Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2019-20
Module Leader
Lecturers
Luca Magri, Prof RS Cant, Dr J Jarrett and Dr J Longley
Lab Leaders
Prof H Babinsky and Dr L Xu
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Luca Magri)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. Hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr JP Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Prof RS Cant)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr JP Longley)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
Turbomachinery
Learning objectives:
- to study the characteristics of a typical centrifugal pump;
- to study the role of the velocity triangles play in the pump characteristics;
- to understand the key non-dimensional groups used to represent the pump characteristics;
- to study the effect of Reynolds number on the pump performance by varying the pump speeds and the viscosity of the working fluids;
- to observe the phenomenon of cavitation in a pump;
- to appreciate the validity and limitations of the simple dimensional analysis for the pump performance;
- to learn different ways of measuring mass flow rate;
- to appreciate the advantage and limitation of using a venturi nozzle to measure mass flow rate.
Practical information:
- Sessions will take place in the Hopkinson Laboratory in the Lent Term;
- This activity does not involve preliminary work, but a preview of the relevant lecture notes as well as the labsheets before the lab would be helpful.
Full Technical Report:
Students will have the option to submit a Full Technical Report based on the lab and research on further reading.
Nozzle and supersonic tunnel
Learning objectives:
- to study the pressure distribution in convergent-divergent nozzles for various pressure ratios;
- to observe the phenomenon of choking;
- to become familiar with the essential features of a supersonic wind tunnel;
- to understand the basic principles of a schlieren system for flow visualisation;
- to observe fundamental flow changes through a normal shock-wave;
- to appreciate the validity and limitations of one-dimensional, adiabatic, inviscid theory.
Practical information:
- Sessions will take place in the Aerolab;
- This activity doesn't involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 16/10/2019 20:08
Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2021-22
Module Leader
Lecturers
Prof R.S. Cant, Dr S.A. Scott, Dr J.P. Longley, Dr J.P. Jarrett
Lab Leaders
Prof H Babinsky and Dr L Xu
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Prof R.S. Cant)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. Hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr JP Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Dr S Scott)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr JP Longley)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
There are 2 parts of coursework, one in Michaelmas and one in Lent (and in these terms only).
The Michaelmas lab will be done live in the lab. Instructions and preparatory material will be on moodle.
You need to book the slots on Moodle early in term.
___________________
If future COVID-19-related policies affect the way that labs are being delivered, the updates will be communicated through Moodle.
Turbomachinery
Learning objectives:
- to study the characteristics of a typical centrifugal pump;
- to study the role of the velocity triangles play in the pump characteristics;
- to understand the key non-dimensional groups used to represent the pump characteristics;
- to study the effect of Reynolds number on the pump performance by varying the pump speeds and the viscosity of the working fluids;
- to observe the phenomenon of cavitation in a pump;
- to appreciate the validity and limitations of the simple dimensional analysis for the pump performance;
- to learn different ways of measuring mass flow rate;
- to appreciate the advantage and limitation of using a venturi nozzle to measure mass flow rate.
Practical information:
- Sessions will take place in the Hopkinson Laboratory in the Lent Term;
- This activity does not involve preliminary work, but a preview of the relevant lecture notes as well as the labsheets before the lab would be helpful.
Full Technical Report:
Students will have the option to submit a Full Technical Report based on the lab and research on further reading.
Nozzle and supersonic tunnel
Learning objectives:
- to study the pressure distribution in convergent-divergent nozzles for various pressure ratios;
- to observe the phenomenon of choking;
- to become familiar with the essential features of a supersonic wind tunnel;
- to understand the basic principles of a schlieren system for flow visualisation;
- to observe fundamental flow changes through a normal shock-wave;
- to appreciate the validity and limitations of one-dimensional, adiabatic, inviscid theory.
Practical information:
- Sessions will take place in the Aerolab;
- This activity doesn't involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 25/01/2022 09:39
Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2020-21
Module Leader
Lecturers
Luca Magri, Dr S Scott, Dr J Jarrett and Dr J Longley
Lab Leaders
Prof H Babinsky and Dr L Xu
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Luca Magri)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. Hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr JP Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Dr S Scott)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr JP Longley)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
There are 2 parts of coursework, one in Michaelmas and one in Lent (and in these terms only).
