solve for P2
The pressure at point 2 is 180 kPa.
This document discusses fluid statics and manometers. It begins with reviewing key concepts such as pressure, density, states of matter, viscosity, and surface tension. It then covers the relationship between pressure, density, and depth in static fluids. Pressure is independent of direction and increases with depth due to the weight of the fluid above. Manometers use measured height differences of fluids in tubes to calculate pressure differences. The document provides examples of calculating pressures and pressure differences using various manometer setups and fluid properties.
This document discusses fluid flow in pipes under pressure. It provides equations to describe:
1) The variation of shearing stress from the wall to the center of the pipe for both laminar and turbulent flow.
2) The Hagen-Poiseuille equation, which describes the parabolic velocity profile and mean flow velocity for laminar flow through a pipe.
3) An equation for discharge (flow rate) as a function of pipe diameter, pressure drop along the pipe, fluid viscosity, and other parameters for laminar flow in horizontal pipes.
This document provides an overview of pressure and velocity measurement techniques for fluid flow applications. It discusses pressure concepts like absolute, gauge, and vacuum pressure. It also covers the Bernoulli equation and how it relates pressure, velocity, and elevation. Measurement devices like manometers and Pitot-static tubes are explained. A sample problem demonstrates how to calculate the uncertainty in a pressure measurement using an inclined manometer.
This document provides an overview of fluid properties including:
1. Intensive and extensive properties such as temperature, pressure, density, mass, volume, and momentum.
2. The continuum model which treats fluids as continuous substances rather than discrete particles.
3. Equations of state relating pressure, temperature, and density including the ideal gas law.
4. Specific properties including specific volume, specific gravity, and specific weight.
5. Concepts of density, vapor pressure, cavitation, energy, specific heats, coefficients of compressibility and volume expansion, viscosity, and surface tension.
The document discusses principles of fluid dynamics including the application of conservation laws and the energy equation to fluid flows. It covers topics such as Bernoulli's equation, velocity and pressure measurement techniques like Pitot tubes, flow through orifices, open channels, and pipes with head losses. Formulas are presented for flow rate calculation using concepts like velocity head, pressure head, and total head.
Here are the key steps to solve this problem:
1. Given: TH = 817°C = 817 + 273 = 1090 K
TL = 25°C = 25 + 273 = 298 K
QR = 25 kW
2. Use the Carnot efficiency equation:
η = (TH - TL)/TH = (1090 - 298)/1090 = 0.726
3. Set up an equation for the heat input using the efficiency and heat rejected:
QA = QR/(1-η) = 25000/(1-0.726) = 87500 kW
Therefore, the heat input (QA) required is 87500 kW.
Thermodynamics (2013 new edition) copyYuri Melliza
Thermodynamics deals with energy transformation between different forms. Some key concepts covered in the document include:
- The first law of thermodynamics states that energy cannot be created or destroyed, only converted from one form to another.
- For a closed system, the heat transfer (Q) equals the change in internal energy (U) plus the work (W) done by the system.
- For an open system, the heat (Q) equals the change in enthalpy (H) of the system plus the sum of kinetic energy (KE), potential energy (PE), and work (W).
- Other concepts defined include systems, surroundings, properties of fluids, phases of substances, forms of energy
1) The document presents Von Karman 3D procedures as a generalization of Westergaard 2D formulae for estimating hydrodynamic forces on dams during earthquakes.
2) Westergaard's 2D formulae have limitations and can produce singularities, while Von Karman's approach is non-periodic and non-singular with easier generalization to 3D.
3) Numerical examples show that accounting for 3D effects through Von Karman procedures can increase estimated overturning moments on dams by up to 7% compared to 2D Westergaard formulae.
The document discusses the first law of thermodynamics and equations for calculating work, heat transfer, and internal energy change. It then provides 5 exercises:
1. A gas compressed from 3L to 1L at 2 atm pressure with initial temperature of 300K is calculated to have a final temperature of 367.9K.
