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The document discusses the fundamental principles of fluid mechanics - conservation of mass, energy, and momentum - and how they are applied to derive equations for open channel flow. It specifically covers the continuity, energy, and momentum equations. The energy equation relates changes in energy within a control volume, while the momentum equation relates the overall forces on the control volume boundaries. The document also discusses topics like specific energy, critical flow, hydraulic jumps, and how these concepts are used to analyze channel transitions and design channel flows.

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Fluid Mechanics Chapter 3. Integral relations for a control volume

Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation

Open Channel VS Pipe Flow

Pipe flow involves fluid completely filling a pipe, while open channel flow has a free surface. In pipe flow, pressure varies along the pipe but remains constant at the free surface in open channels. The main driving force is gravity in open channels and pressure gradient in pipes. Flow properties like cross-sectional area and velocity profile differ between the two flow types.

Part 2 Revision.pdf

This document discusses fluid mechanics concepts related to blood flow in arteries. It covers the following key points in 3 sentences:
The document discusses characteristics of blood flow such as being pulsating, not always laminar, and having short entrance lengths. It also covers physical dimensions and velocity parameters of arteries and veins. Fundamental fluid mechanics concepts are reviewed such as conservation of momentum, Bernoulli's equation, shear forces, and factors that affect the applicability of Bernoulli's equation like steady, incompressible, and frictionless flow.

mass momentum energy equations

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.

Fluid Mechanics Unit-2 (vk-ssm)

This document discusses concepts related to fluid flow through circular conduits including:
- Laminar flow through pipes and boundary layer concepts such as boundary layer thickness.
- The Darcy-Weisbach equation for calculating head loss and how it relates to friction factor.
- The Moody diagram which plots friction factor against Reynolds number for different relative pipe roughnesses.
- Commercial pipes and how piping systems are used to transport fluids with considerations for energy loss due to friction.

Hidráulica

Okay, here are the key steps to solve this problem using Bernoulli's equation:
1) At the free surface in the tank, P1 = Patm, V1 = 0, z1 = 5 m
2) At the outlet, P2 = Patm, z2 = 0
3) Bernoulli's equation:
Patm + 0 + 5g = Patm + V22/2g + 0
4) Solve for V2:
V22/2g = 5g
V2 = √10g = 5√2 m/s
So the velocity of the water at the smooth, rounded outlet is 5√2 m/s.

Fluid machinery hydraulic turbines i

Classification of Hydraulic Turbines
Turbines that use water as the working fluid
for the production of power are known as
hydraulic turbines.
Main categories are impulse and reaction
turbines (based on the interaction of the
fluid on the blades)
Can further be classified on the basis of
head available at the inlet, specific speed, and
according to flow direction
1. Action of water on the runner (the rotating element of
turbine)—impulse and reaction
2. Direction of flow—tangential flow, radial flow, axial flow, and
mixed (radial + axial) flow
3. Available head—high head (H > 300 m), medium head (50 m
< H < 300 m), and low head (H < 50 m)
4. Specific speed is the speed of geometrically similar turbine
which produces unit power when operated under unit head—
low, medium, and high specific speed turbines
Heads and Efficiencies
Two types of heads as far as turbines
are concerned—gross head and net
head.
Gross head indicates the difference in
head and tail race levels.
Net head is the actual head available at
the turbine inlet and is computed as
gross head minus frictional losses in the
penstock

Bernoulli’s equation and its significance

This document discusses Bernoulli's equation and its significance. It provides background on Bernoulli's principle, derives the general Bernoulli's equation, and discusses its different forms. Several applications of Bernoulli's equation are described, including in pumps, ejectors, carburetors, siphons, and pilot tubes. Limitations due to fluid viscosity are also noted. In conclusion, the equation is valid for fluid flow as it obeys the conservation of energy principle.

Fluid Mechanics Chapter 3. Integral relations for a control volume

Introduction, physical laws of fluid mechanics, the Reynolds transport theorem, Conservation of mass equation, Linear momentum equation, Angular momentum equation, Energy equation, Bernoulli equation

Open Channel VS Pipe Flow

Pipe flow involves fluid completely filling a pipe, while open channel flow has a free surface. In pipe flow, pressure varies along the pipe but remains constant at the free surface in open channels. The main driving force is gravity in open channels and pressure gradient in pipes. Flow properties like cross-sectional area and velocity profile differ between the two flow types.