The Michaelmas lab will be done live in the lab. Instructions and preparatory material will be on moodle.
You need to book the slots on Moodle early in term.
___________________
If future COVID-19-related policies affect the way that labs are being delivered, the updates will be communicated through Moodle.
Turbomachinery
Learning objectives:
- to study the characteristics of a typical centrifugal pump;
- to study the role of the velocity triangles play in the pump characteristics;
- to understand the key non-dimensional groups used to represent the pump characteristics;
- to study the effect of Reynolds number on the pump performance by varying the pump speeds and the viscosity of the working fluids;
- to observe the phenomenon of cavitation in a pump;
- to appreciate the validity and limitations of the simple dimensional analysis for the pump performance;
- to learn different ways of measuring mass flow rate;
- to appreciate the advantage and limitation of using a venturi nozzle to measure mass flow rate.
Practical information:
- Sessions will take place in the Hopkinson Laboratory in the Lent Term;
- This activity does not involve preliminary work, but a preview of the relevant lecture notes as well as the labsheets before the lab would be helpful.
Full Technical Report:
Students will have the option to submit a Full Technical Report based on the lab and research on further reading.
Nozzle and supersonic tunnel
Learning objectives:
- to study the pressure distribution in convergent-divergent nozzles for various pressure ratios;
- to observe the phenomenon of choking;
- to become familiar with the essential features of a supersonic wind tunnel;
- to understand the basic principles of a schlieren system for flow visualisation;
- to observe fundamental flow changes through a normal shock-wave;
- to appreciate the validity and limitations of one-dimensional, adiabatic, inviscid theory.
Practical information:
- Sessions will take place in the Aerolab;
- This activity doesn't involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/01/2021 11:28
Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2022-23
Module Leader
Lecturers
Prof A. Agarwal, Prof S.A. Scott, Dr J. Taylor, Dr J.P. Jarrett
Lab Leaders
Prof H Babinsky and Dr J Taylor
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Dr A Agarwal)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. Hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr J Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Dr S Scott)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr J Taylor)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
There are 2 parts of coursework, one in Michaelmas and one in Lent (and in these terms only).
The Michaelmas lab will be done live in the lab. Instructions and preparatory material will be on moodle.
You need to book the slots on Moodle early in term.
___________________
If future COVID-19-related policies affect the way that labs are being delivered, the updates will be communicated through Moodle.
Turbomachinery
Learning objectives:
- to study the characteristics of a typical centrifugal pump;
- to study the role of the velocity triangles play in the pump characteristics;
- to understand the key non-dimensional groups used to represent the pump characteristics;
- to study the effect of Reynolds number on the pump performance by varying the pump speeds and the viscosity of the working fluids;
- to observe the phenomenon of cavitation in a pump;
- to appreciate the validity and limitations of the simple dimensional analysis for the pump performance;
- to learn different ways of measuring mass flow rate;
- to appreciate the advantage and limitation of using a venturi nozzle to measure mass flow rate.
Practical information:
- Sessions will take place in the Hopkinson Laboratory in the Lent Term;
- This activity does not involve preliminary work, but a preview of the relevant lecture notes as well as the labsheets before the lab would be helpful.
Full Technical Report:
Students will have the option to submit a Full Technical Report based on the lab and research on further reading.
Nozzle and supersonic tunnel
Learning objectives:
- to study the pressure distribution in convergent-divergent nozzles for various pressure ratios;
- to observe the phenomenon of choking;
- to become familiar with the essential features of a supersonic wind tunnel;
- to understand the basic principles of a schlieren system for flow visualisation;
- to observe fundamental flow changes through a normal shock-wave;
- to appreciate the validity and limitations of one-dimensional, adiabatic, inviscid theory.
Practical information:
- Sessions will take place in the Aerolab;
- This activity doesn't involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/01/2023 14:47
Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2017-18
Module Leader
Lecturers
Dr A Agarwal, Prof RS Cant, Dr J Jarrett and Dr J Longley
Lab Leaders
Prof H Babinsky and Prof R Miller
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Prof RS Cant)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr JP Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Dr A Agarwal)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr JP Longley)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
Turbomachinery
Nozzle and supersonic tunnel
Learning objectives:
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity [involves/doesn't involve] preliminary work ([estimated duration]).