2. A gas compressed from 5L to 1L at 4 atm constant pressure with initial 400K temperature is found to have a final temperature of 1062.4K.
3. A gas is expanded with calculations to find its final pressure.
4. Work done on a gas compressed at constant temperature is calculated.
5. Final pressure of a gas heated at
This document discusses the hydrodynamic equations that describe neutral gas and plasma, and how they are modified to become the magnetohydrodynamic (MHD) equations when a conducting fluid is in a magnetic field. It introduces the continuity, momentum, and entropy equations for neutral gas hydrodynamics. It then explains how these are updated to the MHD equations by adding magnetic forces and Ohm's law relating current and fields. The key MHD equations derived include equations for momentum, entropy, and the magnetic field evolving due to motion and diffusion.
1. The flow between points P1 and P2 is steady, non-uniform flow since the water depth changes along the length of the ditch but the discharge is constant.
2. Comparing the total head at P1 and P2 using Bernoulli's equation with an energy loss term shows that there is a 0.3 m energy loss between the two points over a 1500 m length of ditch.
3. The flow is classified as one-dimensional flow since the width and depth of flow are much smaller than the length between P1 and P2.
1) The document describes a model for calculating the acceleration of a growing raindrop as it falls through the air by considering the mass, radius, velocity, and force acting on the drop.
2) Three equations are used: an expression relating the change in mass to the change in radius, an expression relating the change in mass to the rate at which water droplets are acquired, and an expression for force equals mass times acceleration.
3) Solving these three equations results in an expression for the acceleration of the raindrop that is independent of variables like density - the acceleration is found to be g/7.
1) The document describes solving three equations to model the growth of a raindrop as it falls, gaining mass from water droplets.
2) It derives an equation that the raindrop's acceleration is g/7, independent of density and average droplet mass density.
3) It notes that using an invalid conservation of energy approach would give a wrong acceleration of g/4, and explains why energy is not conserved due to inelastic collisions.
Meg 506.2 Combined heat and mass transfer a reviewTeddy Adiela
1. The document discusses combined heat and mass transfer, highlighting key equations. It explains that mass transfer is driven by concentration differences while heat transfer is driven by temperature differences.
2. Mass transfer across interfaces between gases and liquids or gases and solids is then examined. For dilute gas-liquid solutions, Henry's law applies such that the gas mole fraction at the liquid surface is proportional to the gas partial pressure. For strongly soluble gases, Raoult's law applies where the gas partial pressure equals the mole fraction times the saturation pressure.
3. Steady state mass diffusion through plane walls and cylinders is also derived analogously to heat conduction, with mass or molar transfer rates proportional to concentration or mole fraction
The first law of thermodynamics states that the change in internal energy of a system is equal to the heat supplied to the system minus the work done by the system. For a closed system undergoing a process, this can be expressed as ΔU=Q-W. The first law applies to both closed systems undergoing non-flow processes as well as open systems undergoing steady flow processes. For non-flow processes such as constant volume, constant pressure, isothermal, and adiabatic processes, the first law allows determining the relationships between heat, work and changes in internal energy or enthalpy. For steady flow processes, the general energy equation accounts for changes in kinetic and potential energy of the fluid in addition to heat
1) The document discusses fluid pressure and its relationship to depth, gravity, and buoyant forces. It explains that pressure is transmitted equally in all directions throughout a confined fluid.
2) Key concepts covered include Pascal's principle, how pressure depends on depth and density, and Archimedes' principle that the buoyant force equals the weight of fluid displaced.
3) Examples and demonstrations are provided to illustrate these fluid mechanics concepts.
1) The document discusses fluid pressure and its relationship to depth, gravity, and buoyant forces. It explains that pressure is transmitted equally in all directions throughout a confined fluid.
2) Key concepts covered include Pascal's principle, how pressure depends on depth and density, and Archimedes' principle that the buoyant force equals the weight of fluid displaced.
