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1 INTRODUCTION

1.1 The safety of hydrogen

The safety of hydrogen is known to be of vital importance to the onset and further development of the hydrogen economy. The development and introduction of hydrogen technologies, as well as the level of public acceptance of hydrogen applications, are presently being constrained by safety barriers. Hydrogen is perceived to be dangerous because it has some properties that make its behaviour during accidents different from that of most other combustible gases. It may cause material embrittlement and diffuses more easily through many conventional materials used for pipelines and vessels. Gaps that are normally small enough to seal other gases safely are found to leak hydrogen profusely. Unlike other combustible gases, it has a Joule-Thompson inversion temperature (i.e. the temperature above which the Joule-Thompson coefficient becomes negative and expansion leads to warming instead of cooling) which is well below that of many applications involving gaseous hydrogen. This makes hydrogen more susceptible to ignition after sudden releases from high pressure containment. When hydrogen's greatest safety asset, buoyancy, is not properly taken into account in the design of infrastructures and technologies for production, storage, transportation and utilisation, it becomes more dangerous than conventional fuels such as gasoline, LPG and natural gas. Many countries' building codes, for example, require garages to have ventilation openings near the ground to remove gasoline vapour, but high-level ventilation is not always addressed. As a result, even very slow releases of hydrogen in such buildings will inevitably lead to the formation of an explosive mixture, initially at the ceiling-level. The safety and combustion literature indicates that releases of hydrogen are more likely to cause explosions than releases of today's fossil fuels do. Moreover, combustion insights have revealed that burning behaviour becomes far less benign when the limiting reactant is also the more mobile constituent of a combustible mixture [1]. Owing to the extreme lightness of the molecule, this is particularly true with hydrogen. A mixture of hydrogen with air has a lower flammability limit which is higher than that of LPG (1.7% [2]) or gasoline (1.0% [2]), but the flammable range is very wide (4-75%) [2]. In the concentration range of 15-45%, the ignition energy of hydrogen is one-tenth of that of gasoline and the quenching gap, i.e. the smallest spacing through which a flame can propagate, is considerably smaller for hydrogen (0.61 mm [3]) than for today's fossil fuels (2.0 mm for methane, 1.8 mm for ethane and propane [3]). This implies that requirements for mitigation, such as flame arrestors and similar equipment, must be more stringent.

For many decades, hydrogen has been used extensively in the process industries (e.g. refineries and ammonia synthesis) and experience has shown that it can be handled safely in industrial applications as long as appropriate standards, regulations and best practices are being followed. This is particularly true for the nuclear industry, where the high safety standards have resulted in the development of sophisticated hydrogen mitigation technologies [4]. Interestingly, these technologies rely on the same anomalous properties, such as the large diffusivity and extreme lightness that make hydrogen so different compared to conventional fuels. For example, these properties are used to preclude the formation of flammable mixtures after accidental hydrogen releases, and to prevent further development towards more dangerous concentrations, once the flammability limit is exceeded (hydrogen removal by buoyancy, application of catalytic re-combiners, or benign burns, dilution by mixing with an inert gas, e.g. steam). This experience, however, is very specific and cannot easily be transferred to the daily use of new hydrogen technologies by the general public. Firstly, because new technologies involve the use of hydrogen under circumstances that are not yet addressed by research, or taken into account by existing codes and recommended practices. For example, vehicle demonstration projects by manufacturers involve the use of hydrogen as a compressed gas at extremely high pressures (over 350 bar), or, in liquefied form at an extremely low temperature (-253 ^�C). There is no precedent for the safe handling of hydrogen by the general public at such conditions and current codes and standards for hydrogen were not written with vehicle fueling in mind. Secondly, in industries, hydrogen is handled by people who received specific training at a professional level, and, installations involving hydrogen are subject to professional safety management and inspection. The hydrogen economy, on the other hand, involves the use of hydrogen technologies by general consumers and a similar dedication to safety, e.g. training general consumers to a professional level, would become impractical. The safety of hydrogen technologies and applications must therefore be ensured before entering the consumer market.

Presently, public acceptance and understanding of the safety of hydrogen is such that accidents with hydrogen not only cause resistance to its use, but also cause people to disregard social, economic, political and environmental improvements that may result from a hydrogen economy. Currently, hydrogen is being produced from fossil fuels, particularly from natural gas by steam reforming. But it can also be produced from a variety of other sources (e.g. nuclear, geothermal, solar, wind, hydroelectric plants, biomass, etc.), some of which can operate at large and small scale in areas that are currently suffering fuel poverty. The replacement of fossil fuels by hydrogen from alternative sources will not only benefit people in fuel poverty areas by reducing their dependency on the diminishing resource of imported fossil fuels - it might also enable fossil fuel importing economies to become leading exporters of hydrogen [5]. The consequential demand for ever increasing quantities of hydrogen, and the possibility of producing hydrogen in fuel poverty areas will lead to social improvement by employment opportunities [5]. The replacement of fossil fuels by hydrogen also contributes to averting disastrous effects from pollutant emissions and global warming. It is well-known that combustion products from fossil fuels cause health problems and acid rain due to emissions of particulates, carbon monoxide, sulfur and nitrogen oxides, and other local air pollutants. Continued fossil fuel consumption will not only increase the number of pollution related deaths in cities like Delhi, Beijing and Mexico City [5], but also the magnitude of problems involving reduced agricultural productivity and the loss of biodiversity [5]. There is also an increasing scientific community which has come to the belief that the use of fossil fuels is causing the world's climate to change because of carbon dioxide emissions [5]. Hydrogen is a clean fuel with no carbon dioxide emissions and can be produced by carbon-free or carbon-neutral processes. When utilised in combustion processes, it produces water only, and reduced amounts of nitrogen oxides.

1.2 Educational and training programmes in hydrogen safety

Educational and training programmes in hydrogen safety are considered to be a key instrument in lifting barriers imposed by the safety of hydrogen. Owing to the impracticality of training general consumers to a professional level in hydrogen safety, such training programmes should primarily target professionals engaged in the conception or creation of new knowledge, products, processes, methods, systems, regulations and project management in the hydrogen economy. Between this community of scientific and engineering professionals, including entrepreneurs developing hydrogen technologies, and general consumers of hydrogen applications, there is another group of vital importance to the successful introduction of hydrogen into our social infrastructure that needs to be targeted as well. These are the educators, local regulators, insurers, fire brigades and rescue personnel, investors, and public service officials. Their involvement is indispensable to the acceptance and use of the new technology by the general public, and hence a consolidated consumer market as the principal driving force behind the hydrogen economy. Without their involvement there will be no transition from our present fossil-fuel economy into a sustainable one based on hydrogen. With this in mind, the European Network of Excellence `Safety of Hydrogen as an Energy Carrier' (NoE HySafe) has begun to establish the e-Academy of hydrogen safety.

