The document discusses characteristics of flow in hoses and pipelines, including:
- The velocity of water flow is determined by gravity and can be calculated using formulas comparing time, velocity, and distance fallen.
- Flow rate in pipes/hoses (Q) is calculated using the formula Q = v x A, where v is velocity and A is cross-sectional area.
- Friction causes loss of pressure in water flow through resistance. The loss of pressure due to friction (Pf) increases with length, velocity, and flow rate while decreasing with diameter. Formulas are provided to calculate Pf.
This document discusses fluid mechanics and defines key terms. It begins by defining fluid mechanics as the science dealing with fluids at rest or in motion. Fluid mechanics is then divided into several categories based on the type of fluid flow, such as hydrodynamics, hydraulics, gas dynamics, and aerodynamics. The document goes on to define properties of fluids like density, specific gravity, vapor pressure, energy, and viscosity. It also discusses concepts like the ideal gas law, temperature scales, and surface tension.
This document discusses different types of hydraulic pressure control valves. It describes pressure relief valves, pilot operated relief valves, sequence control valves, and other types. Pressure relief valves limit pressure by diverting fluid to the reservoir when pressure reaches a set point. Pilot operated relief valves use a piston or spool controlled by a pilot valve. Sequence valves provide flow to a second actuator after the first reaches a threshold pressure. The document also provides examples of applications for different valve types.
The document discusses hydrostatic forces on surfaces submerged in fluids. It defines fluid statics as dealing with fluids at rest, where the only stress is normal stress due to pressure variations from fluid weight. It describes how to calculate the resultant force and center of pressure on plane and curved surfaces for non-uniform pressure distributions. For a rectangular plate, the resultant force is the pressure at the centroid multiplied by the area, and the center of pressure is below the centroid. Examples are provided to demonstrate calculating these values.
This document provides an overview of an online course on applied fluid mechanics for incompressible flow. The course is divided into two parts, with part 1 focusing on incompressible flow (constant density fluids) and part 2 on compressible flow (variable density fluids). Part 1 covers topics like the mechanic energy equation, piping systems, pumps, flow measurement devices, and their applications to problems involving incompressible fluids. The course content is presented through online modules containing theory, examples, practice problems and quizzes. The goal is to teach students and engineers how to apply fluid mechanics concepts to real-world engineering problems involving the movement and processing of incompressible liquids and gases.
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
This document presents information on fluid flow through pipes. It discusses major losses due to friction and minor losses due to changes in flow velocity or direction. It provides the Darcy-Weisbach and Chezy's formulas for calculating head loss due to friction. Minor losses include those due to pipe fittings, bends, enlargements, contractions and obstructions. The document also discusses flow through pipes in series, parallel and equivalent configurations.
The document provides an overview of Tactical Combat Casualty Care (TCCC) guidelines for treating casualties on the battlefield. It discusses the three goals of TCCC - treat the casualty, prevent additional casualties, and complete the mission. It outlines the M-A-R-C-H-(E) technique for casualty assessment and the three phases of care - Care Under Fire, Tactical Field Care, and Tactical Evacuation Care. Key principles discussed include controlling hemorrhage with tourniquets, wound packing, and pressure bandages. It also reviews airway management techniques such as positioning, nasopharyngeal airways, and identifying airway problems in casualties.
This document discusses fluid mechanics and defines key terms. It begins by defining fluid mechanics as the science dealing with fluids at rest or in motion. Fluid mechanics is then divided into several categories based on the type of fluid flow, such as hydrodynamics, hydraulics, gas dynamics, and aerodynamics. The document goes on to define properties of fluids like density, specific gravity, vapor pressure, energy, and viscosity. It also discusses concepts like the ideal gas law, temperature scales, and surface tension.
This document discusses different types of hydraulic pressure control valves. It describes pressure relief valves, pilot operated relief valves, sequence control valves, and other types. Pressure relief valves limit pressure by diverting fluid to the reservoir when pressure reaches a set point. Pilot operated relief valves use a piston or spool controlled by a pilot valve. Sequence valves provide flow to a second actuator after the first reaches a threshold pressure. The document also provides examples of applications for different valve types.
The document discusses hydrostatic forces on surfaces submerged in fluids. It defines fluid statics as dealing with fluids at rest, where the only stress is normal stress due to pressure variations from fluid weight. It describes how to calculate the resultant force and center of pressure on plane and curved surfaces for non-uniform pressure distributions. For a rectangular plate, the resultant force is the pressure at the centroid multiplied by the area, and the center of pressure is below the centroid. Examples are provided to demonstrate calculating these values.
This document provides an overview of an online course on applied fluid mechanics for incompressible flow. The course is divided into two parts, with part 1 focusing on incompressible flow (constant density fluids) and part 2 on compressible flow (variable density fluids). Part 1 covers topics like the mechanic energy equation, piping systems, pumps, flow measurement devices, and their applications to problems involving incompressible fluids. The course content is presented through online modules containing theory, examples, practice problems and quizzes. The goal is to teach students and engineers how to apply fluid mechanics concepts to real-world engineering problems involving the movement and processing of incompressible liquids and gases.