Full Technical Report:
Students [will/won't] have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 06/10/2017 14:55
Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2018-19
Module Leader
Lecturers
Dr A Agarwal, Prof RS Cant, Dr J Jarrett and Dr J Longley
Lab Leaders
Prof H Babinsky and Prof R Miller
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Prof RS Cant)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr JP Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Dr A Agarwal)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr JP Longley)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
Turbomachinery
Nozzle and supersonic tunnel
Learning objectives:
Practical information:
- Sessions will take place in [Location], during week(s) [xxx].
- This activity [involves/doesn't involve] preliminary work ([estimated duration]).
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please see the Booklist for Part IIA Courses for references for this module.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 13/09/2018 14:35
Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2025-26
Module Leader
Lecturers
Prof S.A. Scott, Prof C. Hall, Dr J.P. Jarrett, Dr C Clark
Lab Leaders
Prof H Babinsky and Dr C Clark
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Dr A Agarwal)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. Hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr J Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Prof S Scott)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr J Taylor)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
There are 2 parts of coursework, one in Michaelmas and one in Lent (and in these terms only).
The Michaelmas lab will be done live in the lab. Instructions and preparatory material will be on moodle.
You need to book the slots on Moodle early in term.
___________________
If future COVID-19-related policies affect the way that labs are being delivered, the updates will be communicated through Moodle.
Turbomachinery
Learning objectives:
- to study the characteristics of a typical centrifugal pump;
- to study the role of the velocity triangles play in the pump characteristics;
- to understand the key non-dimensional groups used to represent the pump characteristics;
- to study the effect of Reynolds number on the pump performance by varying the pump speeds and the viscosity of the working fluids;
- to observe the phenomenon of cavitation in a pump;
- to appreciate the validity and limitations of the simple dimensional analysis for the pump performance;
- to learn different ways of measuring mass flow rate;
- to appreciate the advantage and limitation of using a venturi nozzle to measure mass flow rate.
Practical information:
- Sessions will take place in the Hopkinson Laboratory in the Lent Term;
- This activity does not involve preliminary work, but a preview of the relevant lecture notes as well as the labsheets before the lab would be helpful.
Full Technical Report:
Students will have the option to submit a Full Technical Report based on the lab and research on further reading.
Nozzle and supersonic tunnel
Learning objectives:
- to study the pressure distribution in convergent-divergent nozzles for various pressure ratios;
- to observe the phenomenon of choking;
- to become familiar with the essential features of a supersonic wind tunnel;
- to understand the basic principles of a schlieren system for flow visualisation;
- to observe fundamental flow changes through a normal shock-wave;
- to appreciate the validity and limitations of one-dimensional, adiabatic, inviscid theory.
Practical information:
- Sessions will take place in the Aerolab;
- This activity doesn't involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 04/06/2025 13:05
Engineering Tripos Part IIA, 3A3: Fluid Mechanics II (double module), 2023-24
Module Leader
Lecturers
Prof A. Agarwal, Prof S.A. Scott, Dr J. Taylor, Dr J.P. Jarrett
Lab Leaders
Prof H Babinsky and Dr J Taylor
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- To understand fluid flows to a level such that the pressures and resultant forces acting can be estimated in situations involving complex geometries of industrial interest at both subsonic and supersonic speed.
- To understand the effects of viscosity and heat transfer, where relevant
Objectives
As specific objectives, by the end of the course students should be able to:
- Know the concepts of stagnation temperature and stagnation pressure and be able to determine their values from a knowledge of static temperature, static pressure and Mach number.
- Know how conservation principles determine the behaviour of normal shock waves and be able to use tables to quantify that behaviour.
- Evaluate Mach number of a flow from measurements of Pitot and static pressures.
- Determine flow patterns in nozzles under the assumption of one dimensionality, using tables.
- Know how Mach number and other flow properties change under the influence of friction or heat exchange, and be able to quantify this using tables.
- Know how to construct and interpret x-t diagrams for unsteady ID flow.
- Quantify the behaviour of hydraulic jumps and infinitesimal waves in shallow water.