The e-Academy of hydrogen safety is part of the dissemination cluster of the NoE HySafe, whose objectives are [6,7]: (i) to achieve common understanding and common approaches for addressing hydrogen safety issues; (ii) to integrate experience and knowledge within industrial organisations familiar with hydrogen processing technology and research organisations with facilities for experimental research and exploitation of results from numerical prediction tools; (iii) to integrate and harmonise the fragmented research base; (iv) to provide contributions based on safety and risk studies to EU-legal requirements, standards, codes of practice and guidelines; (v) to support education and training in hydrogen safety to achieve an improved technical culture for the safe handling of hydrogen as an energy carrier. To establish the e-Academy of hydrogen safety, the following activities are employed: (i) development of an international curriculum on hydrogen safety engineering; (ii) coherent implementation of teaching/learning on hydrogen safety into existing courses and modules; (iii) development of new courses and modules, including optional modules for existing safety courses; (iv) joint training exploiting different modes of education: short courses, summer schools, block-releases, continuous professional development courses, etc.; (v) creation of a pool of specialists from both academic and non-academic institutions able to deliver teaching on hydrogen safety engineering at the highest level by introduction of latest research results into the educational process; (vi) promotion of academic mobility programmes, e.g. by integration of regional academic programmes into a common European course on hydrogen safety engineering with the possibility to distribute course modules in different countries; (vii) joint supervision of research (PhD) students; (viii) creation of a database of organisations working in hydrogen industry to form a market of potential trainees and to disseminate the results from mutual activities of the network; (ix) and the introduction of joint distance teaching/learning courses in hydrogen safety on the international market.

Due to the absence of a curriculum on the subject, a substantial effort is being devoted to the development of an International Curriculum on Hydrogen Safety Engineering as a first step in the establishment of the e-Academy of hydrogen safety. The development of the International Curriculum on Hydrogen Safety Engineering is led by the University of Ulster and carried out in cooperation with international partners from four other universities (Universidad Politecnica de Madrid, Spain; University of Pisa, Italy; Warsaw University of Technology, Poland; University of Calgary, Canada), three research institutions (Forschungszentrum Karlsruhe and Forschungszentrum Juelich, Germany; Building Research Establishment, United Kingdom), one enterprise (GexCon, Norway) and one foundation (Det Norske Veritas, Norway). This development is also aided by experts from within the NoE HySafe and external experts from all over the world (see Table 1), representing educational institutions, research organisations, industrial corporations and governmental bodies. This report exposes the current structure of the International Curriculum on Hydrogen Safety Engineering, the motivation behind it, and further steps in the development of a system of hydrogen safety education and training are described.

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Table 1: List of contributors to the International Curriculum on Hydrogen Safety Engineering.
Adams, P.	Volvo Technology	Sweden
Amyotte, P.R.	Dalhousie University	Canada
Baraldi, D.	The European Commission's Joint Research Center	The Netherlands
Barthelemy, H.	Air Liquide	France
Bauwens, L.	University of Calgary	Canada
Bell, J.B.	Lawrence Berkeley National Laboratories	United States of America
Bengaouer, A.	Commissariat a l Energie Atomique	France
Bjerketvedt, D.	Telemark University	Norway
Bradley, D.	University of Leeds	United Kingdom
Braken, A.M. van den	Akzo-Nobel Safety Services	The Netherlands
Breitung, W.	Institut fur Kern- und Energietechnik, Forschungszentrum Karlsruhe	Germany
Calhoun, D.	Commissariat a l Energie Atomique	France
Cant, R.S.	University of Cambridge	United Kingdom
Carcassi, M.	University of Pisa	Italy
Crespo, A.	Universidad Polytecnica de Madrid	Spain
Dahoe, A.E.	University of Ulster	United Kingdom
Donze, M.	Delft University of Technology	The Netherlands
Dorofeev, S.B.	FM Global	United States of America
Engebo, A.	Det Norske Veritas	Norway
Fairweather, M.	University of Leeds	United Kingdom
Faudou, J.-Y.	Air Liquide	France
Gallego, E.	Universidad Polytecnica de Madrid	Spain
Garcia, J.	Universidad Polytecnica de Madrid	Spain
Hansen, O.	GexCon	Norway
Hawksworth, S.	Health and Safety Laboratory	United Kingdom
Hayashi, K.	Aoyama Gakuin University	Japan
Hirano, T.	Chiba Institute of Science	Japan
Jordan, T.	Institut fur Kern- und Energietechnik, Forschungszentrum Karlsruhe	Germany
Josephson, B.D.	University of Cambridge	United Kingdom
Kirillov, I.	Kurchatov Institute	Russia
Kuhl, A.L.	Lawrence Livermore National Laboratories	United States of America
Kumar, S.	Building Research Establishment	United Kingdom
Law, C.K.	Princeton University	United States of America
Lee, J.H.S.	McGill University	Canada
Lelyakin, A.	Institut fur Kern- und Energietechnik, Forschungszentrum Karlsruhe	Germany
Makarov, D.V.	University of Ulster	United Kingdom
Makhviladze, G.	University of Central Lancashire	United Kingdom
Marangon, A.	University of Pisa	Italy
Martinfuertes, F.	Universidad Polytecnica de Madrid	Spain
Migoya, E.	Universidad Polytecnica de Madrid	Spain
Molkov, V.V.	University of Ulster	United Kingdom
Nash, J.F., Jr.	Princeton University	United States of America
Newsholme, G.	Health and Safety Excecutive	United Kingdom
Nilsen, S.	Norsk Hydro	Norway
Palliere, H.	Commissariat a l Energie Atomique	France
Pasman, H.J.	Delft University of Technology	The Netherlands
Reinecke, E.	Forschungszentrum Juelich	Germany
Roekaerts, D.J.E.M.	Delft University of Technology	The Netherlands
Schitter, C.	BMW	Germany
Schmidtchen, U.	Bundesanstalt für Materialforschung und -prüfung	Germany
Schneider, H.	Fraunhofer Institut für Chemische Technologie	Germany
Shebeko, Yu. N.	All-Russian Scientific Research Institute for Fire Protection	Russia
Shepherd, J.E.	California Institute of Technology	United States of America
Shirvill, L.	Shell Global Solutions	United Kingdom
Simmie, J.M.	National University of Ireland	Ireland
Skjold, T.	University of Bergen/GexCon	Norway
Stoecklin, M.	BMW	Germany
Tam, V.Y.H.	British Petroleum	United Kingdom
Tchouvelev, A.V.	Tchouvelev & Associates	Canada
Teodorczyck, A.	Warsaw University of Technology	Poland
Tsuruda, T.	NRIFD	Japan
Venetsanos, A.G.	National Centre for Scientific Research Demokritos	Greece
Verfondern, K.	Forschungszentrum Juelich	Germany
Wen, J.X.	Kingston University London	United Kingdom
Westbrook, C.K.	Lawrence Livermore National Laboratories	United States of America
Williams, F.A.	University of California, San Diego	United States of America
Wurster R.	L-B-Systemtechnik	Germany
Zalosh R.G.	Worcester Polytechnic Institute	United States of America

1.3 The role of hydrogen safety education in the transition towards a hydrogen economy

Sufficient and well-developed human resources in hydrogen safety and related key areas are of vital importance to the emerging hydrogen economy. With our present fossil-fuel based economy increasingly being replaced by a hydrogen economy, a shortfall in such knowledge capacity will hamper Europe's innovative strength and productivity growth. A lack of professionals with expert knowledge in hydrogen safety and related key areas will not only impose a serious setback on innovative developments required to propel this transition, but also thwart ongoing efforts to achieve public acceptance of the new technology. Recently, the European Commission identified a shortage of experts in the key disciplines (natural sciences, engineering, technology [8,9,10] relevant to hydrogen safety. The workforce in R&D is presently relatively low, as researchers account for only 5.1 in every thousand of the workforce in Europe, against 7.4 in the US and 8.9 in Japan [10,11]. An even larger discrepancy is observed if one considers only the number of corporate researchers employed in industry: 2.5 in every thousand in Europe, against 7.0 in the US and 6.3 in Japan [9]. Moreover, the number of young people attracted to careers in science and research appears to be decreasing. In the EU, 23% of the people aged between 20 and 29 years are in higher education, compared to 39% in the USA [12]. Knowing that research is a powerful driving force for economic growth, and a continuous supply of a skilled workforce is of paramount importance to the emerging hydrogen economy, this situation calls for drastic improvement.