Part 2 Revision.pdf

This document discusses fluid mechanics concepts related to blood flow in arteries. It covers the following key points in 3 sentences:
The document discusses characteristics of blood flow such as being pulsating, not always laminar, and having short entrance lengths. It also covers physical dimensions and velocity parameters of arteries and veins. Fundamental fluid mechanics concepts are reviewed such as conservation of momentum, Bernoulli's equation, shear forces, and factors that affect the applicability of Bernoulli's equation like steady, incompressible, and frictionless flow.

mass momentum energy equations

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.

Fluid Mechanics Unit-2 (vk-ssm)

This document discusses concepts related to fluid flow through circular conduits including:
- Laminar flow through pipes and boundary layer concepts such as boundary layer thickness.
- The Darcy-Weisbach equation for calculating head loss and how it relates to friction factor.
- The Moody diagram which plots friction factor against Reynolds number for different relative pipe roughnesses.
- Commercial pipes and how piping systems are used to transport fluids with considerations for energy loss due to friction.

Hidráulica

Okay, here are the key steps to solve this problem using Bernoulli's equation:
1) At the free surface in the tank, P1 = Patm, V1 = 0, z1 = 5 m
2) At the outlet, P2 = Patm, z2 = 0
3) Bernoulli's equation:
Patm + 0 + 5g = Patm + V22/2g + 0
4) Solve for V2:
V22/2g = 5g
V2 = √10g = 5√2 m/s
So the velocity of the water at the smooth, rounded outlet is 5√2 m/s.

Fluid machinery hydraulic turbines i

Classification of Hydraulic Turbines
Turbines that use water as the working fluid
for the production of power are known as
hydraulic turbines.
Main categories are impulse and reaction
turbines (based on the interaction of the
fluid on the blades)
Can further be classified on the basis of
head available at the inlet, specific speed, and
according to flow direction
1. Action of water on the runner (the rotating element of
turbine)—impulse and reaction
2. Direction of flow—tangential flow, radial flow, axial flow, and
mixed (radial + axial) flow
3. Available head—high head (H > 300 m), medium head (50 m
< H < 300 m), and low head (H < 50 m)
4. Specific speed is the speed of geometrically similar turbine
which produces unit power when operated under unit head—
low, medium, and high specific speed turbines
Heads and Efficiencies
Two types of heads as far as turbines
are concerned—gross head and net
head.
Gross head indicates the difference in
head and tail race levels.
Net head is the actual head available at
the turbine inlet and is computed as
gross head minus frictional losses in the
penstock

Bernoulli’s equation and its significance

This document discusses Bernoulli's equation and its significance. It provides background on Bernoulli's principle, derives the general Bernoulli's equation, and discusses its different forms. Several applications of Bernoulli's equation are described, including in pumps, ejectors, carburetors, siphons, and pilot tubes. Limitations due to fluid viscosity are also noted. In conclusion, the equation is valid for fluid flow as it obeys the conservation of energy principle.

Two Phase Flow Research

This document discusses two-phase flow models and compares different pressure drop correlation methods. It begins with an introduction to two-phase flow and important variables like liquid holdup, gas void fraction, and slip velocity. It then describes the different flow patterns or regimes that can occur, including dispersed bubble, stratified smooth, wavy, slug, annular, and spray flows. The document outlines factors that affect flow patterns and discusses how patterns vary between horizontal, upward inclined, and downward inclined pipes. It concludes that selecting the most suitable correlation is key to accurately sizing pipelines for different applications.

Fluid flow phenomenon, prepared by Makhdoom ibad ullah hashmi

This document summarizes key concepts related to fluid flow phenomena, including:
1) It defines fluids and describes their behavior under applied forces, discussing concepts like potential flow and boundary layers.
2) It outlines different fluid flow regimes for compressible and incompressible fluids, as well as rheological properties of Newtonian and non-Newtonian fluids.
3) It discusses velocity fields, boundary layer formation and properties, and provides an example of a one-dimensional fluid flow through a circular pipe where the velocity depends only on the radial distance from the centerline.