- Understand the influence of the speed of sound on two-dimensional compressible flow behaviour.
- Apply the two-dimensional method of characteristics for simple flows and flows involving reflection/cancellation.
- Understand the origin of oblique shock waves and their reflection.
- Apply the preceding ideas to practical flows via shock-expansion theory, linearised method of characteristics and linearised potential theory.
- Know how to construct and use numerical solution methods for the equations of fluid flow using finite difference and finite volume approximations
- Know how to estimate the accuracy and analyse the stability of numerical schemes
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Content
One-dimensional Compressible Flow (12L): 2 lectures/week, weeks 1-6 Michaelmas term (Dr A Agarwal)
- Steady, adiabatic and inviscid flow; speed of sound; reversibility; the stagnation state; the effect of area variation on subsonic/supersonic flow, choking; normal shock waves; flow patterns in nozzles; use of table for isentropic flow and for shock waves.
- Fanno and Rayleigh line processes for the effects of friction and heat exchange.
- Introduction to unsteady flow. Hydraulic analogy for steady compressible flow; speed of waves in shallow water; the hydraulic jump; the venturi flume; weirs.
Two-dimensional Compressible Flow (8L): 2 lectures/week, weeks 7-8 Michaelmas term and weeks 1-2 Lent term (Dr J Jarrett)
- Method of characteristics, expansion fan and compression ramp.
- Oblique shock waves, strong and weak solutions.
- Shock-expansion theory
- Potential equation and linearisation.
Equations of Fluid Flow and their Numerical Solution (6L): 2 lectures/week, weeks 3-5 Lent term (Dr S Scott)
- Numerical solution techniques; finite difference approximations; finite volume approximations; order of accuracy, diffusion and dispersion errors; stability considerations for time iterative techniques
- Classification of equations; numerical solution of the Euler equations, nonlinearity and shock waves
Turbomachinery (6L): 2 lectures/week, weeks 6-8 Lent term (Dr J Taylor)
- Identify and understand the operation of different types of turbomachinery.
- Analyse turbomachinery performance.
- Understand the causes of irreversibilities within the blade passages and their affects on the overall efficiency.
- Analyse compressible flow through turbomachines.
Coursework
There are 2 parts of coursework, one in Michaelmas and one in Lent (and in these terms only).
The Michaelmas lab will be done live in the lab. Instructions and preparatory material will be on moodle.
You need to book the slots on Moodle early in term.
___________________
If future COVID-19-related policies affect the way that labs are being delivered, the updates will be communicated through Moodle.
Turbomachinery
Learning objectives:
- to study the characteristics of a typical centrifugal pump;
- to study the role of the velocity triangles play in the pump characteristics;
- to understand the key non-dimensional groups used to represent the pump characteristics;
- to study the effect of Reynolds number on the pump performance by varying the pump speeds and the viscosity of the working fluids;
- to observe the phenomenon of cavitation in a pump;
- to appreciate the validity and limitations of the simple dimensional analysis for the pump performance;
- to learn different ways of measuring mass flow rate;
- to appreciate the advantage and limitation of using a venturi nozzle to measure mass flow rate.
Practical information:
- Sessions will take place in the Hopkinson Laboratory in the Lent Term;
- This activity does not involve preliminary work, but a preview of the relevant lecture notes as well as the labsheets before the lab would be helpful.
Full Technical Report:
Students will have the option to submit a Full Technical Report based on the lab and research on further reading.
Nozzle and supersonic tunnel
Learning objectives:
- to study the pressure distribution in convergent-divergent nozzles for various pressure ratios;
- to observe the phenomenon of choking;
- to become familiar with the essential features of a supersonic wind tunnel;
- to understand the basic principles of a schlieren system for flow visualisation;
- to observe fundamental flow changes through a normal shock-wave;
- to appreciate the validity and limitations of one-dimensional, adiabatic, inviscid theory.
Practical information:
- Sessions will take place in the Aerolab;
- This activity doesn't involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
P4
Understanding use of technical literature and other information sources.