To explore possibilities for improvement it would be helpful to consider what might have caused this situation in the first place. Firstly, there are the quality and attractiveness of Europe for investments in research and development in relation to that of other competing knowledge economies. The quality of research, and the number of young people embarking on higher education in natural sciences, engineering, and technology, depend primarily on investments made in R&D-activities. Presently, this amounts to 1.96% of GDP in Europe, against 2.59% in the United States of America, 3.12% in Japan and 2.91% in Korea. The gap between the United States of America and Europe, in particular, is more than 120 billion euro a year [8], with 80% of it due to the difference in business expenditure in R&D. At this point it is important to notice that the quality of the European research base will not improve, unless larger investments are made in R&D. It has been diagnosed [13] that multinational companies accounting for the greater share of business R&D expenditure, increasingly tend to invest on the basis of a global analysis of possible locations. This results in a growing concentration of transnational R&D expenditure in the United States of America. Moreover, there appears to be a decline in the global attractiveness of Europe as a location for investment R&D as compared to the United States of America. This alarming development could be reversed by improving the quality of the European research base, such that corporate investments in R&D are increased to 3% of GDP in Europe [13]. Secondly, there is the problem of a retiring science and technology workforce that needs to be succeeded by a younger generation of experts. The identified lack of experts in natural sciences, engineering, and technology creates an unstable situation for investment in R&D. This is particularly true if one considers that innovative developments take place over a timespan of several years. No investor will commission research projects to a retiring workforce without a prospect of succession by a capable younger generation. Thirdly, there is the problem of changes in the skill-set sought by employers and investors. The purpose of science and engineering education is to provide the graduate with sufficient skills to meet the requirements of the professional career, and a broad enough basis to acquire additional skills as needed. Because of the transitional nature of the hydrogen economy, and the consequential development and implementation of new technologies, the skill-set sought by employers is expected to change more rapidly than ever before. This phenomenon has already manifested itself in the information technology sector, and is anticipated to occur in the hydrogen economy as well. Science and engineering education related to the hydrogen economy must therefore be broad and robust enough, such, that when today's expert-skills have become obsolete, graduates possess the ability to acquire tomorrow's expert-skills. The International Curriculum on Hydrogen Safety Engineering, aims at tackling these three causes of detriment to Europes research base and innovation strength by extracting the state-of-the-art in hydrogen safety and related key areas, and by the rapid dissemination of this knowledge at all levels in higher and further education and training. According to the Strategic Research Agenda [14], which acts as a guide for defining a comprehensive research programme that will mobilise stakeholders and ensure that European competences are at the forefront of science and technology worldwide, education will continue to play a pivotal role in spreading hydrogen applications to the broader public until 2050. In the short term outlook from 2005 to 2015, training and education efforts are needed to build the necessary human resources to lead research and to allow a steady stream of trained scientists and technicians to develop the area. The Workgroup on Cross Cutting Issues [15], dealing primarily with the non-technical barriers to the successful implementation of the deployment strategy for hydrogen and fuel cells in Europe, indicates that educational and training efforts are needed during this period to avoid any dissonances that might hinder the building of consumer and non-technical executive confidence. The Workgroup on Cross Cutting Issues [15] has estimated that during the framework 7 period (2007-2013), the educated staff needed may amount to 500 new graduates from postgraduate studies on an annual basis in all of Europe.

1.4 The International Curriculum on Hydrogen Safety Engineering

The hydrogen economy requires professionals with a postgraduate degree dedicated to hydrogen safety, which is a subset of the aforementioned 500 new graduates. A preliminary study (see Section 1.5) indicates that this subset amounts to 119 graduates on an annual basis. Because graduates in hydrogen safety will be involved in all aspects of the hydrogen economy to ensure safety, it is important that the following issues are taken into account by the curriculum:

�: what kind of organisations will employ graduates in hydrogen safety (process industry, energy industry, civil works, aerospace industry, automotive industry, transport and distribution, fire and rescue brigades, insurance, teaching institutions, research institutions, legislative bodies, etc.),
�: at what level will graduates in hydrogen safety operate within the organisation (consulting, manufacture, design, teaching, research, operation, construction, legislation, etc.), and,
�: which mode of education is the most appropriate to match the skill-set sought at the various levels of engagement within these organisations (undergraduate education, postgraduate degree, continuing professional development, short courses, etc.).

Click here to view figure. Figure 1: Hydrogen safety in relation to other branches of engineering science.

Click here to view figure. Figure 2: The Hysafe activity matrix.

Moreover, the undergraduate programme should be well-rounded in the engineering science core (see Figure 1) and supplemented by topics and additional courses with an emphasis on hydrogen safety. Duplication of educational efforts may be avoided by defining hydrogen safety engineering in relation to other branches of engineering, and cross-fertilisation with existing engineering programmes may be achieved by the introduction of topics relevant to hydrogen safety into the engineering science core. The postgraduate programme consists of specialised courses covering the nodes of the HySafe activity matrix shown in Figure 2. Because the topics connected to the nodes in Figure 2 are subject to continuous development as the hydrogen economy evolves, the curriculum needs to be comprehensive enough to absorb these changes as new knowledge becomes available.

To comply with the aforementioned requirements, the International Curriculum on Hydrogen Safety Engineering is designed to consist of basic modules, fundamental modules, and applied modules. This approach was inspired by Magnusson et al. [16], who adopted a similar approach for the development of a model curriculum for fire safety engineering. The current modular structure is summarised in Table 2, and the current detailed topical content of the International Curriculum on Hydrogen Safety Engineering is given in subsequent sections.

The five basic modules, i.e. thermodynamics; chemical kinetics; fluid dynamics; heat and mass transfer; solid mechanics, are intended for undergraduate instruction (although these modules contain topics belonging to the postgraduate level). They are similar to any other undergraduate course in the respective subject areas, but comprehensive enough to provide a broad basis for dealing with hydrogen safety issues involving hydrogen embrittlement, unscheduled releases of liquefied and gaseous hydrogen, accidental ignition and combustion of hydrogen, etc. The purpose of these modules is twofold. Firstly, to enable the coupling of knowledge relevant to hydrogen safety into existing engineering curricula, and secondly, to support the knowledge framework contained in the fundamental and applied modules.

The six fundamental modules, i.e. introduction to hydrogen as an energy carrier; fundamentals of hydrogen safety; release, mixing and distribution; hydrogen ignition; hydrogen fires; explosions: deflagrations and detonations, form the backbone of hydrogen safety. While these modules, except for the first one, are intended for instruction at the postgraduate level, their topical content may also be used to develop teaching materials for undergraduate instruction to supplement existing engineering curricula with courses dedicated to hydrogen safety. The topical content of these modules is connected to the nodes in the HySafe activity matrix. These topics are initially based on the existing literature, and updated continuously as new knowledge becomes available, particularly from the NoE HySafe.