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
This document presents information on fluid flow through pipes. It discusses major losses due to friction and minor losses due to changes in flow velocity or direction. It provides the Darcy-Weisbach and Chezy's formulas for calculating head loss due to friction. Minor losses include those due to pipe fittings, bends, enlargements, contractions and obstructions. The document also discusses flow through pipes in series, parallel and equivalent configurations.
The document provides an overview of Tactical Combat Casualty Care (TCCC) guidelines for treating casualties on the battlefield. It discusses the three goals of TCCC - treat the casualty, prevent additional casualties, and complete the mission. It outlines the M-A-R-C-H-(E) technique for casualty assessment and the three phases of care - Care Under Fire, Tactical Field Care, and Tactical Evacuation Care. Key principles discussed include controlling hemorrhage with tourniquets, wound packing, and pressure bandages. It also reviews airway management techniques such as positioning, nasopharyngeal airways, and identifying airway problems in casualties.
This document discusses chest trauma, including types of injuries like flail chest, pneumothorax, and cardiac contusion. It describes signs and symptoms of these injuries as well as management, which includes stabilizing the patient's airway and breathing, administering oxygen, and rapidly transporting to the hospital. Special considerations are given to open chest wounds, tension pneumothorax, and impaled objects.
The ABCDE mnemonic is commonly used in first aid training and medical education to guide the assessment and initial management of trauma patients. It stands for:
A - Airway, B - Breathing, C - Circulation, D - Disability (neurological status), E - Exposure/environmental control. The mnemonic provides a systematic framework to survey a patient and identify any life-threatening injuries while beginning resuscitation efforts. Variations on the mnemonic order and additions have been developed for different contexts and levels of training.
1. Bernoulli's principle states that within a horizontal flow of fluid, the highest fluid pressure occurs where the flow speed is lowest, and lowest pressure where flow speed is highest.
2. Bernoulli's principle explains how the difference in pressure above and below a wing produces an upward force, allowing for flight. It is also applied to explain how air flows over mountains.
3. Bernoulli's equation expresses the conservation of energy for flowing fluids, relating pressure, flow velocity, and elevation. It states that the total mechanical energy per unit volume remains constant within a streamline.
The document is the solutions manual for a fluid mechanics textbook. It contains solutions to example problems from Chapter 1 which covers basic concepts in fluid mechanics, including definitions of different types of flows, fluid properties, forces, and units. The solutions provide concise explanations and calculations for each question with the relevant equations, assumptions, analysis, and discussions of the results.
The document defines key terms and concepts related to industrial pneumatics, including:
- The physical states of matter and how gases differ from liquids
- Common gas laws such as Boyle's law, Charles' law, and the combined gas law
- Fundamental pneumatic terms like pressure, vacuum, and compressibility
- Primary components of compressed air systems like filters, regulators, lubricators
- Types of pneumatic valves, actuators, and motors
This document provides information on the definition, causes, classifications, pathophysiology, and management of burn injuries. It defines burns as damage to body tissues caused by heat, chemicals, electricity, sunlight, or radiation. It describes the different classifications of burns from superficial to deep full-thickness burns. It explains the pathophysiological changes that occur due to fluid shifts, electrolyte imbalances, metabolic changes, and infections in burn patients. Finally, it outlines the various treatment approaches for burns, including airway management, fluid resuscitation, wound care, and rehabilitation.
This document provides an overview of fluid kinematics, which is the study of fluid motion without considering forces. It discusses key concepts like streamlines, pathlines, and streaklines. It describes Lagrangian and Eulerian methods for describing fluid motion. It also covers various types of fluid flow such as steady/unsteady, laminar/turbulent, compressible/incompressible, and one/two/three-dimensional flow. Important topics like continuity equation, velocity, acceleration, and stream/velocity potential functions are also summarized. The document is intended to outline the syllabus and learning objectives for a course unit on fluid kinematics.
Convection is the movement of molecules within fluids and is one of the major modes of heat and mass transfer. Forced convection occurs when an external source, like a fan or pump, generates fluid motion. This allows for very efficient heat transport and is commonly used in heating, cooling, and machinery. Extended surfaces like fins and pins can be added normal to a surface to increase the surface area and improve heat transfer between the surface and surrounding fluid according to Newton's Law of Cooling. Comparing finned and unfinned surfaces under the same conditions demonstrates the effect of extended surfaces.
This document provides information on explosion proof electrical equipment for hazardous locations. It discusses the hazard triangle of spark, explosion and flammable materials. It defines hazardous locations as areas where explosive gases or combustible dusts may be present. It describes the classification systems for hazardous areas including Zone/Division systems and gas grouping. It outlines explosion proof standards and methods of protection for electrical equipment used in these hazardous locations to prevent ignition sources from causing explosions.
The document provides information on lightning strikes and basic first aid recommendations. It outlines preventative measures one can take during a lightning storm, including seeking shelter in dense forests or low-lying areas and staying away from lone objects. The document recommends turning off electronic devices and removing metallic objects during a storm. It advises laying down with your head pointed towards potential flashes and protecting your ears if struck by lightning to aid resuscitation efforts and treat resulting injuries like burns.