Unit41.pptx

Okay, let's solve this step-by-step:
* Given: Mass flow rate = 3 kg/s
* Inlet conditions: P1 = 1400 kPa, T1 = 200°C
* Exit conditions: P2 = 200 kPa
* Process is isentropic
* Properties of CO2 at given conditions: k = 1.3, R = 188 J/kg-K
* Using the continuity equation: ρ1A1V1 = ρ2A2V2
* Using the isentropic relations for ideal gases:
P1/P2 = (ρ2/ρ1)^k / (T2/T1)^(k-1)

Lecture 3 bernoulli_s_theorm_it_s_applications

The document discusses Bernoulli's theorem and its applications. It begins by defining different types of fluid flow, including steady and unsteady, uniform and non-uniform, laminar and turbulent flow. It then explains the concepts of discharge, continuity equation, and the different types of energies and heads in fluids. Bernoulli's theorem states that the total energy remains constant in ideal fluid flow. The document outlines the assumptions and limitations of the theorem. It concludes by discussing applications of Bernoulli's theorem in venturi meters, orifice meters, and Pitot tubes.

Chapter 1..ppt

The document summarizes open channel flow concepts including:
- Open channel flow has a free surface exposed to atmospheric pressure, unlike confined pipe flow.
- Flow can be classified as uniform, gradually varied, or rapidly varied based on depth changes.
- Critical flow occurs when the specific energy is minimum and Froude number is 1.
- The Manning equation relates velocity, hydraulic radius, slope, and roughness for uniform flow calculations.

T1 - Essential Fluids - 2023.pptx

This document discusses fluid mechanics concepts including:
- Identifying vocabulary related to fluid mechanics and energy conservation.
- Explaining physical properties of fluids like density, pressure, and viscosity.
- Recognizing types of fluid flows like laminar, turbulent, compressible, incompressible.
- Understanding concepts like no-slip condition, boundary layers, and streamlines.
- Deriving conservation laws for mass and energy in ideal fluids using Bernoulli's equation.

E04653033

The document studies and compares the rate of energy dissipation in stepped overflows before and after the hydraulic jump using laboratory models. It finds that using the depth of flow before the hydraulic jump (y1) overestimates energy dissipation compared to using the depth after the hydraulic jump (y2) and calculating y1, due to air bubbles in the flow before the jump. The study builds and tests a physical model of a stepped spillway. It measures depths before and after the hydraulic jump under different discharges and calculates energy dissipation rates using both methods. The results show greater errors in the calculation using y1 as discharge increases due to more air in the flow.

UNIT 4 Unsteady Flow.pptx

Unsteady flow:
Equation of motion for unsteady flow,
Celerity of the gravity wave,
deep and shallow water waves,
open channel positive and negative surge.
The flow of water in rivers, canals, reservoirs, lakes, pools, and free- surface flow in storm water drains, conduits, pipes , galleries, tunnels and culverts, in which the velocities change with time, is defined as unsteady flow ( non - permanent, non - stationary , or time -variable free- surface water flow).
This unsteadiness may arise naturally or may be caused by human action. Floods in rivers, water level variation in estuaries due to tidal action etc. are examples of unsteady flows occurring naturally.
Surges created in power channels, water level variation in irrigation canals due to gate operation etc. are unsteady flows caused by human action

Fluid kinematics

This document discusses key concepts in fluid dynamics, including:
(i) Fluid kinematics describes fluid motion without forces/energies, examining geometry of motion through concepts like streamlines and pathlines.
(ii) Fluids can flow steadily or unsteadily, uniformly or non-uniformly, laminarly or turbulently depending on properties of the flow and fluid.
(iii) The continuity equation states that mass flow rate remains constant for an incompressible, steady flow through a control volume according to the principle of conservation of mass.

Fluid mechanics(2130602)

Topics:- Fluid , Properties & Types
Fluid Dynamics & Kinematics.

FLUID-MECHANICS-AND-MASS-TRANSFAR-FM7.pdf

This document discusses fluid flow, including laminar and turbulent flow, transition between the two, and the effects of turbulence. It also covers topics like pipe flow, the Reynolds number parameter, and pressure drops and head losses in pipes. Some key points made include:
- At moderate Reynolds numbers, smooth laminar flow becomes fluctuating turbulent flow due to transition.
- Turbulence enhances heat and mass transfer compared to laminar flow.
- Fully developed pipe flow can be modeled using logarithmic velocity profiles and relationships between friction factor and Reynolds number.
- Minor losses from fittings add to overall pressure drops beyond just major losses in straight pipe sections.