Obviously, the fundamental modules play a pivotal role in the curriculum development as the hydrogen economy evolves: new knowledge enters the curriculum through the fundamental modules, and this information is subsequently used to tune the basic and applied modules. Together, these six fundamental modules form the hydrogen safety engineering science core to support the applied modules.

The four applied modules, i.e. fire and explosion effects on people, structures, and the environment; accident prevention and mitigation; computational hydrogen safety engineering; risk assessment, are intended to provide graduates with the skill-set needed to solve hydrogen safety problems. These are postgraduate modules, but their topical content may also be used to develop undergraduate courses on hydrogen safety to complement existing undergraduate engineering curricula. The topics covered by these modules also coincide with the nodes in the HySafe-activity matrix. Like the fundamental modules, the role of these modules is also pivotal in the development of the curriculum. Methodologies and front-line techniques for dealing with hydrogen safety problems are extracted from the HySafe-network and incorporated into these modules. Modification of these modules due to new information is followed by the tuning and refinement of the topical content of the basic and fundamental modules to preserve coherence throughout the entire curriculum.

Table 2: Structure of the International Curriculum on Hydrogen Safety Engineering.

Basic modules
	Module thermodynamics
	Module chemical kinetics
	Module fluid dynamics
	Module heat and mass transfer
	Module solid mechanics
Fundamental modules
	Module introduction to hydrogen as an energy carrier
	Module fundamentals of hydrogen safety
	Module release, mixing and distribution
	Module hydrogen ignition
	Module hydrogen fires
	Module explosions: deflagrations and detonations
Applied modules
	Module fire and explosion effects on people, structure, and the environment
	Module accident prevention and mitigation
	Module computational hydrogen safety engineering
	Module risk assessment

1.5 Assessment of the need for hydrogen safety education and formation of a market of potential trainees

The development of a curriculum in any branch of engineering would obviously be meaningless without a market of trainees. Since the level of interest in hydrogen safety education primarily depends on the number of people involved in hydrogen related activities, the e-Academy of hydrogen safety has developed, and maintains a database of organisations working in the hydrogen industry. A first attempt to use this database to assess the market of potential trainees in hydrogen safety was made by sending a questionnaire to 600 companies and institutions in the database. There were 28 respondents and an analysis of their replies indicates that 119 potential trainees would be interested in hydrogen safety education on an annual basis. This implies that a projected market of 5000 companies and institutions would yield 1000 trainees on an annual basis. As a result, it will be necessary to deploy educational/training resources at a number of universities throughout Europe to meet this demand for hydrogen safety education. Further analysis of the replies indicates that the relative interest in the various modes of hydrogen safety education is as follows: postgraduate certificate (PGC): 10.7%, postgraduate diploma (PGD): 1.5%, master of science (MSc): 29.3%, short course (SC): 42.2%, and continuing professional development (CPD): 16.3%. It was also attempted to resolve the employment pattern, and hence the skill-set sought by employers. Within these 28 companies and institutions the employment pattern appears to be: 1.3% in design, 13.0% in manufacture, 0.9% in legislation, 0.4% in maintenance, 1.1% in installation, 19.0% in research and 19.0% in teaching (these percentages do not sum up to 100% because of the limited set defining the pattern). Given the small size of the catchment population, these outcomes must be considered preliminary. The process of arriving at these results nevertheless illustrates the mechanism of how the market of trainees in hydrogen safety could be assessed, and how the employment pattern of people working in hydrogen related areas, and the skill-set sought by employers might be resolved.

1.6 e-Learning and the European Summer School on Hydrogen Safety

The European Commission has launched a number of measures [17,18] to co-ordinate e-learning activities with the aim to propel Europe towards becoming the most competitive and dynamic knowledge-based economy in the world. Universities are using e-learning as a source of added value for their students, and for providing off-campus, flexible, virtual learning through web-based resources. Some universities are entering into strategic partnerships and adopting new business models to serve the changing education market and to face the challenges posed by global competition. From an employer point of view, greater emphasis is being placed on cost savings and on flexible, just-in-time education and training, to provide employees with the necessary skills and competence that match changing business needs. Owing to the transitional nature of the hydrogen economy, the continual introduction of new technologies, and the consequential rapid diversification of the skill-set sought by employers, e-learning is expected to become important in providing education and training in hydrogen safety. Because e-learning does not confine trainees to a specific campus location, employees are given maximal opportunity to acquire new skills and competencies while continuing in full-time employment, and to maintain family and domestic commitments. Moreover, e-learning makes it possible for experts working at the forefront of hydrogen safety to deliver teaching on the state-of-the-art in the field, while continuing their research of scientific endeavour. This is in line with the University of Ulster's aim to promote the further development and expansion of e-learning and blended learning programmes.

While the e-learning market in Europe is estimated at 12 billion euro per year, and is experiencing rapid growth, the lack of good quality e-learning content remains a matter of concern. This is true for well-established subject areas, and even more so for hydrogen safety. To cope with this situation, the European Commission has funded a series of annual European Summer Schools on Hydrogen Safety (HyCourse, contract MSCF-CT- 2005-029822, 2006-2010, coordinated by the University of Ulster). The First European Summer School on Hydrogen Safety was held at the University of Ulster in Belfast from 15 to 24 August 2006. During each event at least 12 leading experts from all over the world will deliver keynote lectures to an international audience of at least 60 researchers on topics such as: hydrogen release, mixing, and distribution; mechanisms of hydrogen ignition; hydrogen fires; deflagration, detonation and transitional phenomena; computational modelling in hydrogen safety; thermal, pressure and missile effects from fires and explosions; development and validation of mitigation techniques; safety assessment and risk analysis; and standards, guidelines and legal requirements. The nodal points of the HySafe activity matrix will be covered from fundamentals to applications following the topical content of the International Curriculum on Hydrogen Safety Engineering, and junior researchers are given the opportunity to benefit from the experience of leading world-class experts. With hydrogen safety being a novel area, and therefore lacking the prerequisites to prepare a skilled workforce for the technological challenges to come, this approach is considered to be the way forward to create the next generation of researchers and educators in this subject area, and to preserve the life-blood of research. The lecture notes and presentations of the keynote lectures at the European Summer School on Hydrogen Safety are used for the further development of two high-quality WebCT-based modules, namely, `Principles of Hydrogen Safety' and `Applied Hydrogen Safety', for the delivery of teaching on hydrogen safety in the distance learning mode. An on-line postgraduate certificate course in hydrogen safety engineering is offered by the University of Ulster from January 2007 where these two modules are taught.

2 BASIC MODULES

2.1 MODULE THERMODYNAMICS

2.1.1 INTRODUCTORY STATEMENT

This is a background module in classical thermodynamics and intended for undergraduate instruction only. It is similar to any other undergraduate engineering thermodynamics course, but comprehensive enough to provide a broad basis for dealing with hydrogen safety issues involving hydrogen embrittlement, unscheduled releases of liquefied and gaseous hydrogen, and accidental ignition and combustion of hydrogen. The topics covered by this module are based on the texts by Abbott & Van Ness (1972) [19], Atkins & de Paula (2006) [20], Metz (1976) [21], Moran & Shapiro (2000) [22], Smith, Van Ness & Abbott (2001) [23], and Sonntag, Borgnakke & Van Wylen (2003) [24]. Specific references are given along with the topics.