Bernoulli's equation relates pressure, velocity, and elevation along a streamline of an incompressible fluid. It states that the sum of pressure energy, kinetic energy, and potential energy remains constant. The document provides examples of how to use Bernoulli's equation to solve problems involving fluid flow through pipes of varying diameters and elevations, including determining velocities, pressures, and flow rates. Practical applications discussed include venturimeters, orificemeters, and Pitot tubes for measuring fluid flow rates.
Mechanical seals fail for two basic reasons: component damage or faces opening up. To analyze failures, one must carefully examine all components, the equipment, and application. There are various types of seals that differ in design and how they are balanced or unbalanced. Environmental controls like temperature regulation, fluid quality, and impurities removal can also affect seal life.
1) Hydraulics is the study of fluids in pipes and how they can be used to transmit and modify force and motion. It includes hydrostatics, dealing with fluids at rest, and hydrodynamics, dealing with fluids in motion.
2) Pascal's law states that pressure applied to a confined fluid is transmitted undiminished in all directions, allowing hydraulic systems to multiply applied forces. Bramah's press demonstrated this principle to multiply mechanical advantage.
3) Hydraulic systems use confined fluids to transmit power through linear or rotary actuators, providing advantages like speed and direction control as well as force multiplication and overload protection.
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.
Hydraulics today has become a way of life as most applications have some form of system ingrained. This paper is an endevor to present the very basics of hydraulics and overcome its basic fear.
This document provides an introduction and overview of a fluid mechanics course taught by Dr. Mohsin Siddique. It outlines the course details including goals, topics, textbook, and assessment methods. The course aims to provide an understanding of fluid statics and dynamics concepts. Key topics covered include fluid properties, fluid statics, fluid flow measurements, dimensional analysis, and fluid flow in pipes and open channels. Students will be evaluated through assignments, quizzes, a midterm exam, and a final exam. The course intends to develop skills relevant to various engineering fields involving fluid mechanics.
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.
Rev. August 2014 ME495 - Pipe Flow Characteristics… Page .docxjoyjonna282
Rev. August 2014 ME495 - Pipe Flow Characteristics… Page 2
2
ME495—Thermo Fluids Laboratory
~~~~~~~~~~~~~~
PIPE FLOW CHARACTERISTICS
AND PRESSURE TRANSDUCER
CALIBRATION
~~~~~~~~~~~~~~
PREPARED BY: GROUP LEADER’S NAME
LAB PARTNERS: NAME
NAME
NAME
TIME/DATE OF EXPERIMENT: TIME , DATE
~~~~~~~~~~~~~~
OBJECTIVE— The objectives of this experiment are
to: a) observe the characteristics of flow in a pipe,
b) evaluate the flow rate in a pipe using velocity
and pressure difference measurements, and c)
perform the calibration of a pressure transducer.
Upon completing this experiment you should have
learned (i) how to measure the flow rate and average
velocity in a pipe using a Pitot tube and/or a resistance
flow meter, and (ii) how to classify the general
characteristics of a pipe flow.
Nomenclature
a = speed of sound, m/s
A = area, m
2
C = discharge coefficient, dimensionless
d = pipe diameter, m
d0 = orifice diameter, m
E = velocity approach factor, dimensionless
f = Darcy friction factor, dimensionless
K0 = flow coefficient, dimensionless
k = ratio of specific heats (cp/cv), dimensionless
L = length of pipe, m
M = Mach number, dimensionless
p = pressure, Pa
p0 = stagnation pressure, Pa
p1, p2 = pressure at two axial locations along a
pipe, Pa
Q = volumetric flow rate, m
3
/s
R = specific gas constant, J·kg/K
Re = Reynolds number, dimensionless
T = temperature, K
V = local velocity, m/s
V = average velocity, m/s
Y = adiabatic expansion factor, dimensionless
= ratio of orifice diameter to pipe diameter,
dimensionless
p = pressure drop across an orifice meter, Pa
= dynamic viscosity, Pa·s
= air density, kg/m3
INTRODUCTION— The flow of a fluid (liquid or
gas) through pipes or ducts is a common part of many
engineering systems. Household applications include
the flow of water in copper pipes, the flow of natural
gas in steel pipes, and the flow of heated air through
metal ducts of rectangular cross-section in a forced-air
furnace system. Industrial applications range from the
flow of liquid plastics in a manufacturing plant, to the
flow of yogurt in a food-processing plant. Because the
purpose of a piping system is to transport a desired
quantity of fluid, it is important to understand the
various methods of measuring the flow rate.
In order to work with a fluid system, and certainly to
design a fluid system that will deliver a prescribed
flow, it is necessary to understand certain fundamental
aspects of the fluid flow. For this, one should be able
to answer questions like: Are compressibility effects
important? Is the flow laminar or turbulent? Is the
viscosity of the fluid important or not? Is the flow
steady or varying with time? What are the primary
forces of importance? For internal ...
This document provides information about fluid flow through pipes, including definitions and equations. It defines types of fluid flow such as steady/unsteady, uniform/non-uniform, laminar/turbulent. It also defines compressible/incompressible flow and rotational/irrotational flow. Bernoulli's equation and its assumptions are described. Darcy-Weisbach and Hagen-Poiseuille equations for head loss due to friction are given. Reynolds number range for laminar and turbulent flow is provided. Shear stress, velocity distribution, and average velocity equations are listed. Factors affecting frictional head loss are also mentioned.
