Special Issue "Teaching and Learning of Fluid Mechanics"

A special issue of Fluids (ISSN 2311-5521).

Deadline for manuscript submissions: closed (20 December 2019).

Special Issue Editor

Dr. Ashwin Vaidya
E-Mail Website
Guest Editor
Department of Mathematics, Montclair State University, Montclair, NJ 07043, USA
Interests: mathematical fluid mechanics; non-linear partial differential equations; hydrodynamic stability; non-Newtonian fluid mechanics; fluid–structure interaction; experimental fluid mechanics; philosophy of science
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is devoted to the various ways of teaching and learning about fluid mechanics. Fluid mechanics occupies a privileged position in the sciences; it is taught in various science departments including physics, mathematics, mechanical, chemical and civil engineering and environmental sciences, each highlighting a different aspect or interpretation of the foundation and applications of fluids. While scholarship in fluid mechanics is vast, expanding in the areas of experimental, theoretical and computational fluid mechanics, there is little discussion among scientists about the different possible ways of teaching this subject. Our Special Issue is therefore devoted to this very theme. We think there is much to be learned, for teachers and students alike, from an interdisciplinary dialogue about fluids. We invite all kinds of articles, including research on the pedagogical aspects of fluid mechanics, communications, discussions, essays, letters, short notes and tutorials at the undergraduate or graduate level. Articles on historical aspects of fluids, novel and interesting experiments or theoretical calculations which can convey complex ideas in creative ways are welcome. Research articles are not appropriate for this issue. However, research presented in a simple manner and contextualized within the framework of the fluid mechanics curriculum may be acceptable.

All articles will undergo a rigorous peer review process.

Prof. Dr. Ashwin Vaidya
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Fluids is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Flow visualization
  • Experimental studies
  • Computer simulations
  • Mathematical modeling
  • Fluid flow in the arts
  • History of fluids
  • Undergraduate education
  • Applications of fluids

Published Papers (15 papers)

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Editorial

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Editorial
Teaching and Learning of Fluid Mechanics
Fluids 2020, 5(2), 49; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids5020049 - 13 Apr 2020
Cited by 2 | Viewed by 863
Abstract
Fluid mechanics is arguably one of the oldest branches of physics, and the literature on this subject is vast and complex [...] Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)