2.1.2 PREREQUISITE MATTER

Calculus up to ordinary differential equations, classical mechanics.

2.1.3 CONTENTS OF THE MODULE

2.1.3.1 Fundamental concepts and first principles (U: 6 hrs)

Contents: The three primitive gas laws [20]: Boyle's law (Boyle-Mariotte law), Charles's law or Gay-Lussac's law, combinend gas law (Boyle-Gay-Lussac's law). Avogrado's hypothesis [20] (equal volumes of ideal or perfect gases, at the same temperature and pressure, contain the same number of particles, or molecules). Ideal gas law (adding Avogrado's hypothesis to the combined gas law) [20]. Dalton's law (the pressure exerted by mixtures of gases is the sum of the partial pressures of its constituents) and mixtures of gases [20]. Macroscopic and microscopic point of view. Kinetic theory of gases [20] (postulates: constant random motion, elastic collision, volume occupied by molecules, attraction forces between molecules; definition of ideal gas in the light of postulates; definition of real gas in the light of postulates (molecular interactions affect the equation of state [20]); Maxwell's distribution for the speed of molecules [20,25], calculation of the root-mean-square velocity of molecules [20]; definition of pressure; mechanical equilibrium (the condition of equality of pressure on either side of a movable wall [20]); definition of absolute temperature and Boltzmann's constant; diathermic boundary (a boundary that permits the passage of energy as heat [20]); adiabatic boundary (a boundary that prevents the passage of energy as heat [20]); thermal equilibrium (the condition in which no change of state occurs when two objects are brought in contact through a diathermic boundary [20]); relationship between Boltzmann's constant, universal gas constant and Avogrado's number (Carnot's law [26]); collision frequency [20]; mean free path [20]). Thermodynamic properties: intensive properties (density, pressure, temperature, internal energy, entropy, chemical potential of a species, mole fraction of a species, mass fraction of a species) and extensive properties (volume, mass, kinetic energy, potential energy, internal energy (Joule's law [27]: in a perfect gas the internal energy is a function of the absolute temperature alone), entropy, enthalpy, Helmholtz energy, Gibbs energy). Thermodynamic property tables. State functions. Exact and inexact differentials. Statement of the thermodynamic laws: Zeroth law of thermodynamics (if A is in thermal equilibrium with B, and B is in thermal equilibrium with C, then C is also in thermal equilibrium with A [20]), First law of thermodynamics (the internal energy of an isolated system is constant [20]; energy defined as the capacity to do work), Second law of thermodynamics (Kelvin's statement: no process is possible in which the sole result is the absorption of heat from a reservoir and its complete conversion into work [20], statement in terms of entropy: the entropy of an isolated system increases in the course of spontaneous change [20]; entropy as an indicator of the direction of spontaneous change [20], thermodynamic definition of entropy (concept of irreversibility, concept of availability), relation between entropy and the distribution and dispersal of energy, Boltzmann's definition of entropy, examples of spontaneous change (expansion of gas into a vacuum, conversion of diamond into graphite, the helix-coil transitions in polypeptides, models of origins (propagation of genetic properties, evolution of biological species)), the widespread misinterpretation that the second law of thermodynamics does not permit order to spontaneously arise from disorder (counter-example: the spontaneous formation of snowflakes with six-sided crystalline symmetric structure from randomly moving water vapour molecules; reversibility of the transition between water and ice at the melting point; irreversibility of the transition of water to ice below the melting point; irreversibility of the transition of ice to water above the melting point)), Third law of thermodynamics (the entropy of all crystalline substances is zero at zero absolute temperature [20]). Zeroth law of thermodynamics (existence of temperature as an intensive property; existence of an equation of state between temperature, pressure, volume and amount of substance). First law of thermodynamics (existence of total energy as an extensive property consisting of internal energy, potential energy and kinetic energy; isolated systems (systems with a boundary through which neither matter nor energy can be transferred), closed systems (systems with a boundary through which energy can be transferred but matter cannot) and open systems (systems with a boundary through which both energy and matter can be transferred)). Second law of thermodynamics (existence of an absolute scale for temperature; existence of an extensive property called entropy; inequality of Clausius [24]: reversibility and irreversibility). Third law of thermodynamics (existence of a zero entropy reference offset for evaluating entropies of pure substances [23,24]; zero entropy of a perfect crystal at the absolute zero of temperature [24]; entropy from the microscopic point of view: Boltzmann's definition of entropy in terms of disorder [23,24]). Thermodynamic equilibrium (mechanical equilibrium, thermal equilibrium, chemical equilibrium). References: Batchelor (1994) [26], Feynman, Leighton & Sands (1989) [25], and Milne-Thomson (1968) [27].

2.1.3.2 Volumetric properties of a pure substance (U: 6hrs)

Contents: States of matter: solid, liquid, gas. Stability of phases [20]: phase transition, stable phase, metastable phase, allotropy, transition temperature. Phase boundaries: boiling point, melting point, vapour pressure, sublimation vapour pressure, fusion curve, sublimation curve, vaporisation curve, triple point, critical point, critical properties. Phase diagrams. The PT-diagram of a pure substance (solid region, liquid region, vapour region, gas region, fluid region) [23]. The PV-diagram of a pure substance (solid region, liquid region, liquid-vapour region, vapour region, gas region, super-heated vapor, sub-cooled liquid) [23]. The compressibility factor. The virial equations of state [19,23]. Extended virial equation of state: the Benedict-Webb-Rubin equation [23]. Cubic equations of state: the van der Waals equation of state [19,23,24], relation between the van der Waals constants and critical properties of a pure substance [19,24], the Redlich-Kwong equation of state [19,24], the Beattie-Bridgeman equation of state [24]. Corresponding-states correlations for gases: the two-parameter theorem of corresponding states, the acentric factor, the three-parameter theorem of corresponding states, the Pitzer correlations for the compressibility factor [23], the Pitzer correlations for the second virial coefficient [23], the Lee-Kesler equation, the Soave-Redlich-Kwong equation, the Peng-Robinson equation. Generalised correlations for liquids: Rackett's correlation [23], the Lydersen-Greenkorn-Hougen correlation [23].

2.1.3.3 The first law of thermodynamics (U: 6 hrs)

Contents: Work, heat and energy: when is work done?, what is the energy of a system?, what is the relationship between energy of a system and heat?, diathermic and adiabatic boundaries, exothermic and endothermic processes. The First Law: internal energy as an extensive property, internal energy as a state function, the conservation of energy, the mechanical definition of heat. Work and heat: expansion work, the general expression for work, free expansion, expansion against constant pressure, reversible expansion, isothermal reversible expansion. Heat transactions: heat capacity, the molar heat capacity at constant volume, the specific heat capacity at constant volume. Enthalpy: its definition, relating enthalpy and internal energy, the variation of enthalpy with temperature, the specific heat at constant pressure, the relation between the constant pressure specific heat capacity and the constant volume specific heat capacity, specific heat ratio. Temperature dependence of the specific heat capacity. The work of adiabatic change: isotherms and adiabats in the PVT-diagram. The isentropic adiabatic compression laws. Polytropic process. Enthalpies of physical change (latent heats of pure substances): standard heat of vaporisation, standard heat of fusion. Temperature dependence of the heat of vaporisation: the Clapeyron equation, the Riedel equation for the prediction of the effect of temperature on heat of vaporisation.