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 30/05/2023 15:18
Engineering Tripos Part IIA, 3A1: Fluid Mechanics I (double module), 2020-21
Module Leader
Lecturers
Prof H Babinsky, Prof P G Tucker, Prof S Hochgreb and Dr J Li
Lab Leaders
Dr M S Davies Wykes, Prof P G Tucker
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- Develop an understanding of when and where fluid flows can be modelled as incompressible and inviscid.
- Develop simple analytical and computational methods to solve incompressible and inviscid flows, and build up physical understanding through a range of practical examples.
- Introduce the effects of viscosity, and discuss boundary layer flows in some detail.
- Bring the ideas developed together in two applications sections, which consider the aerodynamics of aircraft wings and road vehicles.
Objectives
As specific objectives, by the end of the course students should be able to:
- Know when and where incompressible fluid flows can be modelled as irrotational.
- For two-dimensional incompressible flow, use the complex potential to determine the velocity and pressure distribution in simple geometries eg. corner flow.
- For two-dimensional incompressible flow, superimpose elementary solutions to calculate velocity and pressure distributions in a range of practical flows.
- For two-dimensional incompressible flow, know that the panel method leads to an efficient computational scheme.
- For two-dimensional incompressible flow, understand the relationship between circulation and lift.
- Use images to investigate ground effects and the influence of wind-tunnel walls.
- Use elementary solutions to calculate velocity and pressure in some simple three-dimensional flows.
- Use vortex dynamics to explain the development of simple three-dimensional flows.
- For boundary layer flows, understand the coupling between the viscous-dominated near-field flow and the inviscid far-field.
- Understand classical and integral solution techniques.
- Understand the difference between laminar and turbulent flows and transition.
- Understand the nature of flow around an aircraft.
- Understand the interaction between lift and induced velocity.
- Estimate the lift and drag of aircraft wings
- Qualitatively understand the effects of viscosity on the flow around airfoils and wings
- Describe the physical features of the flow around a road vehicle.
- Understand the origins of the aerodynamic forces on a road vehicle
- Explain how the aerodynamic forces are affected by road vehicle shape.
Content
Incompressible Flow (10L); 2 lectures/week, weeks 1-5 Michaelmas term (Prof S Hochgreb)
- Irrotational flow and the velocity potential.
- Two-dimensional flow:stream function and streamline; complex potential; sources, sinks and vortices; superposition of elementary sources to determine real flows; panel method; circulation and lift; use of images.
- Three-dimensional flow:sources and sinks; vorticity in 3D, Kelvin's circulation theorem.
- Viscous effects: Navier Stokes equation, vorticity equation.
Boundary Layer Flows (10L); 2 lectures/week, weeks 6-8 Michaelmas term and 1-2 Lent (Dr J Li)
- The boundary layer equations.
- Laminar boundary layers, similarity solutions
- Thwaites method, numerical methods.
- Turbulent boundary layers, the log law.
- Turbulent boundary layers with roughness
- Pipe flows
Applications I - Aerofoils and Wings (8L); 2 lectures/week, weeks 3-6 Lent term (Prof H Babinsky)
Two-dimensional aerofoil flows:
- modelling assumptions;
- vortex sheet panel method;
- thin aerofoil theory;
- lumped parameter modelling;
- viscous effects and stall.
Three dimensional wing flows:
- general features;
- panel methods in 3D;
- lifting line theory;
- lumped parameter modelling;
- wing stall;
Applications II - Aerodynamics of Road Vehicles (4L); 2 lectures/week, weeks 7-8 Lent term (Prof P G Tucker)
- Review of fundamental concepts : bluff-body aerodynamics, friction vs pressure drag, 2 and 3 dimensional bodies, ground effect
- Drag of passenger cars ; boat-tailing, tail shapes, skirts
- Lift/downforce: spoilers, wings, diffusers
- Drag of haulage vehicles: tractor/trailer junction, trailer shape effects, cross-wind stability .
Coursework
Flow Around Bodies of Revolution
Learning objectives:
- To measure the drag forces on three bodies of revolution over a range of flow speeds.
- To observe some aspects of the flow structures with oil flow and a tuft mast.
- To obtain curves of drag coefficient versus Reynolds number.
- To find the critical Reynolds Number at which the flow pattern on a sphere changes from a high drag regime to a low drag one.