3) Examples and demonstrations are provided to illustrate these fluid mechanics concepts.
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إضغ بين إيديكم من أقوى الملازم التي صممتها
ملزمة تشريح الجهاز الهيكلي (نظري 3)
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تتميز هذهِ الملزمة بعِدة مُميزات :
1- مُترجمة ترجمة تُناسب جميع المستويات
2- تحتوي على 78 رسم توضيحي لكل كلمة موجودة بالملزمة (لكل كلمة !!!!)
#فهم_ماكو_درخ
3- دقة الكتابة والصور عالية جداً جداً جداً
4- هُنالك بعض المعلومات تم توضيحها بشكل تفصيلي جداً (تُعتبر لدى الطالب أو الطالبة بإنها معلومات مُبهمة ومع ذلك تم توضيح هذهِ المعلومات المُبهمة بشكل تفصيلي جداً
5- الملزمة تشرح نفسها ب نفسها بس تكلك تعال اقراني
6- تحتوي الملزمة في اول سلايد على خارطة تتضمن جميع تفرُعات معلومات الجهاز الهيكلي المذكورة في هذهِ الملزمة
واخيراً هذهِ الملزمة حلالٌ عليكم وإتمنى منكم إن تدعولي بالخير والصحة والعافية فقط
كل التوفيق زملائي وزميلاتي ، زميلكم محمد الذهبي 💊💊
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A Visual Guide to 1 Samuel | A Tale of Two HeartsSteve Thomason
These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.
Philippine Edukasyong Pantahanan at Pangkabuhayan (EPP) CurriculumMJDuyan
(𝐓𝐋𝐄 𝟏𝟎𝟎) (𝐋𝐞𝐬𝐬𝐨𝐧 𝟏)-𝐏𝐫𝐞𝐥𝐢𝐦𝐬
𝐃𝐢𝐬𝐜𝐮𝐬𝐬 𝐭𝐡𝐞 𝐄𝐏𝐏 𝐂𝐮𝐫𝐫𝐢𝐜𝐮𝐥𝐮𝐦 𝐢𝐧 𝐭𝐡𝐞 𝐏𝐡𝐢𝐥𝐢𝐩𝐩𝐢𝐧𝐞𝐬:
- Understand the goals and objectives of the Edukasyong Pantahanan at Pangkabuhayan (EPP) curriculum, recognizing its importance in fostering practical life skills and values among students. Students will also be able to identify the key components and subjects covered, such as agriculture, home economics, industrial arts, and information and communication technology.
𝐄𝐱𝐩𝐥𝐚𝐢𝐧 𝐭𝐡𝐞 𝐍𝐚𝐭𝐮𝐫𝐞 𝐚𝐧𝐝 𝐒𝐜𝐨𝐩𝐞 𝐨𝐟 𝐚𝐧 𝐄𝐧𝐭𝐫𝐞𝐩𝐫𝐞𝐧𝐞𝐮𝐫:
-Define entrepreneurship, distinguishing it from general business activities by emphasizing its focus on innovation, risk-taking, and value creation. Students will describe the characteristics and traits of successful entrepreneurs, including their roles and responsibilities, and discuss the broader economic and social impacts of entrepreneurial activities on both local and global scales.
Level 3 NCEA - NZ: A Nation In the Making 1872 - 1900 SML.pptHenry Hollis
The History of NZ 1870-1900.
Making of a Nation.
From the NZ Wars to Liberals,
Richard Seddon, George Grey,
Social Laboratory, New Zealand,
Confiscations, Kotahitanga, Kingitanga, Parliament, Suffrage, Repudiation, Economic Change, Agriculture, Gold Mining, Timber, Flax, Sheep, Dairying,
This presentation was provided by Rebecca Benner, Ph.D., of the American Society of Anesthesiologists, for the second session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session Two: 'Expanding Pathways to Publishing Careers,' was held June 13, 2024.
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024