2.1.3.4 The first law of thermodynamics and flow processes (U: 6 hrs)

Contents: The first law of thermodynamics as a rate equation. Conservation of mass and the control volume. The first law of thermodynamics for a control volume. Energy equations for closed systems. The uniform-state, uniform flow process. The steady-state flow process. Energy equations for steady-state flow processes. General energy equations.

2.1.3.5 The second law of thermodynamics (U: 6 hrs)

Contents: Entropy and the direction of spontaneous change. The inequality of Clausius. Reversibility and irreversibility. Entropy as an extensive property. The thermodynamic definition of entropy. Example: entropy change for the adiabatic free expansion of an ideal gas into an evacuated space (Joule expansion). Entropy as a state function. Entropy as a system property. Entropy of a pure substance. Thermodynamic diagrams: temperature-entropy diagram, pressure-enthalpy diagram (Mollier diagram). Effciency of the heat cycle (conversion of heat into work) of heat. Example: the Carnot cycle. The first and second proposition regarding the efficiency of the Carnot engine. The absolute thermodynamic temperature scale. Entropy change of a reversible process. Thermodynamic relationships between entropy, enthalpy and internal energy. Factors that render a process irreversible: friction, unrestrained expansion, heat transfer through a finite temperature difference, hysteresis, I² R loss in electrical circuits, mixing of two different substances. Impossibility of the perpetuum mobile. Entropy change of an irreversible process. Lost work. Entropy change of an ideal gas. The reversible polytropic process for an ideal gas. Principle of the increase of entropy. Entropy calculations [21]: isothermal expansions, phase transitions, temperature changes, adiabatic processes, isothermal mixing. Heat pumps and power cycles: the Rankine cycle (effect of presure and temperature on efficiency), the reheat cycle, the regenerative cycle, deviation of actual power cycles from ideal cycles (friction losses, turbine losses, pump losses, condenser losses), the Carnot cycle (revisited), the Joule cycle, the Otto cycle, the Diesel cycle, the Ericsson cycle, the Stirling cycle, the Brayton cycle. Refrigeration cycles: vapor compression refrigeration cycles, the ammonia absorption refrigeration cycle, the air standard refrigeration cycle.

2.1.3.6 The second law of thermodynamics and flow processes (U: 6 hrs)

Contents: The second law of thermodynamics for a control volume. The steady-state, steady-flow process and the uniform-state, uniform-flow process. The steam turbine. The reversible steady-state steady-flow process, the idealised simple steam power plant. Principle of the increase of entropy for a control volume. Irreversibility and availability. Duct flow of compressible fluids [23]: pipe flow, nozzles (efficiency of of a nozzle, converging nozzle, diverging nozzle, converging-diverging nozzle, relation between velocity and pressure in an isentropic nozzle), throttling process (isenthalpic process, flashing of droplets during throttling to a lower pressure, Joule-Thompson inversion temperature, Joule-Thompson coefficient [28], Joule-Thompson inversion curve, reduced Joule-Thompson inversion curve). Expansion process (turbines, enthalpy-entropy diagram, efficiency of a turbine). Compression process (compressors, enthalpy-entropy diagram, efficiency of an adiabatic compressor, efficiency of a cooled compressor). References: Hirschfelder, Curtiss & Bird [28].

2.1.3.7 The first and second law of thermodynamics, and chemically reacting systems (U: 6 hrs)

Contents: Chemical reaction. Chemical reaction stoichiometry. Stoichiometric coefficients. Reaction coordinates. Enthalpies of chemical change: standard heat of reaction, Hess's law, standard enthalpies of formation, heat of reaction in terms of standard enthalpies of formation, the temperature dependence of the heat of reaction (Kirchhof's law). Property changes of reaction: the Gibbs function change of reaction. The Gibbs energy. The Helmholtz energy. Maxwell's Equations. The Gibbs-Helmholtz equation. Third law of thermodynamics: entropy changes in chemical reactions. Simple combustion process and stoichiometric reactions. Enthalpy of formation. Heat of reaction. Heat of combustion. The adiabatic flame temperature. Comment on non-equilibrium concentration of species in a flame. Partial molar properties. Chemical potential. Fugacity. Gibbs-Duhem equation.

2.1.3.8 Phase equilibrium (U: 6 hrs)

Contents: One-component phase diagrams. Clapeyron equation. Clausius-Clapeyron equation. Vapour pressure. Saturation. Partial molar quantities. Equality of fugacity as a criterion for phase equilibrium. Activity coefficient. Vapour pressure diagrams. Henry's law. Boiling diagrams. Colligative properties. Gibbs phase rule. Two-component phase-diagrams: cooling curves, bubble point, dew point. Dewdrop pressure. Capillarity. Ionic strength.

2.1.3.9 Thermodynamics and electrochemistry (U: 4 hrs)

Contents: Electrical work. Open cell potential and its relation with Gibbs energy. Faraday number. Electrochemical cells. Half-cells. Reduction potentials. Electrode potentials. Volt-ampere characteristics. Polarization. Cells with no salt bridge. Cell from reaction.

2.2 MODULE CHEMICAL KINETICS

2.2.1 INTRODUCTORY STATEMENT

This is a background module in chemical kinetics for instruction at the undergraduate and the graduate level. Its purpose is to provide a basis for dealing with hydrogen safety issues involving hydrogen embrittlement, and accidental ignition and combustion of hydrogen. The topics covered by this module are based on the texts by Atkins & de Paula (2002) [20], Kuo (2005) [29] and Turns (2000) [3]. Additional references are given along with the topics.

2.2.2 PREREQUISITE MATTER

Calculus up to ordinary differential equations, linear algebra, thermodynamics.

2.2.3 CONTENTS OF THE MODULE

2.2.3.1 The rates of chemical reactions (U: 6 hrs; G: 4 hrs)

Contents: The stoichiometric equation. Definition of the rate of reaction via concentrations of reactants/products in batch reactors. Relationship between reaction rate and chemical species concentration, the Rate Law. Rate constants and half-lives. Order of a reaction. Consecutive and parallel reactions. Rate-determining steps. Reversible/opposing reactions. Classification of the speed of reactions: relatively slow (non-explosive reactions), very fast explosive reactions. Global versus elementary reactions. Molecularity. Elementary reactions and their Rate Laws from the Law of Mass Action. Molecularity. Third bodies/chaperons. Rate constants. Total collission frequency. Temperature dependence of reaction rates. The Arrhenius Equation. A-factors and activation energies. Simple theories of reaction rates: simple and modified collision theory. Reactions at equilibrium. Fundamental relationship between kinetics (forward & reverse rate constants) and thermodynamics (equilibrium constant). Re-definition of reaction rate using stoichiometric coefficients. Kinetics in plug and continuously-stirred flow reactors. Complex versus elementary reactions. One-step chemical reactions of various orders: first- order reactions, second-order reactions, third-order reactions. Consecutive reactions: formation of intermediates, the steady-state approximation, pre-equilibria. Unimolecular reactions: isomerisation, decomposition, dissociation, the Lindeman-Hinselwood mechanism. The fall-off reaction rate: the Lindemann fall-off rate constant, the Stewart fall-off rate constant, the Troe fall-off rate constant. Termolecular reactions: recombination reactions involving a third body. The activation energy of a composite reaction. Competitive reactions. Opposing reactions: first-order reaction opposed by a first-order reaction. First-order reaction opposed by a second-order reaction. Second-order reaction opposed by a second-order reaction.