Fluid mechanics-ppt

This document discusses fluid mechanics and its various branches and concepts. It begins by defining mechanics, statics, dynamics, and fluid mechanics. It then discusses specific types of fluid mechanics like hydrodynamics, hydraulics, gas dynamics, and aerodynamics. It also discusses classifications of fluid flow such as viscous vs inviscid flow, internal vs external flow, and compressible vs incompressible flow. Finally, it covers key concepts like laminar vs turbulent flow, steady vs unsteady flow, and dimensional flows.

Comparison of flow analysis of a sudden and gradual change

IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and TechnologyIJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology

Comparison of flow analysis of a sudden and gradual change of pipe diameter u...

Abstract This paper describes an analytical approach to describe the areas where Pipes (used for flow of fluids) are mostly susceptible to damage and tries to visualize the flow behaviour in various geometric conditions of a pipe. Fluent software was used to plot the characteristics of the flow and gambit software was used to design the 2D model. Two phase Computational fluid dynamics calculations, using K-epsilon model were employed. This simulation gives the values of pressure and velocity contours at various sections of the pipe in which water as a media. A comparison was made with the sudden and gradual change of pipe diameter (i.e., expansion and contraction of the pipe). The numerical results were validated against experimental data from the literature and were found to be in good agreement. Index Terms: gambit, fluent software.

Flow Measurement

The document discusses different types of flowmeters used to measure volumetric and mass flow rates of fluids, including orifice meters, rotameters, magnetic flowmeters, and Coriolis mass flowmeters. It explains the basic operating principles of rotameters, which measure flow using a float inside a tapered tube, and magnetic flowmeters, which induce a voltage in conductive fluids using the Faraday's law of induction. It also describes how Coriolis mass flowmeters measure the mass flow rate of a fluid using sensors to detect distortions in the vibration of oscillating measuring tubes caused by the Coriolis force.

Lesson 4 bernoulli's theorem

The document discusses Bernoulli's theorem and fluid mechanics. It defines key terms like total pressure, static pressure, velocity pressure, velocity head, and static head. It explains how Bernoulli's theorem relates pressure and velocity in flowing fluids. Specifically, it states that as velocity increases, static pressure decreases. The document also demonstrates how to calculate fluid velocity through pipes when flow rate is constant but pipe diameter changes.

Poster_phd_symp_A0size

Open channel confluences are where rivers and canals meet. They are complex with variable flow patterns that can cause flooding, scouring, and sediment accumulation. The document presents a conceptual model of a 90-degree asymmetrical confluence with rectangular channels to systematically study key parameters like discharge ratio. Laboratory experiments are conducted using measurement techniques like ADV and LSSPIV to analyze velocities and turbulence. Numerical modeling is also used to efficiently study parameters and provide additional data for validation. The overall aim is to improve understanding of confluence hydrodynamics to help address engineering issues.

Fluid Flow inside and outside of the pipe

- Internal flow is completely bounded by surfaces on all sides, such as pipe flows. External flow is over bodies immersed in a fluid that is unbounded, like flow over airfoils.
- Major losses in pipes are due to friction or viscous effects and are quantified using Darcy's friction factor. Minor losses are due to fittings.
- Laminar flow is smooth and orderly while turbulent flow is chaotic with eddies. The transition between them depends on the Reynolds number.
- In developing pipe flow, the boundary layer grows along the pipe until it fills the cross-section and the flow is fully developed.

9-Viscous flow in ducts.pptx

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

Chapter 4. diffrential

This chapter discusses differential analysis of fluid flow. It introduces the concepts of stream function and vorticity. The key equations derived are:
1) The differential equations of continuity, linear momentum, and mass conservation which relate the time rate of change of fluid properties like density and velocity within an infinitesimal control volume.
2) The Navier-Stokes equations which model viscous flow using Newton's laws and relate stresses to strain rates via viscosity.
3) Equations for inviscid, irrotational flow where viscosity and vorticity are neglected.
4) The stream function, a potential function whose contour lines represent streamlines, allowing 2D problems to be solved using a

ML Based Model for NIDS MSc Updated Presentation.v2.pptx

ML Based model for NIDS

LLM Fine Tuning with QLoRA Cassandra Lunch 4, presented by Anant

Slides for the 4th Presentation on LLM Fine-Tuning with QLoRA Presented by Anant, featuring DataStax Astra

Two Phase Flow Research

This document discusses two-phase flow models and compares different pressure drop correlation methods. It begins with an introduction to two-phase flow and important variables like liquid holdup, gas void fraction, and slip velocity. It then describes the different flow patterns or regimes that can occur, including dispersed bubble, stratified smooth, wavy, slug, annular, and spray flows. The document outlines factors that affect flow patterns and discusses how patterns vary between horizontal, upward inclined, and downward inclined pipes. It concludes that selecting the most suitable correlation is key to accurately sizing pipelines for different applications.