Research

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Article
Understanding Fluid Dynamics from Langevin and Fokker–Planck Equations
Fluids 2020, 5(1), 40; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids5010040 - 23 Mar 2020
Cited by 2 | Viewed by 1182
Abstract
The Langevin equations (LE) and the Fokker–Planck (FP) equations are widely used to describe fluid behavior based on coarse-grained approximations of microstructure evolution. In this manuscript, we describe the relation between LE and FP as related to particle motion within a fluid. The [...] Read more.
The Langevin equations (LE) and the Fokker–Planck (FP) equations are widely used to describe fluid behavior based on coarse-grained approximations of microstructure evolution. In this manuscript, we describe the relation between LE and FP as related to particle motion within a fluid. The manuscript introduces undergraduate students to two LEs, their corresponding FP equations, and their solutions and physical interpretation. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Suite-CFD: An Array of Fluid Solvers Written in MATLAB and Python
Fluids 2020, 5(1), 28; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids5010028 - 25 Feb 2020
Cited by 1 | Viewed by 2432
Abstract
Computational Fluid Dynamics (CFD) models are being rapidly integrated into applications across all sciences and engineering. CFD harnesses the power of computers to solve the equations of fluid dynamics, which otherwise cannot be solved analytically except for very particular cases. Numerical solutions can [...] Read more.
Computational Fluid Dynamics (CFD) models are being rapidly integrated into applications across all sciences and engineering. CFD harnesses the power of computers to solve the equations of fluid dynamics, which otherwise cannot be solved analytically except for very particular cases. Numerical solutions can be interpreted through traditional quantitative techniques as well as visually through qualitative snapshots of the flow data. As pictures are worth a thousand words, in many cases such visualizations are invaluable for understanding the fluid system. Unfortunately, vast mathematical knowledge is required to develop one’s own CFD software and commercial software options are expensive and thereby may be inaccessible to many potential practitioners. To that extent, CFD materials specifically designed for undergraduate education are limited. Here we provide an open-source repository, which contains numerous popular fluid solvers in 2 D (projection, spectral, and Lattice Boltzmann), with full implementations in both MATLAB and Python3. All output data is saved in the . v t k format, which can be visualized (and analyzed) with open-source visualization tools, such as VisIt or ParaView. Beyond the code, we also provide teaching resources, such as tutorials, flow snapshots, measurements, videos, and slides to streamline use of the software. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Floodopoly: Enhancing the Learning Experience of Students in Water Engineering Courses
Fluids 2020, 5(1), 21; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids5010021 - 08 Feb 2020
Cited by 1 | Viewed by 1518
Abstract
This study focuses on the utilisation of lab-based activities to enhance the learning experience of engineering students studying water engineering and geosciences courses. Specifically, the use of “floodopoly” as a physical model demonstration in improving the students’ understanding of the relevant processes of [...] Read more.
This study focuses on the utilisation of lab-based activities to enhance the learning experience of engineering students studying water engineering and geosciences courses. Specifically, the use of “floodopoly” as a physical model demonstration in improving the students’ understanding of the relevant processes of flooding, infrastructure scour and sediment transport, and improve retention and performance in simulation of these processes in engineering design courses, is discussed. The effectiveness of lab-based demonstration is explored using a survey assessing the weight of various factors that might influence students’ performance and satisfaction. It reveals how lab-centred learning, overall course success is linked with student motivation and the students’ perception of an inclusive teaching environment. It also explores the effectiveness of the implementation of student-centred and inquiry-guided teaching and various methods of assessment. The analysis and discussion are informed by students’ responses to a specifically designed questionnaire, showing an improvement of the satisfaction rates compared to traditional class-based learning modules. For example, more students (85%) reported that they perceived the lab-based environment as an excellent contribution to their learning experience, while less students (about 57%) were as satisfied for a traditional class-based course delivery. Such findings can be used to improve students’ learning experience by introducing physical model demonstrations, similar to those offered herein. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Computing Effective Permeability of Porous Media with FEM and Micro-CT: An Educational Approach
Fluids 2020, 5(1), 16; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids5010016 - 24 Jan 2020
Cited by 3 | Viewed by 1373
Abstract
Permeability is a parameter that measures the resistance that fluid faces when flowing through a porous medium. Usually, this parameter is determined in routine laboratory tests by applying Darcy’s law. Those tests can be complex and time-demanding, and they do not offer a [...] Read more.