2.2.3.2 The kinetics of complex reactions (U: 6 hrs; G: 4 hrs)

Contents: Intermediates in complex reactions. Chain reactions. Chain carriers. Radicals. Classification of reaction steps: initiation (thermolysis, photolysis), propagation (the branching step), termination. Branching chain reactions. The structure of chain reactions. The rate laws of chain reactions. Steady-state analysis of simple chain reactions. Activation energy of a chain reaction. Complex reactions: the hydrogen-bromine reaction. Chain-branching explosions. Photochemical reactions: quantum yield, photochemical rate laws, photosentisation, quenching. Catalysis: homogeneous catalysis, autocatalysis. Oscillating reactions: the Lotka-Volterra mechanism, the brusselator, the oregonator, bistability. Chemical chaos. Departures from Arrhenius behaviour. Explosions: autocatalytic, thermal & branched-chain reactions. Hydrogen-oxygen explosion diagram in static reactor. First, second and third limits. Dependence explosion limits of hydrogen-oxygen systems on vessel shape, nature of surface, added inert gases. Comprehensive reaction mechanisms of hydrogen-oxygen systems: the Dougherty & Rabitz mechanism, the Miller mechanism, the Marinov, Westbrook & Pitz mechanism, the O'Conaire, Curran, Simmie, Pitz & Westbrook mechanism [30], the Saxena & Williams mechanism [31]. Validation of kinetic mechanisms from critically-reviewed experiments including stretch-free laminar burning velocities, flow reactor species profiles, ignition delay times in shock tubes, etc. Importance of thermodynamic and transport data in a detailed mechanism[32,33]. Software tools for analysing detailed chemical kinetic mechanisms.

2.2.3.3 Surface reactions (U: 6hrs; G: 4 hrs)

Contents: Surface adsorption processes: relation to catalysis, improvement of the miners' safety lamp due to Henry in 1824 by the addition of platinum powder to the reacting surface, Faraday's view on the role of adsorption to the surface in catalysis, physiosorption, van der Waals adsorption, chemisorption, Langmuir's concept of the unimolecular layer, Langmuir's adsorption isotherm, monolayer adsorption, multi-layer adsorption, adsorption with dissociation, competitive adsorption. Surface reaction processes: reaction mechanism, the Langmuir-Hinselwood mechanism, the Langmuir-Rideal-Eley mechanism, the precursor mechanism, Unimolecular surface reactions. Bimolecular surface reactions. Desorption. Kinetic model of hydrogen-oxygen reaction on the platinum surface. Kinetic rates of hydrogen-oxygen reaction on the platinum surface.

2.2.3.4 Application of sensitivity analysis to reaction mechanisms (G: 6hrs)

Contents: Role of sensitivity analysis in chemical kinetics: reduce number of reactions, identify rate limiting steps in reaction mechanism, resolve relative importance of reactions in a mechanism. Sensitivity coefficients. First-order sensitivity matrix. Sensitivity matrices of higher order. Deterministic sensitivity analysis: the direct method, the Green's function method, the Taylor series expansion method. Stochastic sensitivity analysis: the FAST method, Monte Carlo methods, pattern methods. Local sensitivity analysis: effect of a small change in one parameter on the first-order sensitivity coefficients. Application of local sensitivity analysis: time-dependent zero-dimensional problems, steady-state one-dimensional problems, time-dependent one-dimensional problems, one-dimensional flame fronts. Global sensitivity analysis: average effect of simulataneous parameter variations of arbitrary magnitudes.

2.2.3.5 Reduction of complex reaction systems to simpler reaction mechanisms (G: 6hrs)

Contents: Quasi-Steady-State Assumption (QSSA). Partial equilibrium assumption. The method of Intrinsic Low-Dimensional Manifolds (ILDM) [34], Computational Singular Perturbation (CSP) methods for stiff equations [35]. Example: a four-step reduced mechanism for hydrogen-air mixtures using CSP [36]. References: Lam & Goussis (1994) [35], Maas & Pope (1992) [34] and Lu, Ju & Law (2001) [36].

2.2.3.6 Chemical kinetics and the detonation of combustible mixtures (G: 5hrs)

Contents: Initial conditions for self-sustained detonation: mixture composition, thermodynamic state, fluid mechanical state, ignition source properties. Boundary conditions for self-sustained detonation: size and geometry of combustible mixture. Application of chemical kinetics to predict detonation limits of hydrogen-air and hydrogen-oxygen mixtures [37,29]. Detonability critera, detonation cell size and chemical kinetics [29]. Chemical kinetics of detonation in hydrogen-air-diluent mixtures [38,29]. Application of chemical kinetics to detonability critera through induction times measured in shock tubes [29]. The onset of detonation by the gradient field of induction times (due to concentration-temperature nonuniformity) through the mechanism of shock wave amplification by coherent energy release (the SWACER mechanism) [39,40,41,42]. Photochemical initiation of detonation in hydrogen-oxygen and hydrogen-chlorine mixtures with nonuniform concentration. References: Belles (1959) [37], Knystautas, Lee, Moen & Wagner (1979) [41], Lee, Knystautas & Yoshikawa (1978) [43], Lee & Moen (1980) [42] and Shepherd (1986) [38].

2.3 MODULE FLUID DYNAMICS

2.3.1 INTRODUCTORY STATEMENT

This module serves as a first introduction to fluid dynamics at the undergraduate level, and extends to cover more advanced topics at the graduate level. This, to aid the understanding of fluid dynamical problems related to hydrogen safety engineering. The topics in this module are based on the texts by Batchelor (1994) [26], Bird, Stewart & Lightfoot (1960) [44], Drazin & Reid (1981) [45] Hughes & Brighton (1999) [46], Kundu & Cohen [47], Lighthill [48], Massey & Ward-Smith (1998) [49], Milne-Thomson (1968) [27], Prasuhn (1980) [50], Schlichting (1968) [51], and White (2003) [52]. Additional references are given along with the topics.

2.3.2 PREREQUISITE MATTER

Calculus, classical mechanics, thermodynamics.