Practical information:
- Due to COVID-19 restrictions, data normally obtained in the laboratory may be provided by other means.
- Any practical sessions will take place in the 3rd-floor Aerodynamics Laboratory, during Michaelmas week(s) 1-4 (approx).
- This activity does not involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Turbulent Boundary Layer
Learning objectives:
- To observe with the aid of a hot-wire anemometer and a stethoscope the transition from a laminar to a turbulent boundary layer on a flat plate under various conditions.
- To obtain the transition Reynolds numbers.
-
To measure the angle of the turbulent wedge that is formed downstream of a roughnesselement.
-
To measure the mean and turbulence profiles of the boundary layer when it is fully turbulent.
-
To use the mean flow velocity profile to estimate the skin friction coefficient.
Practical information:
- Due to COVID-19 restrictions, data normally obtained in the laboratory may be provided by other means.
- Any practical sessions will take place in the 2nd-floor Aerodynamics Laboratory, during a limited period in the Lent term.
- This activity does not involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
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Apply appropriate quantitative science and engineering tools to the analysis of problems.
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Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
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Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
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Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
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A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
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Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
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A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
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A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
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An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 21/09/2020 15:13
Engineering Tripos Part IIA, 3A1: Fluid Mechanics I (double module), 2024-25
Module Leader
Lecturers
Prof H Babinsky, Dr J Li, Prof M Juniper
Lab Leaders
Dr S Mandre, Prof P Tucker
Timing and Structure
Michaelmas and Lent. 32 lectures.
Aims
The aims of the course are to:
- Develop an understanding of when and where fluid flows can be modelled as incompressible and inviscid.
- Develop simple analytical and computational methods to solve incompressible and inviscid flows, and build up physical understanding through a range of practical examples.
- Introduce the effects of viscosity, and discuss boundary layer flows in some detail.
- Bring the ideas developed together in two applications sections, which consider the aerodynamics of aircraft wings and road vehicles.
Objectives
As specific objectives, by the end of the course students should be able to:
- Know when and where incompressible fluid flows can be modelled as irrotational.
- For two-dimensional incompressible flow, use the complex potential to determine the velocity and pressure distribution in simple geometries eg. corner flow.
- For two-dimensional incompressible flow, superimpose elementary solutions to calculate velocity and pressure distributions in a range of practical flows.
- For two-dimensional incompressible flow, know that the panel method leads to an efficient computational scheme.
- For two-dimensional incompressible flow, understand the relationship between circulation and lift.
- Use images to investigate ground effects and the influence of wind-tunnel walls.
- Use elementary solutions to calculate velocity and pressure in some simple three-dimensional flows.
- Use vortex dynamics to explain the development of simple three-dimensional flows.
- For boundary layer flows, understand the coupling between the viscous-dominated near-field flow and the inviscid far-field.
- Understand classical and integral solution techniques.
- Understand the difference between laminar and turbulent flows and transition.
- Understand the nature of flow around an aircraft.
- Understand the interaction between lift and induced velocity.
- Estimate the lift and drag of aircraft wings
- Qualitatively understand the effects of viscosity on the flow around airfoils and wings
- Describe the physical features of the flow around a road vehicle.
- Understand the origins of the aerodynamic forces on a road vehicle
- Explain how the aerodynamic forces are affected by road vehicle shape.
Content
Incompressible Flow (10L); 2 lectures/week, weeks 1-5 Michaelmas term (Prof M Juniper)
- Irrotational flow and the velocity potential.
- Two-dimensional flow:stream function and streamline; complex potential; sources, sinks and vortices; superposition of elementary sources to determine real flows; panel method; circulation and lift; use of images.
- Three-dimensional flow:sources and sinks; vorticity in 3D, Kelvin's circulation theorem.
- Viscous effects: Navier Stokes equation, vorticity equation.
- Recorded lectures will be provided.
Boundary Layer Flows (10L); 2 lectures/week, weeks 6-8 Michaelmas term and 1-2 Lent (Dr J Li)
- The boundary layer equations.
- Laminar boundary layers, similarity solutions
- Thwaites method, numerical methods.
- Turbulent boundary layers, the log law.