Fluid flow phenomenon, prepared by Makhdoom ibad ullah hashmi

This document summarizes key concepts related to fluid flow phenomena, including:
1) It defines fluids and describes their behavior under applied forces, discussing concepts like potential flow and boundary layers.
2) It outlines different fluid flow regimes for compressible and incompressible fluids, as well as rheological properties of Newtonian and non-Newtonian fluids.
3) It discusses velocity fields, boundary layer formation and properties, and provides an example of a one-dimensional fluid flow through a circular pipe where the velocity depends only on the radial distance from the centerline.

Unit41.pptx

Okay, let's solve this step-by-step:
* Given: Mass flow rate = 3 kg/s
* Inlet conditions: P1 = 1400 kPa, T1 = 200°C
* Exit conditions: P2 = 200 kPa
* Process is isentropic
* Properties of CO2 at given conditions: k = 1.3, R = 188 J/kg-K
* Using the continuity equation: ρ1A1V1 = ρ2A2V2
* Using the isentropic relations for ideal gases:
P1/P2 = (ρ2/ρ1)^k / (T2/T1)^(k-1)

Lecture 3 bernoulli_s_theorm_it_s_applications

The document discusses Bernoulli's theorem and its applications. It begins by defining different types of fluid flow, including steady and unsteady, uniform and non-uniform, laminar and turbulent flow. It then explains the concepts of discharge, continuity equation, and the different types of energies and heads in fluids. Bernoulli's theorem states that the total energy remains constant in ideal fluid flow. The document outlines the assumptions and limitations of the theorem. It concludes by discussing applications of Bernoulli's theorem in venturi meters, orifice meters, and Pitot tubes.

Chapter 1..ppt

The document summarizes open channel flow concepts including:
- Open channel flow has a free surface exposed to atmospheric pressure, unlike confined pipe flow.
- Flow can be classified as uniform, gradually varied, or rapidly varied based on depth changes.
- Critical flow occurs when the specific energy is minimum and Froude number is 1.
- The Manning equation relates velocity, hydraulic radius, slope, and roughness for uniform flow calculations.

T1 - Essential Fluids - 2023.pptx

This document discusses fluid mechanics concepts including:
- Identifying vocabulary related to fluid mechanics and energy conservation.
- Explaining physical properties of fluids like density, pressure, and viscosity.
- Recognizing types of fluid flows like laminar, turbulent, compressible, incompressible.
- Understanding concepts like no-slip condition, boundary layers, and streamlines.
- Deriving conservation laws for mass and energy in ideal fluids using Bernoulli's equation.

E04653033

The document studies and compares the rate of energy dissipation in stepped overflows before and after the hydraulic jump using laboratory models. It finds that using the depth of flow before the hydraulic jump (y1) overestimates energy dissipation compared to using the depth after the hydraulic jump (y2) and calculating y1, due to air bubbles in the flow before the jump. The study builds and tests a physical model of a stepped spillway. It measures depths before and after the hydraulic jump under different discharges and calculates energy dissipation rates using both methods. The results show greater errors in the calculation using y1 as discharge increases due to more air in the flow.

UNIT 4 Unsteady Flow.pptx

Unsteady flow:
Equation of motion for unsteady flow,
Celerity of the gravity wave,
deep and shallow water waves,
open channel positive and negative surge.
The flow of water in rivers, canals, reservoirs, lakes, pools, and free- surface flow in storm water drains, conduits, pipes , galleries, tunnels and culverts, in which the velocities change with time, is defined as unsteady flow ( non - permanent, non - stationary , or time -variable free- surface water flow).
This unsteadiness may arise naturally or may be caused by human action. Floods in rivers, water level variation in estuaries due to tidal action etc. are examples of unsteady flows occurring naturally.
Surges created in power channels, water level variation in irrigation canals due to gate operation etc. are unsteady flows caused by human action

Fluid kinematics

This document discusses key concepts in fluid dynamics, including:
(i) Fluid kinematics describes fluid motion without forces/energies, examining geometry of motion through concepts like streamlines and pathlines.
(ii) Fluids can flow steadily or unsteadily, uniformly or non-uniformly, laminarly or turbulently depending on properties of the flow and fluid.
(iii) The continuity equation states that mass flow rate remains constant for an incompressible, steady flow through a control volume according to the principle of conservation of mass.