2.3.3 CONTENTS OF THE MODULE

2.3.3.1 Fluid statics (U: 4 hrs)

Contents: The usefulness of fluid statics: examples of immediate application to engineering problems without becoming involved in complex notions. The two kinds of forces to be considered in fluid statics: body forces (forces acting on the fluid particles at a distance: gravity, magnetic field, etc.) and surface forces (forces due to direct contact with other fluid particles or solid walls: pressure, shear stress, surface tension, etc.). Mechanical equilibrium of a fluid: a state in which each fluid particle is either at rest or has no relative motion with respect to other particles. Representation of surface forces by the stress tensor [26]: normal stresses, tangential stresses, principal axes of the stress tensor, principal stresses). The stress tensor in a fluid: decomposition into a symmetric part (isotropic part) and an anti-symmetric part (departure of the stress tensor from the isotropic form, also known as the deviatoric stress tensor [26,46]). Definition of the static fluid pressure [26]: the stress tensor in a fluid at rest [26], zero deviatoric stress tensor, definition of the static fluid pressure as the magnitude of the normal components in the isotropic part of the stress tensor in a fluid at rest, consequences of this definition (independence of direction, acting equally in all directions). Conditions for mechanical equilibrium in a fluid [26]: balance between body force and static fluid pressure gradient, a body floating in fluid at rest (Archimedes' theorem), fluids at rest under gravity (linear decrease of pressure with elevation in incompressible fluids (Pascal's law) [26,46]; exponential decrease of pressure with elevation in a compressible fluid e.g. Earth's atmosphere [46], pressure distribution in a self-gravitating star [26]). Manometry: determination of pressure differences using Pascal's law, the U-tube manometer [46], the two-fluid manometer [46]. Fluid forces on submerged bodies: application Archimedes' theorem for determining the force on submerged bodies [26,46], horizontal plane surface [46], inclined plane surface [46], curved surface [46], buoyancy and Archimedes' principle (the upward force equals the weight of the fluid displaced) [46]. Accelerating fluids in the absence of shear stress: fluids moving as a rigid body (each fluid particle has no motion relative to its immediate neighbour), accelerating container of fluid [46], rotating container of fluid [46]. Surface tension.

2.3.3.2 Kinematics of the flow field (U: 6 hrs)

Contents: Specification of the flow field [26]: Eulerian type and Lagrangian type, the Eulerian fluid element and the material fluid element. Streamline [27]: its definition as a line drawn in the fluid so that its tangent is in the direction of the fluid velocity, it alters from instant to instant because it depends on position and time, the aggregate of all streamlines at a given instant constitutes the flow pattern at that instant, set of differential equations of which the solution at a given time is the family of streamlines [26]. Differentiation following the motion of the fluid [26]: the notion of material volumes, surfaces and lines consisting always of the same fluid particles and moving with them, acceleration of a fluid element, material derivative (time derivative following the motion of the fluid). Particle path [27]: its definition as the path described by a fluid particle during its motion, tangency of fluid particle motion to the particle path, tangency between the particle path and the streamline which passes through the instantaneous position of the fluid particle, concept of a streak line [26]. Connection between streamlines and particle paths [27]: streamlines show how each particle is moving at a given instant, particle paths show how a given particle is moving at each instant, particle paths coincide with streamlines when the motion is steady. Virtual mass and added mass (hydrodynamic mass) [53,54,48,27,55]: the presence of the fluid effectively increases the mass of a moving rigid body, the added mass is equal to that of the liquid displaced by the Darwin drift (the net displacement of fluid particles due to the passage of rigid bodies), added mass of a cylinder [48], added mass of a sphere [48], trajectory of the particle path due to the passage of a rigid body (net displacement between the undisturbed initial and final position of a fluid particle in the direction of the moving body, tangents at the beginning and end point of the particle path are parallel to the direction of motion of the body) [27]. Stream tube: its definition as a collection of stream lines through each point of a closed curve. Stream filament [27]: its definition as a stream tube whose cross-section is a curve of infinitesimal dimensions, constancy of the product between the speed and cross-sectional area along a stream filament of a fluid in steady motion. Conservation of mass: general condition of mass conservation (Gauss' divergence theorem) [26], general condition of mass conservation in the form of a differential equation (continuity equation) [26], rate of expansion (rate of dilatation) [26], solenoidal flow fields [26] (incompressible fluids, compressible fluids in the incompressible limit), use of a stream function to satisfy mass conservation (exact differential relating velocity components to a differential change in the stream function [26], stream function as an equation defining stream lines [26], relation between the stream function and the volume flux between two points [26], existence of the stream function as a mere consequence of the continuity and incompressibility of the fluid [27]). The relative motion near a point: stress-strain rate relationships [26,46], the velocity gradient tensor [26,46], decomposition of the velocity gradient into a rate-of-strain tensor (symmetric part, deformation motion (dilatation, shear strain)) and a rotation tensor (anti-symmetric part, rigid body motion (translation, rotation)) [26,46], angular velocity vector and vorticity [26,46], example of irrotational flow in a sink vortex [46], example of rotational flow in a curved pipe [46], the velocity vector becoming the gradient of a scalar function of position called the velocity potential when the motion is irrotational [27]. Flow fields with a specified rate of expansion and vorticity: velocity distributions (concept of a point source [26], concept of a source doublet (dipole) [26]), vorticity distributions (vortex-line [26], vortex-tube [26], concept of circulation and the strength of the vortex tube [26], line vortices [26], sheet vortices [26]). Flow fields with a zero rate of expansion and vorticity: incompressible potential flow (solenoidal irrotational flow [26,44]). References: Darwin (1953) [53], Lighthill (1956) [54], and Rankine [55].

2.3.3.3 Kinematics of incompressible potential flow (U: 8 hrs)

Contents: Incompressible potential flow: its definition as a flow for which the velocity is derivable from the velocity potential [46]. Further considerations that make incompressible potential flow distinct [26,44,46,27]: the velocity potential becomes harmonic (under conditions of incompressibility, substitution of the velocity in terms of the velocity potential into the continuity equation results in Laplace's equation), the stream function becomes harmonic (substitution of the velocity in terms of the stream function into the condition of irrotationality results in Laplace's equation), velocity potential and stream function satisfy the Cauchy-Riemann equations, solutions of different flows (e.g. source, sinks, potential vortex, uniform flow) may be superposed to represent new ones, Rankine's method for constructing a new streamline pattern from two existing ones [27]), values of the velocity potential and stream function at every point in space may be added directly to obtain new values of the velocity potential and stream function, determination of the velocity components from the equipotential lines and streamlines using the Cauchy-Riemann equations and determination of the pressure field from the equation of motion of an ideal fluid once the velocity components are known [44]. Deducing the equations of the streamlines for some simple flow patterns: uniform flow [46], sources and sinks [46], the potential vortex [46]. Examples of superposition of two or more potential flows: flow over a Rankine oval [46], reflection about a solid boundary by the method of images from a source near the wall [46]. The complex potential and the complex velocity [26,44,27]: any analytic function of a complex variable can be regarded as the complex potential of a certain flow field, the use of complex variable theory and conformal transformations (examples: Mercator projection as a conformal mapping of the Earth onto a flat surface, the Joukowski transformation for mapping concentric circles into confocal ellipses [27], mapping a uniform flow into the flow in a corner [46]), definition of a holomorphic function [27], Cauchy-Riemmann equations arising from differentiation of a holomorphic function [27], conjugate functions of a holomorphic function [27], two systems of orthogonal curves (i.e. equipotential lines and streamlines) arising from equating conjugate functions to constants [27], any holomorphic function satisfying Laplace's equation [27], the Area theorem [27], Cauchy's integral theorem [27], Morera's theorem [27], obtaining the complex velocity directly from the complex potential by differentiation [27]. Deducing the complex potential for some simple flow patterns: uniform flow [46], sources and sinks [46], the potential vortex [46], the dipole flow [46], streaming motion past a circular cylinder [46]. The complex potential of more complicated flow patterns: circular cylinder held in a stream of uniform velocity [26], flow past an elliptic cylinder [27], flow past a plate (degenerate elliptic cylinder) [27], flow over a ditch or mound [27], flow past a cylindrical log [27], impinging jets [27], direct impact of two equal jets [27], direct impact of two unequal jets [27], flow through an aperture [