Permeability is a parameter that measures the resistance that fluid faces when flowing through a porous medium. Usually, this parameter is determined in routine laboratory tests by applying Darcy’s law. Those tests can be complex and time-demanding, and they do not offer a deep understanding of the material internal microstructure. Currently, with the development of new computational technologies, it is possible to simulate fluid flow experiments in computational labs. Determining permeability with this strategy implies solving a homogenization problem, where the determination of the macro parameter relies on the simulation of a fluid flowing through channels created by connected pores present in the material’s internal microstructure. This is a powerful example of the application of fluid mechanics to solve important industrial problems (e.g., material characterization), in which the students can learn basic concepts of fluid flow while practicing the implementation of computer simulations. In addition, it gives the students a concrete opportunity to work with a problem that associates two different scales. In this work, we present an educational code to compute absolute permeability of heterogeneous materials. The program simulates a Stokes flow in the porous media modeled with periodic boundary conditions using finite elements. Lastly, the permeability of a real sample of sandstone, modeled by microcomputed tomography (micro-CT), is obtained. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Using Legitimation Code Theory to Conceptualize Learning Opportunities in Fluid Mechanics
Fluids 2019, 4(4), 203; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4040203 - 06 Dec 2019
Cited by 4 | Viewed by 1605
Abstract
With widespread industry feedback on engineering graduates’ lack of technical skills and research demonstrating that higher education does not effectively facilitate the development of open-ended problem-solving competencies, many educators are attempting to implement measures that address these concerns. In order to properly formulate [...] Read more.
With widespread industry feedback on engineering graduates’ lack of technical skills and research demonstrating that higher education does not effectively facilitate the development of open-ended problem-solving competencies, many educators are attempting to implement measures that address these concerns. In order to properly formulate sensible interventions that result in meaningful improvements in student outcomes, useful educational measurement and analysis approaches are needed. Legitimation Code Theory (LCT) has rapidly emerged as an effective, theoretically informed ‘toolkit’ offering a suite of dimensions through which to observe, analyze, interpret, and design teaching and learning practices. LCT Semantics has been used to help engineering educators unpack both levels of engineering knowledge abstraction and the complexity of engineering terms, while LCT Specialization focuses on knowledge practices (using the epistemic plane) and enables a visualization and differentiation between kinds of phenomena and the fixed versus open-ended methods with which to approach a particular phenomenon. Drawing on a range of initiatives to enable an improved practical grasp of fluid mechanics concepts, this paper presents a description and graphic LCT analysis of student learning that has been designed to anchor the ‘purist’ principles underpinning applied fluid mechanics concepts (such as in piping and pump network design) by way of concerted ‘doctrinal’ practices, and the exposure to more open-ended practical situations involving peer learning/group work, allowing educators to visualize the code clash between the curriculum and the world of work. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Forty Years’ Experience in Teaching Fluid Mechanics at Strasbourg University
Fluids 2019, 4(4), 199; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4040199 - 29 Nov 2019
Cited by 5 | Viewed by 1167
Abstract
A summary of the personal investment in teaching fluid mechanics over 40 years in a French university is presented. Learning and Teaching Science and Engineering has never been easy, and in recent years it has become a crucial challenge for curriculum developers and [...] Read more.
A summary of the personal investment in teaching fluid mechanics over 40 years in a French university is presented. Learning and Teaching Science and Engineering has never been easy, and in recent years it has become a crucial challenge for curriculum developers and teaching staff to offer attractive courses and optimized assessments. One objective is to ensure that students acquire competitive skills in higher science education that enable them to compete in the employment market, as the mechanical field is a privileged sector in industry. During the last decade, classical learning and teaching methods have been coupled with hands-on practice for future schoolteachers in a specific course on subjects including fluid mechanics. The hands-on/minds-on/hearts-on approach has demonstrated its effectiveness in training primary school teachers, and fluids are certainly a nice source of motivation for pupils in science learning. In mechanical engineering, for undergraduate and graduate students, the development of teaching material and the learning and teaching experience covers up to 40 years, mostly on fluid dynamics and related topics. Two periods are identified, those prior to and after the Bologna Process. Most recently, teaching instruction has focused on the Fluid Mechanics Concept Inventory (FMCI). This inventory has been recently introduced in France, with some modifications, and remedial tools have been developed and are proposed to students to remove misconceptions and misunderstandings of key concepts in fluid mechanics. The FMCI has yet to be tested in French higher education institutions, as are the innovative teaching methods that are emerging in fluid mechanics. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Bottle Emptying: A Fluid Mechanics and Measurements Exercise for Engineering Undergraduate Students
Fluids 2019, 4(4), 183; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4040183 - 11 Oct 2019
Cited by 2 | Viewed by 1576
Abstract
A comprehensive exercise, suitable for an undergraduate engineering audience studying fluid mechanics, is presented, in which participants were tasked with emptying a bottle. That simple request yielded data collected by students and the author for N = 454 commercially available bottles, spanning nearly [...] Read more.