- Turbulent boundary layers with roughness
- Pipe flows
Applications I - Aerofoils and Wings (8L); 2 lectures/week, weeks 3-6 Lent term (Prof H Babinsky)
Two-dimensional aerofoil flows:
- modelling assumptions;
- vortex sheet panel method;
- thin aerofoil theory;
- lumped parameter modelling;
- viscous effects and stall.
Three dimensional wing flows:
- general features;
- panel methods in 3D;
- lifting line theory;
- lumped parameter modelling;
- wing stall;
Applications II - Aerodynamics of Road Vehicles (4L); 2 lectures/week, weeks 7-8 Lent term (tbc)
- Review of fundamental concepts : bluff-body aerodynamics, friction vs pressure drag, 2 and 3 dimensional bodies, ground effect
- Drag of passenger cars ; boat-tailing, tail shapes, skirts
- Lift/downforce: spoilers, wings, diffusers
- Drag of haulage vehicles: tractor/trailer junction, trailer shape effects, cross-wind stability .
Coursework
Flow Around Bodies of Revolution
Learning objectives:
- To measure the drag forces on three bodies of revolution over a range of flow speeds.
- To observe some aspects of the flow structures with oil flow and a tuft mast.
- To obtain curves of drag coefficient versus Reynolds number.
- To find the critical Reynolds Number at which the flow pattern on a sphere changes from a high drag regime to a low drag one.
Practical information:
- Due to COVID-19 restrictions, data normally obtained in the laboratory may be provided by other means.
- Any practical sessions will take place in the 3rd-floor Aerodynamics Laboratory, during Michaelmas week(s) 1-4 (approx).
- This activity does not involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Turbulent Boundary Layer
Learning objectives:
- To observe with the aid of a hot-wire anemometer and a stethoscope the transition from a laminar to a turbulent boundary layer on a flat plate under various conditions.
- To obtain the transition Reynolds numbers.
-
To measure the angle of the turbulent wedge that is formed downstream of a roughnesselement.
-
To measure the mean and turbulence profiles of the boundary layer when it is fully turbulent.
-
To use the mean flow velocity profile to estimate the skin friction coefficient.
Practical information:
- Due to COVID-19 restrictions, data normally obtained in the laboratory may be provided by other means.
- Any practical sessions will take place in the 2nd-floor Aerodynamics Laboratory, during a limited period in the Lent term.
- This activity does not involve preliminary work.
Full Technical Report:
Students will have the option to submit a Full Technical Report.
Booklists
Please refer to the Booklist for Part IIA Courses for references to this module, this can be found on the associated Moodle course.
Examination Guidelines
Please refer to Form & conduct of the examinations.
UK-SPEC
This syllabus contributes to the following areas of the UK-SPEC standard:
Toggle display of UK-SPEC areas.
GT1
Develop transferable skills that will be of value in a wide range of situations. These are exemplified by the Qualifications and Curriculum Authority Higher Level Key Skills and include problem solving, communication, and working with others, as well as the effective use of general IT facilities and information retrieval skills. They also include planning self-learning and improving performance, as the foundation for lifelong learning/CPD.
IA1
Apply appropriate quantitative science and engineering tools to the analysis of problems.
KU1
Demonstrate knowledge and understanding of essential facts, concepts, theories and principles of their engineering discipline, and its underpinning science and mathematics.
KU2
Have an appreciation of the wider multidisciplinary engineering context and its underlying principles.
E1
Ability to use fundamental knowledge to investigate new and emerging technologies.
E2
Ability to extract data pertinent to an unfamiliar problem, and apply its solution using computer based engineering tools when appropriate.
E3
Ability to apply mathematical and computer based models for solving problems in engineering, and the ability to assess the limitations of particular cases.
P1
A thorough understanding of current practice and its limitations and some appreciation of likely new developments.
P3
Understanding of contexts in which engineering knowledge can be applied (e.g. operations and management, technology, development, etc).
US1
A comprehensive understanding of the scientific principles of own specialisation and related disciplines.
US2
A comprehensive knowledge and understanding of mathematical and computer models relevant to the engineering discipline, and an appreciation of their limitations.
US3
An understanding of concepts from a range of areas including some outside engineering, and the ability to apply them effectively in engineering projects.
Last modified: 26/07/2024 14:34
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