Fluid mechanics(2130602)

Topics:- Fluid , Properties & Types
Fluid Dynamics & Kinematics.

FLUID-MECHANICS-AND-MASS-TRANSFAR-FM7.pdf

This document discusses fluid flow, including laminar and turbulent flow, transition between the two, and the effects of turbulence. It also covers topics like pipe flow, the Reynolds number parameter, and pressure drops and head losses in pipes. Some key points made include:
- At moderate Reynolds numbers, smooth laminar flow becomes fluctuating turbulent flow due to transition.
- Turbulence enhances heat and mass transfer compared to laminar flow.
- Fully developed pipe flow can be modeled using logarithmic velocity profiles and relationships between friction factor and Reynolds number.
- Minor losses from fittings add to overall pressure drops beyond just major losses in straight pipe sections.

Fluid mechanics-ppt

This document discusses fluid mechanics and its various branches and concepts. It begins by defining mechanics, statics, dynamics, and fluid mechanics. It then discusses specific types of fluid mechanics like hydrodynamics, hydraulics, gas dynamics, and aerodynamics. It also discusses classifications of fluid flow such as viscous vs inviscid flow, internal vs external flow, and compressible vs incompressible flow. Finally, it covers key concepts like laminar vs turbulent flow, steady vs unsteady flow, and dimensional flows.

Comparison of flow analysis of a sudden and gradual change

IJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and TechnologyIJRET : International Journal of Research in Engineering and Technology is an international peer reviewed, online journal published by eSAT Publishing House for the enhancement of research in various disciplines of Engineering and Technology. The aim and scope of the journal is to provide an academic medium and an important reference for the advancement and dissemination of research results that support high-level learning, teaching and research in the fields of Engineering and Technology. We bring together Scientists, Academician, Field Engineers, Scholars and Students of related fields of Engineering and Technology

Comparison of flow analysis of a sudden and gradual change of pipe diameter u...

Abstract This paper describes an analytical approach to describe the areas where Pipes (used for flow of fluids) are mostly susceptible to damage and tries to visualize the flow behaviour in various geometric conditions of a pipe. Fluent software was used to plot the characteristics of the flow and gambit software was used to design the 2D model. Two phase Computational fluid dynamics calculations, using K-epsilon model were employed. This simulation gives the values of pressure and velocity contours at various sections of the pipe in which water as a media. A comparison was made with the sudden and gradual change of pipe diameter (i.e., expansion and contraction of the pipe). The numerical results were validated against experimental data from the literature and were found to be in good agreement. Index Terms: gambit, fluent software.

Flow Measurement

The document discusses different types of flowmeters used to measure volumetric and mass flow rates of fluids, including orifice meters, rotameters, magnetic flowmeters, and Coriolis mass flowmeters. It explains the basic operating principles of rotameters, which measure flow using a float inside a tapered tube, and magnetic flowmeters, which induce a voltage in conductive fluids using the Faraday's law of induction. It also describes how Coriolis mass flowmeters measure the mass flow rate of a fluid using sensors to detect distortions in the vibration of oscillating measuring tubes caused by the Coriolis force.

Lesson 4 bernoulli's theorem

The document discusses Bernoulli's theorem and fluid mechanics. It defines key terms like total pressure, static pressure, velocity pressure, velocity head, and static head. It explains how Bernoulli's theorem relates pressure and velocity in flowing fluids. Specifically, it states that as velocity increases, static pressure decreases. The document also demonstrates how to calculate fluid velocity through pipes when flow rate is constant but pipe diameter changes.

Poster_phd_symp_A0size

Open channel confluences are where rivers and canals meet. They are complex with variable flow patterns that can cause flooding, scouring, and sediment accumulation. The document presents a conceptual model of a 90-degree asymmetrical confluence with rectangular channels to systematically study key parameters like discharge ratio. Laboratory experiments are conducted using measurement techniques like ADV and LSSPIV to analyze velocities and turbulence. Numerical modeling is also used to efficiently study parameters and provide additional data for validation. The overall aim is to improve understanding of confluence hydrodynamics to help address engineering issues.