A comprehensive exercise, suitable for an undergraduate engineering audience studying fluid mechanics, is presented, in which participants were tasked with emptying a bottle. That simple request yielded data collected by students and the author for N = 454 commercially available bottles, spanning nearly four orders of magnitude for volume V , and representing the largest experimental dataset available in the literature. Fundamental statistics are used to describe the emptying time, T ¯ e , for any single bottle. Dimensional analysis is used to transform the raw data to yield a predictive trend, and a method of least-squares regression analysis is performed to find an empirical correlation relating dimensionless time T ¯ e g / d and dimensionless volume V / d 3 . We find that volume, V , and neck diameter, d, can be used to estimate the emptying time for any bottle, although the data suggests that the shape of the neck plays a role. Furthermore, two basic analytical models found in the literature compare favorably to our data and empirical correlation when recast using our dimensionless groups. The documented exercise provides students with the opportunity to use basic engineering statistics and to see the utility of dimensional analysis. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Fluids in Music: The Mathematics of Pan’s Flutes
Fluids 2019, 4(4), 181; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4040181 - 10 Oct 2019
Cited by 1 | Viewed by 1583
Abstract
We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at [...] Read more.
We discuss the mathematics behind the Pan’s flute. We analyze how the sound is created, the relationship between the notes that the pipes produce, their frequencies and the length of the pipes. We find an equation which models the curve that appears at the bottom of any Pan’s flute due to the different pipe lengths. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
An Efficient Strategy to Deliver Understanding of Both Numerical and Practical Aspects When Using Navier-Stokes Equations to Solve Fluid Mechanics Problems
Fluids 2019, 4(4), 178; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4040178 - 01 Oct 2019
Cited by 1 | Viewed by 1054
Abstract
An efficient and thorough strategy to introduce undergraduate students to a numerical approach of calculating flow is outlined. First, the basic steps, especially discretization, involved when solving Navier-Stokes equations using a finite-volume method for incompressible steady-state flow are developed with the main aim [...] Read more.
An efficient and thorough strategy to introduce undergraduate students to a numerical approach of calculating flow is outlined. First, the basic steps, especially discretization, involved when solving Navier-Stokes equations using a finite-volume method for incompressible steady-state flow are developed with the main aim being for the students to follow through from the mathematical description of a given problem to the final solution of the governing equations in a transparent way. The well-known ‘driven-cavity’ problem is used as the problem for testing coding written by the students, and the Navier-Stokes equations are initially cast in the vorticity-streamfunction form. This is followed by moving on to a solution method using the primitive variables and discussion of details such as, closure of the Navier-Stokes equations using turbulence modelling, appropriate meshing within the computation domain, various boundary conditions, properties of fluids, and the important methods for determining that a convergence solution has been reached. Such a course is found to be an efficient and transparent approach for introducing students to computational fluid dynamics. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
CFD Julia: A Learning Module Structuring an Introductory Course on Computational Fluid Dynamics
Fluids 2019, 4(3), 159; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4030159 - 23 Aug 2019
Cited by 9 | Viewed by 8916
Abstract
CFD Julia is a programming module developed for senior undergraduate or graduate-level coursework which teaches the foundations of computational fluid dynamics (CFD). The module comprises several programs written in general-purpose programming language Julia designed for high-performance numerical analysis and computational science. The paper [...] Read more.
CFD Julia is a programming module developed for senior undergraduate or graduate-level coursework which teaches the foundations of computational fluid dynamics (CFD). The module comprises several programs written in general-purpose programming language Julia designed for high-performance numerical analysis and computational science. The paper explains various concepts related to spatial and temporal discretization, explicit and implicit numerical schemes, multi-step numerical schemes, higher-order shock-capturing numerical methods, and iterative solvers in CFD. These concepts are illustrated using the linear convection equation, the inviscid Burgers equation, and the two-dimensional Poisson equation. The paper covers finite difference implementation for equations in both conservative and non-conservative form. The paper also includes the development of one-dimensional solver for Euler equations and demonstrate it for the Sod shock tube problem. We show the application of finite difference schemes for developing two-dimensional incompressible Navier-Stokes solvers with different boundary conditions applied to the lid-driven cavity and vortex-merger problems. At the end of this paper, we develop hybrid Arakawa-spectral solver and pseudo-spectral solver for two-dimensional incompressible Navier-Stokes equations. Additionally, we compare the computational performance of these minimalist fashion Navier-Stokes solvers written in Julia and Python. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Teach Second Law of Thermodynamics via Analysis of Flow through Packed Beds and Consolidated Porous Media
Fluids 2019, 4(3), 116; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4030116 - 27 Jun 2019
Cited by 5 | Viewed by 2040
Abstract
The second law of thermodynamics is indispensable in engineering applications. It allows us to determine if a given process is feasible or not, and if the given process is feasible, how efficient or inefficient is the process. Thus, the second law plays a [...] Read more.
The second law of thermodynamics is indispensable in engineering applications. It allows us to determine if a given process is feasible or not, and if the given process is feasible, how efficient or inefficient is the process. Thus, the second law plays a key role in the design and operation of engineering processes, such as steam power plants and refrigeration processes. Nevertheless students often find the second law and its applications most difficult to comprehend. The second law revolves around the concepts of entropy and entropy generation. The feasibility of a process and its efficiency are directly related to entropy generation in the process. As entropy generation occurs in all flow processes due to friction in fluids, fluid mechanics can be used as a tool to teach the second law of thermodynamics and related concepts to students. In this article, flow through packed beds and consolidated porous media is analyzed in terms of entropy generation. The link between entropy generation and mechanical energy dissipation is established in such flows in terms of the directly measurable quantities such as pressure drop. Equations are developed to predict the entropy generation rates in terms of superficial fluid velocity, porous medium characteristics, and fluid properties. The predictions of the proposed equations are presented and discussed. Factors affecting the rate of entropy generation in flow through packed beds and consolidated porous media are identified and explained. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
What Can Students Learn While Solving Colebrook’s Flow Friction Equation?
Fluids 2019, 4(3), 114; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4030114 - 27 Jun 2019
Cited by 2 | Viewed by 1509
Abstract
Even a relatively simple equation such as Colebrook’s offers a lot of possibilities to students to increase their computational skills. The Colebrook’s equation is implicit in the flow friction factor and, therefore, it needs to be solved iteratively or using explicit approximations, which [...] Read more.
Even a relatively simple equation such as Colebrook’s offers a lot of possibilities to students to increase their computational skills. The Colebrook’s equation is implicit in the flow friction factor and, therefore, it needs to be solved iteratively or using explicit approximations, which need to be developed using different approaches. Various procedures can be used for iterative methods, such as single the fixed-point iterative method, Newton–Raphson, and other types of multi-point iterative methods, iterative methods in a combination with Padé polynomials, special functions such as Lambert W, artificial intelligence such as neural networks, etc. In addition, to develop explicit approximations or to improve their accuracy, regression analysis, genetic algorithms, and curve fitting techniques can be used too. In this learning numerical exercise, a few numerical examples will be shown along with the explanation of the estimated pedagogical impact for university students. Students can see what the difference is between the classical vs. floating-point algebra used in computers. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Article
Teaching Fluid Mechanics and Thermodynamics Simultaneously through Pipeline Flow Experiments
Fluids 2019, 4(2), 103; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4020103 - 01 Jun 2019
Cited by 5 | Viewed by 2797
Abstract
Entropy and entropy generation are abstract and illusive concepts for undergraduate students. In general, students find it difficult to visualize entropy generation in real (irreversible) processes, especially at a mechanistic level. Fluid mechanics laboratory can assist students in making the concepts of entropy [...] Read more.
Entropy and entropy generation are abstract and illusive concepts for undergraduate students. In general, students find it difficult to visualize entropy generation in real (irreversible) processes, especially at a mechanistic level. Fluid mechanics laboratory can assist students in making the concepts of entropy and entropy generation more tangible. In flow of real fluids, dissipation of mechanical energy takes place due to friction in fluids. The dissipation of mechanical energy in pipeline flow is reflected in loss of pressure of fluid. The degradation of high quality mechanical energy into low quality frictional heat (internal energy) is simultaneously reflected in the generation of entropy. Thus, experiments involving measurements of pressure gradient as a function of flow rate in pipes offer an opportunity for students to visualize and quantify entropy generation in real processes. In this article, the background in fluid mechanics and thermodynamics relevant to the concepts of mechanical energy dissipation, entropy and entropy generation are reviewed briefly. The link between entropy generation and mechanical energy dissipation in pipe flow experiments is demonstrated both theoretically and experimentally. The rate of entropy generation in pipeline flow of Newtonian fluids is quantified through measurements of pressure gradient as a function of flow rate for a number of test fluids. The factors affecting the rate of entropy generation in pipeline flows are discussed. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Other

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Essay
Teaching and Learning Pressure and Fluids
Fluids 2019, 4(4), 194; https://0-doi-org.brum.beds.ac.uk/10.3390/fluids4040194 - 25 Nov 2019
Cited by 3 | Viewed by 1033
Abstract
This essay is a synthesis of more than twenty years of research, already published, on teaching and learning fluids and pressure. We examine teaching fluids globally, i.e., the content to be taught and its transformations, students’ alternative conceptions and their remediation, the sequence [...] Read more.
This essay is a synthesis of more than twenty years of research, already published, on teaching and learning fluids and pressure. We examine teaching fluids globally, i.e., the content to be taught and its transformations, students’ alternative conceptions and their remediation, the sequence of educational activities, being right for students’ understanding, as well as tasks for evaluating their conceptual evolution. Our samples are junior high school students and primary school student-teachers. This long-term study combines research and development concerning teaching and learning fluids and has evolved through iteratively based design application and reflective feedback related to empirical data. The results of our research include several publications. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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