This document discusses chest trauma, including types of injuries like flail chest, pneumothorax, and cardiac contusion. It describes signs and symptoms of these injuries as well as management, which includes stabilizing the patient's airway and breathing, administering oxygen, and rapidly transporting to the hospital. Special considerations are given to open chest wounds, tension pneumothorax, and impaled objects.
The ABCDE mnemonic is commonly used in first aid training and medical education to guide the assessment and initial management of trauma patients. It stands for:
A - Airway, B - Breathing, C - Circulation, D - Disability (neurological status), E - Exposure/environmental control. The mnemonic provides a systematic framework to survey a patient and identify any life-threatening injuries while beginning resuscitation efforts. Variations on the mnemonic order and additions have been developed for different contexts and levels of training.
1. Bernoulli's principle states that within a horizontal flow of fluid, the highest fluid pressure occurs where the flow speed is lowest, and lowest pressure where flow speed is highest.
2. Bernoulli's principle explains how the difference in pressure above and below a wing produces an upward force, allowing for flight. It is also applied to explain how air flows over mountains.
3. Bernoulli's equation expresses the conservation of energy for flowing fluids, relating pressure, flow velocity, and elevation. It states that the total mechanical energy per unit volume remains constant within a streamline.
The document is the solutions manual for a fluid mechanics textbook. It contains solutions to example problems from Chapter 1 which covers basic concepts in fluid mechanics, including definitions of different types of flows, fluid properties, forces, and units. The solutions provide concise explanations and calculations for each question with the relevant equations, assumptions, analysis, and discussions of the results.
The document defines key terms and concepts related to industrial pneumatics, including:
- The physical states of matter and how gases differ from liquids
- Common gas laws such as Boyle's law, Charles' law, and the combined gas law
- Fundamental pneumatic terms like pressure, vacuum, and compressibility
- Primary components of compressed air systems like filters, regulators, lubricators
- Types of pneumatic valves, actuators, and motors
This document provides information on the definition, causes, classifications, pathophysiology, and management of burn injuries. It defines burns as damage to body tissues caused by heat, chemicals, electricity, sunlight, or radiation. It describes the different classifications of burns from superficial to deep full-thickness burns. It explains the pathophysiological changes that occur due to fluid shifts, electrolyte imbalances, metabolic changes, and infections in burn patients. Finally, it outlines the various treatment approaches for burns, including airway management, fluid resuscitation, wound care, and rehabilitation.
This document provides an overview of fluid kinematics, which is the study of fluid motion without considering forces. It discusses key concepts like streamlines, pathlines, and streaklines. It describes Lagrangian and Eulerian methods for describing fluid motion. It also covers various types of fluid flow such as steady/unsteady, laminar/turbulent, compressible/incompressible, and one/two/three-dimensional flow. Important topics like continuity equation, velocity, acceleration, and stream/velocity potential functions are also summarized. The document is intended to outline the syllabus and learning objectives for a course unit on fluid kinematics.
Convection is the movement of molecules within fluids and is one of the major modes of heat and mass transfer. Forced convection occurs when an external source, like a fan or pump, generates fluid motion. This allows for very efficient heat transport and is commonly used in heating, cooling, and machinery. Extended surfaces like fins and pins can be added normal to a surface to increase the surface area and improve heat transfer between the surface and surrounding fluid according to Newton's Law of Cooling. Comparing finned and unfinned surfaces under the same conditions demonstrates the effect of extended surfaces.
This document provides information on explosion proof electrical equipment for hazardous locations. It discusses the hazard triangle of spark, explosion and flammable materials. It defines hazardous locations as areas where explosive gases or combustible dusts may be present. It describes the classification systems for hazardous areas including Zone/Division systems and gas grouping. It outlines explosion proof standards and methods of protection for electrical equipment used in these hazardous locations to prevent ignition sources from causing explosions.
The document provides information on lightning strikes and basic first aid recommendations. It outlines preventative measures one can take during a lightning storm, including seeking shelter in dense forests or low-lying areas and staying away from lone objects. The document recommends turning off electronic devices and removing metallic objects during a storm. It advises laying down with your head pointed towards potential flashes and protecting your ears if struck by lightning to aid resuscitation efforts and treat resulting injuries like burns.
Bernoulli's equation relates pressure, velocity, and elevation along a streamline of an incompressible fluid. It states that the sum of pressure energy, kinetic energy, and potential energy remains constant. The document provides examples of how to use Bernoulli's equation to solve problems involving fluid flow through pipes of varying diameters and elevations, including determining velocities, pressures, and flow rates. Practical applications discussed include venturimeters, orificemeters, and Pitot tubes for measuring fluid flow rates.
Mechanical seals fail for two basic reasons: component damage or faces opening up. To analyze failures, one must carefully examine all components, the equipment, and application. There are various types of seals that differ in design and how they are balanced or unbalanced. Environmental controls like temperature regulation, fluid quality, and impurities removal can also affect seal life.
1) Hydraulics is the study of fluids in pipes and how they can be used to transmit and modify force and motion. It includes hydrostatics, dealing with fluids at rest, and hydrodynamics, dealing with fluids in motion.
2) Pascal's law states that pressure applied to a confined fluid is transmitted undiminished in all directions, allowing hydraulic systems to multiply applied forces. Bramah's press demonstrated this principle to multiply mechanical advantage.
3) Hydraulic systems use confined fluids to transmit power through linear or rotary actuators, providing advantages like speed and direction control as well as force multiplication and overload protection.
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.
Hydraulics today has become a way of life as most applications have some form of system ingrained. This paper is an endevor to present the very basics of hydraulics and overcome its basic fear.
This document provides an introduction and overview of a fluid mechanics course taught by Dr. Mohsin Siddique. It outlines the course details including goals, topics, textbook, and assessment methods. The course aims to provide an understanding of fluid statics and dynamics concepts. Key topics covered include fluid properties, fluid statics, fluid flow measurements, dimensional analysis, and fluid flow in pipes and open channels. Students will be evaluated through assignments, quizzes, a midterm exam, and a final exam. The course intends to develop skills relevant to various engineering fields involving fluid mechanics.
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.
Rev. August 2014 ME495 - Pipe Flow Characteristics… Page .docxjoyjonna282
Rev. August 2014 ME495 - Pipe Flow Characteristics… Page 2
2
ME495—Thermo Fluids Laboratory
~~~~~~~~~~~~~~
PIPE FLOW CHARACTERISTICS
AND PRESSURE TRANSDUCER
CALIBRATION
~~~~~~~~~~~~~~
PREPARED BY: GROUP LEADER’S NAME
LAB PARTNERS: NAME
NAME
NAME
TIME/DATE OF EXPERIMENT: TIME , DATE
~~~~~~~~~~~~~~
OBJECTIVE— The objectives of this experiment are
to: a) observe the characteristics of flow in a pipe,
b) evaluate the flow rate in a pipe using velocity
and pressure difference measurements, and c)
perform the calibration of a pressure transducer.
Upon completing this experiment you should have
learned (i) how to measure the flow rate and average
velocity in a pipe using a Pitot tube and/or a resistance
flow meter, and (ii) how to classify the general
characteristics of a pipe flow.
Nomenclature
a = speed of sound, m/s
A = area, m
2
C = discharge coefficient, dimensionless
d = pipe diameter, m
d0 = orifice diameter, m
E = velocity approach factor, dimensionless
f = Darcy friction factor, dimensionless
K0 = flow coefficient, dimensionless
k = ratio of specific heats (cp/cv), dimensionless
L = length of pipe, m
M = Mach number, dimensionless
p = pressure, Pa
p0 = stagnation pressure, Pa
p1, p2 = pressure at two axial locations along a
pipe, Pa
Q = volumetric flow rate, m
3
/s
R = specific gas constant, J·kg/K
Re = Reynolds number, dimensionless
T = temperature, K
V = local velocity, m/s
V = average velocity, m/s
Y = adiabatic expansion factor, dimensionless
= ratio of orifice diameter to pipe diameter,
dimensionless
p = pressure drop across an orifice meter, Pa
= dynamic viscosity, Pa·s
= air density, kg/m3
INTRODUCTION— The flow of a fluid (liquid or
gas) through pipes or ducts is a common part of many
engineering systems. Household applications include
the flow of water in copper pipes, the flow of natural
gas in steel pipes, and the flow of heated air through
metal ducts of rectangular cross-section in a forced-air
furnace system. Industrial applications range from the
flow of liquid plastics in a manufacturing plant, to the
flow of yogurt in a food-processing plant. Because the
purpose of a piping system is to transport a desired
quantity of fluid, it is important to understand the
various methods of measuring the flow rate.
In order to work with a fluid system, and certainly to
design a fluid system that will deliver a prescribed
flow, it is necessary to understand certain fundamental
aspects of the fluid flow. For this, one should be able
to answer questions like: Are compressibility effects
important? Is the flow laminar or turbulent? Is the
viscosity of the fluid important or not? Is the flow
steady or varying with time? What are the primary
forces of importance? For internal ...
This document provides information about fluid flow through pipes, including definitions and equations. It defines types of fluid flow such as steady/unsteady, uniform/non-uniform, laminar/turbulent. It also defines compressible/incompressible flow and rotational/irrotational flow. Bernoulli's equation and its assumptions are described. Darcy-Weisbach and Hagen-Poiseuille equations for head loss due to friction are given. Reynolds number range for laminar and turbulent flow is provided. Shear stress, velocity distribution, and average velocity equations are listed. Factors affecting frictional head loss are also mentioned.
A pumping test was conducted to determine the permeability of an unconfined aquifer. Observations from the test included a discharge of 240 m3/hour from a well with a diameter of 20 cm. The original water surface level was 240.5 m, and dropped to 235.6 m at the pumping well. An observation well 50 m away recorded a water level of 239.8 m. Using these observations and equations for unconfined radial flow, the permeability was calculated to be 49.13 m/day. Assuming a radius of influence of 300 m instead led to an error of 9.1% in the calculated permeability. The actual radius of influence based on observations was 154 m.
محاضرة هيدروليك هندسة مدني(2) 26-2-2022.pdfn2002asr
The document discusses Bernoulli's principle and its applications in determining discharge velocity from a water tank and the maximum height of a water jet. It also provides the equation to calculate the time required to drain water from a tank. An example problem calculates this time for a cylindrical tank with given dimensions. The document also covers head losses in pipes from friction, the Darcy-Weisbach equation, and the Moody diagram for determining the friction factor. An example solves for the discharge capacity of a pipe using the friction factor from the Moody chart.
This document discusses fluid flow in pipes. It explains that for circular pipes, equations for non-circular cross sections can be modified using hydraulic radius. It then derives the Hagen-Poiseuille law for head loss due to friction in laminar pipe flow and proves that the mean velocity is half the maximum velocity for laminar flow. It also discusses turbulent flow, developing flow, and the formation of boundary layers in pipe flow.
The document discusses hydraulics and hydraulic principles related to irrigation systems. It defines hydraulics as the study of liquid behavior in pipes and channels. Important concepts covered include:
- Flow rate, velocity, cross-sectional area, and how they relate mathematically.
- Different forms of energy in water systems including kinetic, potential, and pressure energy. It defines related terms like head, velocity head, elevation head, and pressure head.
- Friction loss and how it is calculated using equations like Hazen-Williams. It provides examples of calculating friction loss in pipes of different diameters and lengths.
- Head losses in fittings, valves, bends and how to calculate them using resistance coefficients.
Friction losses in turbulent flow (Fanning Equation).pdfSharpmark256
This document discusses fluid flow in pipes, including laminar and turbulent flow regimes. It defines key terms like Reynolds number, friction factor, pressure drop, and boundary layers. For laminar flow, the friction factor can be predicted from the Reynolds number using theoretical equations. For turbulent flow, the friction factor must be determined experimentally and depends on both the Reynolds number and pipe roughness.
This document discusses compressible flow and its applications in chemical engineering. It begins by defining compressible flow as fluid flow with significant changes in density, usually when the Mach number is greater than 0.3. It then discusses how to distinguish compressible fluids using the Mach number and provides some historical examples. The effects of compressibility, such as choked flow, shock waves, and changes in density with pressure changes are described. Finally, some applications of compressible flow in chemical engineering are mentioned, such as high-speed gas flow in pipes and nozzles and compressible gas flow in chemical processing industries.
The document discusses numerical prediction of slugging problems in pipes. It provides a literature review of existing models for key slugging parameters like liquid holdup, pressure drop, and slug frequency. It analyzes Gregory et al's 1978 correlation for liquid holdup against simulations of a 3000 bopd deepwater oil field case study. The simulation results matched the trend of the correlation but overpredicted liquid holdup. Sensitivity analysis showed that increasing superficial gas velocity decreases liquid holdup. Pressure drop models like Beggs and Brill are also discussed. The goal is to better understand the interaction between gas surge and liquid slugs during slugging.
This document describes an experiment conducted to determine the friction factor of water flowing through a pipe. The experiment measured the volumetric flow rate, velocity, temperature, and pressure drop of water flowing through a pipe. These measurements were used to calculate the Reynolds number, theoretical friction factor based on equations, and experimental friction factor. The results showed that at higher Reynolds numbers, the friction factor was lower, following trends in friction factor charts. Sources of error included inaccurate measurements of pressure drop and flow time. The experiment demonstrated how friction factor depends inversely on Reynolds number for turbulent flow in a pipe.
Pipe corrosion is caused by several factors related to water chemistry and physical properties. Low pH, high oxygen content, carbon dioxide, and bacteria can all promote corrosion by speeding up the electrochemical oxidation process. Water temperature also affects corrosion rates, with higher temperatures generally causing faster corrosion. Physical factors like flow turbulence at locations with sudden changes in direction can lead to erosion corrosion. Galvanic corrosion can occur when dissimilar metals are in contact within the piping system. Proper material selection and water treatment can help reduce corrosion in pipe lines.
1. The document discusses flow in ducts and pipes, including circular and non-circular cross-sections. It also covers topics like hydraulic diameter, average velocity, laminar and turbulent flow regimes.
2. Entrance effects are explained, including the development of boundary layers and velocity profiles. Equations are given for estimating the hydrodynamic entry length in laminar and turbulent flows.
3. The force balance on a control volume is used to derive equations for the velocity profile in fully developed laminar pipe flow.
4. Head loss and pressure drop correlations are presented, making use of the Darcy-Weisbach friction factor and Colebrook equation.
5. Turbulent flow near walls is analyzed
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 ...
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This document discusses the basic equations of fluid flow, including:
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2. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
The laws governing the velocity of
particles of water correspond to the same
laws that govern free falling bodies.
Ignoring air resistance, free falling bodies
accelerate at the rate of 9.81 metre per
second per second or 9.81 meters per
second squared (9.81m/s²).
3. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
Thus, the velocity of any falling body at
the end of a given number of seconds,
after falling from rest, is found by
multiplying the number of seconds (time)
by the constant g.
v = gt,
where v = velocity in metres per second
(m/s),
g = gravity, and
t = time in seconds.
4. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
What is the velocity of a free-falling
droplet of water at the end of 10 seconds
from rest?
5. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
What is the velocity of a free-falling
droplet of water at the end of 10 seconds
from rest?
v = gt
= 9.81 x 10
= 98.1 seconds
6. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
The velocity of a free-falling droplet of
water is 19.62 m/s when it strikes the
ground calculate how long the droplet of
water fell for.
7. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
The velocity of a free-falling droplet of
water is 19.62 m/s when it strikes the
ground calculate how long the droplet of
water fell for.
v = gt v = gt
t = v/g 19.62 = 9.81 x t
= 19.62 /9.81 19.62 / 9.81 = t
= 2 seconds 2 = t
t = 2
seconds
8. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
If the distance fallen = average velocity x
time
Then the distance (H) = v x t = gt x t
2 2
= gt2 or
2
= ½ gt2
Where H is in metres (m)
9. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
If the distance or height through which a
body
falls is compared with the velocity it attains,
it is
found that there is a direct relationship.
V = gt H = gt2
2
H = ½ gt2
10. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
If the distance or height through which a
body
falls is compared with the velocity it attains,
it is
found that there is a direct relationship.
From this relationship the following
formulas
are derived:
v = √2gH or 4.43 √H ≈ 4.4 √H
11. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
These laws apply equally to the flow of
water through a pipe, where the particles
have a certain velocity due to height
(head) from which they have fallen (if
gravity fed) or due to the pressure applied
by some other source, such as a pump.
12. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
The value of this formula can be seen when
calculating the velocity of water issuing
from a
nozzle.
What is the velocity of the water issuing
from a
nozzle when the nozzle pressure is 5 bar?
13. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
Thus far, the only formula we have to
calculate
velocity is:
v = gt, v = √2gH or 4.43 √H or 4.4 √H
We are given a nozzle pressure of 5 bar
and we
have a formula with a pressure head (H) or
height. we can calculate H
H = P × 10.19 (metre)
14. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity, or rate of flow)
v = gt, v = √2gH or 4.4 √H
H = P × 10 = 5 x 10 = 50
we can now calculate v
v = 4.4 √H
= 4.4 √50
= 4.4 x 7
= 31 m/s
15.
16. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
To enable water to flow along a hose or a
pipe,
a difference in head or pressure at the two
ends is necessary.
18. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
The amount of water a hose or pipe will
transmit or convey in a given time depends
on :
(i) Its size (cross-sectional area)
(ii) The speed at which the water is
passing through it (i.e velocity)
19. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
The formula for calculating the quality of
water
passing through a hose or pipe is:
Q = v x A
Where Q is the quantity of water in cubic
metres per second, v is velocity in metre
per second and A is the cross-sectional
area of the pipe in square metres.
20. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
Firemen prefer however, to deal in
discharges
from pipes or hose in litres per minute and
to
refer to the diameter of such hose or pipes
in
millimetres.
Taking the formula Q = v x A and
transposing,
21. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
v = 21.2L or v ≈ 20L
d2 d2
Where L the flow in litres per minute and
d is diameter in millimetres
22. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
Conversely, if the velocity is known the
discharge can be found by transposing the
formula to:
L = vd2
20
23. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
What is the velocity of water in a 70 mm
diameter hose if the discharge is 1000 litres
per
minute?
Use the formula: v = 20L
d2
24. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
What is the velocity of water in a 70 mm
diameter hose if the discharge is 1000 litres
per
minute?
v = 20L = 20 x 1000
d2 702
= 20,000
4,900
= 4.08 m/s or 4 m/s
25. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
It is apparent that there is a direct
relationship
between velocity and quantity delivered;
doubling the velocity will result in twice the
quantity being delivered.
26. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Velocity of water in hose
and pipes)
The velocity at which the water travels
through
a pipe or hose is also dependent on the
pressure applied or the difference in head,
but
it will be shown that there is another factor
–
loss of head due to friction which also plays
a
27. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Loss of pressure due to
friction)
To propel water through a hose or pipe,
work
has to be performed to overcome friction,
which is caused by the particles of which
water
is composed rubbing against each other
and
against the walls of the hose or pipe
through
which the water is passing.
28. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Loss of pressure due to
friction)
There are five (5) principal laws governing
loss
of pressure due to friction, namely
Friction loss varies directly with the length
of pipe.
For the same velocity, friction loss
decreases directly with the increase in
diameter.
Friction loss increases directly as the
square of the velocity.
29. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Loss of pressure due to
friction)
Friction loss increases with the
roughness of the interior of the pipe.
Friction loss, for all practical purposes is
independent of pressure.
30. Friction loss varies directly with the length of
pipe
This is obvious, as the longer the hose the
more pressure is required to pump the
water
through. If the length of hose is doubled,
the
loss of pressure due to friction is doubled.
31. For the same velocity, friction loss
decreases directly with the increase in
diameter
This is extremely important, for if the diameter of
a
pipe is doubled, the surface area is doubled, but
the
cross-sectional area is quadrupled (the cross-
sectional area being proportional to the square
of
the diameter). Therefore for any given velocity, if
the
diameter of the hose is doubled, the quantity of
water is increased to four times, and the loss of
pressure due to friction is consequently halved.
32. Friction loss increases directly as the
square of the velocity
This is another very important factor, as, if the
velocity of the water is halved, the loss of
pressure
due to friction is reduced to (½)2 or one-quarter.
This has its most important application when
pumping over long distances. If 2000 litres of
water
per minute are being delivered through one line
of
hose with a loss of pressure due to friction of 6
bar, the act of twinning the hose and 1000
litres/min
33. Friction loss increases with the roughness
of the interior of the pipe
That friction increases with roughness is
apparent when attempting to rub one’s
finger
over sandpaper compared with a polished
surface. Similarly, it is more difficult to
force
water through a pipe with a rough interior,
than with a smooth inside surface.
The degree of internal roughness of a
34. Friction loss, for all practical purposes is
independent of pressure
Experiments show that loss of pressure due to
friction is independent of pressure or head at
which
the system is operating. Thus, if the friction loss
for a
given flow rate in a certain line of hose or pipe is
such that a pump pressure of 7 bar is required
to
maintain a nozzle pressure of 3 bar, then it will
be
found that in order to maintain a nozzle pressure
of
35. Friction loss, for all practical purposes is
independent of pressure
With hose, increase in pressure may result in
certain
indirect effects, such as a slight stretching giving
an
increase in cross-sectional area and thus a
slight
reduction in friction loss. On the other hand, a
rise in
pressure may result in some increase in length
and,
therefore, a somewhat greater frictional loss.
These
36.
37. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
To force water through a hose, sufficient
pressure or head must be available at the
pump to overcome all the factors affecting
friction loss, and to provide a margin which
will enable an efficient jet to be maintained
with a plain nozzle at the branch, or, in the
case of a spray with a diffuser branch, to
break
up the water stream and project the spray
effectively.
38. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
The formula for the head loss due to friction
in
a length of pipe or is given as:
Hf = 2flv2
Dg where,
Hf = head loss due to friction (metres)
f = frictional factor
l = length of pipe or hose (metres)
v = velocity of water (m/s)
D = diameter of pipe or hose (metres)
39. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
It is important to remember when using this
formula that all measurements must be in
metres and the result will give the friction
loss
in metres head.
But it is useful to know the loss of pressure
in
bar rather than in metres head and to
express
40. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
The formula can be converted to:
Pf = 20flv2
d where,
Pf = pressure loss due to friction (bar)
f = frictional factor
l = length of pipe or hose (metres)
v = velocity of water (m/s)
d = diameter of pipe or hose (millimetres)
41. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
A line of 90 mm hose is 500 metres long.
Water is flowing through it at a velocity of
2
metres per second. Using a friction factor
of
0.007, what is the loss of pressure due to
friction?
Pf = 20flv2
d
42. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
A line of 90 mm hose is 500 metres long. Water is flowing
through it at a velocity of 2 metres per second. Using a
friction
factor of 0.007, what is the loss of pressure due to
friction?
Pf = 20flv2
d
f = 0.007, l = 500 metres, v = 2 m/s,
d = 90 mm
Pf = 20 x 0.007 x 500 x 22
90
43. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
Pf = 20flv2
d
In this formula, one requires to know the
velocity in metres per second. Firemen,
however, generally deal instead with
discharges
in litres per minutes (L). We can therefore
substitute 21.2L for v
d2
giving the formula:
44. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
Pf = 9000flL2
d5
45. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
A line of 90 mm hose is 500 metres long.
Water is being discharge at 764 litres per
minute. Using a friction factor of 0.007,
what is
the loss of pressure due to friction?
Pf = 9000flL2
d5
46. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
A line of 90 mm hose is 500 metres long.
Water is being discharge at 764 litres per
minute. Using a friction factor of 0.007,
what is
the loss of pressure due to friction?
Pf = 9000flL2
d5
= 9000 x 0.007 x 500 x 7642
90 x 90 x 90 x 90 x 90
= 3.12 bar
47. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
It should be borne in mind that it is
impossible
to calculate friction losses with any great
degree of accuracy when dealing with fire
service hose, as there are a number of
factors
which affect the result. For example, hose
will
increase both in diameter and in length
when
48. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
Test have been carried out with hose of
various
sizes, and for all practical purposes the
friction
factor (f) of the fire service hose is shown:
Type of hose Friction factor
Non-percolating hose
90 mm diameter fitted with
standard instantaneous
49. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
Type of hose Friction factor
All other hose 0.005
Percolating hose
Excluding 90 mm hose 0.010
50. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
Calculate the pressure required at the
pump to
maintain a branch pressure of 4 bar at a 25
mm
nozzle at the end of 150 metres of 70 mm
non-
percolating hose at a discharge of 830 litres
per
minute.
Pf = 9000flL2
51. CHARACTERISTICS OF FLOW IN HOSE
AND PIPELINES (Calculation of friction
loss)
Calculate the pressure required at the pump to maintain a
branch pressure of 4 bar at a 25 mm nozzle at the end of
150
metres of 70 mm non-percolating hose at a discharge of
830
litres per minute.
Pf = 9000flL2
d5
= 9000 x .005 x 150 x 8302
70 x 70 x 70 x 70 x 70
= 2.77 bar