Fluid Flow inside and outside of the pipe

- Internal flow is completely bounded by surfaces on all sides, such as pipe flows. External flow is over bodies immersed in a fluid that is unbounded, like flow over airfoils.
- Major losses in pipes are due to friction or viscous effects and are quantified using Darcy's friction factor. Minor losses are due to fittings.
- Laminar flow is smooth and orderly while turbulent flow is chaotic with eddies. The transition between them depends on the Reynolds number.
- In developing pipe flow, the boundary layer grows along the pipe until it fills the cross-section and the flow is fully developed.

9-Viscous flow in ducts.pptx

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

Chapter 4. diffrential

This chapter discusses differential analysis of fluid flow. It introduces the concepts of stream function and vorticity. The key equations derived are:
1) The differential equations of continuity, linear momentum, and mass conservation which relate the time rate of change of fluid properties like density and velocity within an infinitesimal control volume.
2) The Navier-Stokes equations which model viscous flow using Newton's laws and relate stresses to strain rates via viscosity.
3) Equations for inviscid, irrotational flow where viscosity and vorticity are neglected.
4) The stream function, a potential function whose contour lines represent streamlines, allowing 2D problems to be solved using a

Two Phase Flow Research

Two Phase Flow Research

Fluid flow phenomenon, prepared by Makhdoom ibad ullah hashmi

Fluid flow phenomenon, prepared by Makhdoom ibad ullah hashmi

Unit41.pptx

Unit41.pptx

Lecture 3 bernoulli_s_theorm_it_s_applications

Lecture 3 bernoulli_s_theorm_it_s_applications

Chapter 1..ppt

Chapter 1..ppt

T1 - Essential Fluids - 2023.pptx

T1 - Essential Fluids - 2023.pptx

E04653033

E04653033

UNIT 4 Unsteady Flow.pptx

UNIT 4 Unsteady Flow.pptx

Fluid kinematics

Fluid kinematics

Fluid mechanics(2130602)

Fluid mechanics(2130602)

FLUID-MECHANICS-AND-MASS-TRANSFAR-FM7.pdf

FLUID-MECHANICS-AND-MASS-TRANSFAR-FM7.pdf

Fluid mechanics-ppt

Fluid mechanics-ppt

Comparison of flow analysis of a sudden and gradual change

Comparison of flow analysis of a sudden and gradual change

Comparison of flow analysis of a sudden and gradual change of pipe diameter u...

Comparison of flow analysis of a sudden and gradual change of pipe diameter u...

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官方认证美国密歇根州立大学毕业证学位证书原版一模一样

官方认证美国密歇根州立大学毕业证学位证书原版一模一样

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- 1. The equations which describe the flow of fluid are derived from three fundamental laws of physics (r/ship of fluid motion): Conservation of matter (or mass) Conservation of energy Conservation of momentum Assumptions have been done with in the control volume in each principles. 1.4. Energy & Momentum Principles in Open Channel Flow
- 2. A. Continuity equation For any control volume during the small time interval dt the principle of conservation of mass implies that the mass of flow entering the control volume minus the mass of flow leaving the control volume equals the change of mass within the control volume. If the flow is steady and the fluid incompressible the mass entering is equal to the mass leaving, so there is no change of mass within the control volume.
- 3. B. Energy Equation oConsider the forms of energy available for the above control volume. If the fluid moves from the upstream face 1, to the downstream face 2 in time dt over the length L. Similarly the total energy per unit weight of section two also computed and consider no energy is supplied between the inlet and outlet of the control volume, energy leaving equal to energy entering.
- 5. C. Momentum Equation The law of conservation of momentum says that a moving body cannot gain or lose momentum unless acted upon by an external force. The resultant force acting on a free body of fluid in any direction is equal to the time rate of change of momentum in that direction The flow may be compressible or incompressible, real (with friction) or ideal (frictionless), steady or unsteady moreover, the equation is not only valid along a streamline
- 6. Energy Equation Momentum Equation Relates the change in energy within the control volume Relates the overall forces on the boundary of the control volume Applicable to only steady flows in which the energy changes are negligible Applicable to steady and unsteady flows The fluid is ideal, incompressible, one dimensional Conditions within the control volume is not taken in to consideration. The theorem is useful when energy changes are known and velocity and pressure distribution are required The theorem is useful when energy changes are unknown and only overall knowledge of the flow is required Used to determine velocity distribution or pressure distribution Useful to determine the resultant force acting on the boundary of flow passage To determine the characteristics of flow when there is abrupt change of flow section ( sudden enlargement in pipe, hydraulic jump..) Useful when detailed information of the flow condition inside the control volume is not known
- 7. Application of Bernoulli's Equation for Uniform Flow interrupted by raised humbs velocity and depth of flow over the raised hump.
- 8. Specific Energy Equation We have to understand the flow condition
- 9. In order to adjust the water level in open channel “Channel Transitions” are incorporated Rise in bed elevation Drop in bed elevation Sudden enlargement in width Sudden Contraction in width The objective here in designing is to minimize the energy loss due to such channel transitions Concept of momentum , continuity and specific energy is used to solve such flow problems
- 10. Specific Energy Considering the energy correction factor= 1 and slope is insignificant The head attained by a fluid element per unit weight wrt channel bed as a datum:-
- 11. The two alternate depths represent two totally different flow regimes: slow & deep on the upper limb of the curve (sub- critical flow) & fast & shallow on the lower limb of the curve, (Super critical flow) Check this
- 13. Salient feature of critical flow Specific energy for a given discharge is minimum. The discharge for a given specific energy is maximum. The Froude number is equal to unity The velocity head is equal to one half of the hydraulic depth
- 14. Example A channel of a rectangular section, 7 m wide, discharges water at a rate of 18 m3/s with an average velocity of 3 m/s. Find: (10 points) A. Specific-energy head of the flowing water, B. Depth of water, when specific energy is minimum, C. Velocity of water, when specific energy is minimum, D. Minimum specific-energy head of the flowing water, E. Type of flow.
- 17. Home Study & Assignment Work Case 2…….When Specific energy is constant Y= f (Q) Critical depth in rectangular channels Critical depth for Non rectangular channels Computation of critical flow
- 18. 1.5. Hydraulic Jump Topics • Definition • Impulse momentum equation • Advantage of Hydraulic jump • Assumptions made for analysis of hydraulic jump
- 19. The hydraulic jump is an important feature in open channel flow and is an example of rapidly varied flow. A hydraulic jump occurs when a super-critical flow and a sub-critical flow meet. The jump is the mechanism for the two surfaces to join. They join in an extremely turbulent manner which causes large energy losses. Because of the large energy losses the energy or specific energy equation cannot be use in analysis, the momentum equation is used instead. If energy actually leaks from the system via frictional head loss the Bernoulli equation will overstate the energy available to the flow and the related predictions of velocity and depth will proportionately be in error. To recall our earlier strategy, we minimize this error by considering only short reaches of channel and only gradual transitions. In certain flow phenomena, however, we simply can no longer ignore the energy losses and we must look to alternative ways of describing the flow.
- 20. When subcritical flow accelerates into the supercritical state the transition often is smooth with gradually increasing velocity and decreasing depth bringing about a smooth drop in the water surface until the alternate depth is achieved. Any disturbance to the water surface is smoothed out by the surface or gravity wave propagation mechanism discussed earlier. In these circumstances energy losses are not great and the Bernoulli equation does a credible job of describing the changes to the flow. When supercritical flow changes to subcritical flow, however, there is no smoothing of the water surface upstream of the transition because the high downstream velocity prevents upstream diffusion of the water-surface deformation. As a result the transition to subcritical flow is sudden and marked by an abrupt discontinuity, or hydraulic jump, in the water.
- 22. Flow over weir ( Look The Linked Video)
- 23. Purposes of hydraulic jump To increase the water level on the d/s of the hydraulic structures To reduce the net up lift force by increasing the downward force due to the increased depth of water, To increase the discharge from a sluice gate by increasing the effective head causing flow For removing air pockets in a pipe line.
- 24. Analysis of Hydraulic Jump Assumptions The length of the hydraulic jump is small, consequently, the loss of head due to friction is negligible, The channel is horizontal as it has a very small longitudinal slope. The weight component in the direction of flow is negligible. The portion of channel in which the hydraulic jump occurs is taken as a control volume & it is assumed the just before & after the control volume, the flow is uniform & pressure distribution is hydrostatic. Objective: To describe (drive) geometry of channel undertaking hydraulic jump Let us consider a small reach of a channel in which the hydraulic jump occurs. The momentum of water passing through section (1) per unit time is given as:
- 25. The momentum of water passing through section (1) per unit time is given as: