# Forty Years’ Experience in Teaching Fluid Mechanics at Strasbourg University

## Abstract

**:**

## 1. Introduction

## 2. Teaching and Learning Fluids with Future Schoolteachers

#### 2.1. Hypothetico-Deductive (H-D) Method in Sciences

- Identify a broad problem area;
- Define the problem statement;
- Develop hypotheses;
- Determine measures;
- Data collection;
- Data analysis.

- Observation and questioning related to initial representations, problem identification;
- Theoretical framework, background research, preliminary information gathering;
- Elaboration of hypotheses (testable, falsifiable afterwards);
- Definition, design of test experiments;
- Predictions of results associated to the test experiences;
- Experimentation, data recording and collection, and analysis/interpretation;
- Validation or invalidation of hypotheses and predictions, as well as their assessment;
- Elaboration of a theory or law based on robust validations.

#### 2.2. Practical Work and Projects in Fluid Mechanics

- ➢
- Have two weeks to update their knowledge in fluids (Newton’s laws, free fall bodies in a void, fall in air or water/oil, the Archimedes’ principle, the Bernoulli law of perfect fluids) and investigate the concepts of viscosity and drag force (Reynolds number, Stokes’ law, terminal fall velocity), writing all in a science notebook.
- ➢
- Must imagine simple inexpensive experiments that identify and highlight relevant science notions and concepts, with some available material being listed and some experience items being proposed, such as:
- Galileo’s experiments of falling objects, using sport balls in air from different heights up to 20 m (to observe differences in terminal velocities for different spheres (diameters, density));
- Making a classic Cartesian diver (understanding pressure, Archimedean buoyancy);
- Building a parachute with fabric and string/building a wind turbine;
- Observing the settling of sand grains in water;
- Observing bubbles rising in oil or water, or the fall of a golf ball in water (viscosity calculation);
- Galileo’s experiment with rolling balls down an inclined plane (the calculation of gravity);
- The levitation of a ping pong ball (Coanda effect, Bernoulli equation);
- The measurement of the density of objects (cork, lead sinkers) based on the Archimedes’ principle.

- ➢
- Investigate and execute creative experiments while setting up the hypothetico-deductive teaching strategies.
- ➢
- Elaborate several lesson preparation cards for pupils in primary schools on a topic related to fluid mechanics.

- Improvement in organization of their working hours;
- Efficient use of available information and resources (in books, articles, the internet);
- Investment and teamwork (organizing small students’ groups for interactive pedagogy learning);
- Scientific curiosity, creativity, motivation, and the pleasure of learning;
- Acquisition of reflective practice and scientific questioning;
- Implementing the HD method coupled with a project-based approach;
- Problem solving, formulating and testing hypotheses, theories, or laws;
- Analyzing and understanding scientific phenomena;
- Learning to measure and calculate with efficiency;
- Developing various abilities and skills, including the acquisition of transversal competences such as creativity and critical thinking.

#### 2.2.1. Example of an Experiment: Free Fall of Bodies

#### 2.2.2. Example of an Experiment: Viscosity Calculation

_{D}is the drag coefficient as function of the Reynolds number Re. The derived equation for U is nevertheless implicit since the drag coefficient C

_{D}is itself a function of U.

#### 2.2.3. Some Scientific Questions Treated in a Preparation Sheet

## 3. Teaching Fluid Mechanics from 1976 to 2002

## 4. Teaching and Learning Fluids after the Bologna Process

#### 4.1. Case of Undergraduate Students

^{3}for water), as well as between kinematic and dynamic viscosity, is not uncommon. More worrying is that students are unable to write down the volume of a sphere $V=4\pi {R}^{3}/3$ or the surface of a disk $S=\pi {R}^{2}$ without the support of an internet connection or a smartphone. Archimedes’ buoyancy force is seldom understood, and students think that the buoyancy force increases with depth in water, as is the case with static pressure.

#### 4.2. Case of Graduate Students: A Revealing Illustration

_{p}, located at X at time t, and moving with velocity vector V(t) in a fluid of density ${\rho}_{f}$ with the fictitious velocity at the center of the particle U(t), is obtained by solving the set of equations

_{d}is the drag coefficient, C

_{a}the added mass coefficient, C

_{h}the Basset history term coefficient, and the particle Reynolds number is based on the particle–fluid slip velocity $\left|V-U\right|$. Master’s and even PhD students in mechanical engineering now have real difficulty in understanding and handling this type of equation, not to mention solving it numerically. Adding a Magnus force (and torque equation) is even more complicated for them.

## 5. Fluid Mechanics Remediation Test

#### 5.1. Conceptual vs. Procedural Knowledge, Misconceptions

#### 5.2. Concept Inventories (CI)

#### 5.3. The American Fluid Mechanics Concept Inventory (FMCI)

- -
- Statics of fluids, seven questions (Q7, Q9, Q10, Q12, Q14, Q18, Q30);
- -
- Ideal fluids and conservation laws (Bernouilli, Euler), 10 questions (Q3, Q4, Q6, Q13, Q17, Q22, Q23, Q25, Q27, Q31);
- -
- External viscous flows, seven questions (Q5, Q19, Q20, Q24, Q26, Q28, Q29);
- -
- Internal viscous flows, six questions (Q8, Q11, Q15, Q16, Q21, Q32).

## 6. Work in Progress in Learning and Teaching Fluid Mechanics

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Height (in meters) | T = (2 h/g)^{1/2} (s) | V (m/s) = gT |
---|---|---|

1 | 0.45 | 4.4 |

2 | 0.64 | 6.3 |

3 | 0.78 | 7.6 |

5 | 1 | 9.8 |

10 | 1.43 | 14 |

**Table 2.**Concepts tested on the existing American Fluid Mechanics Concept Inventory (FMCI) [56].

Targeted Concepts | |
---|---|

3 Continuity; compressible 4 Bernoulli; incompressible 5 Boundary conditions 6 Momentum; incompressible 7 Pressure definition 8 Boundary layers; incompressible 9 Pascal’s Law 10 Manometry; compressible 11 Bernoulli; incompressible 12 Forces on submerged surface 13 Ideal Gas Law 14 Manometry; compressible 15 Shear stress; compressible 16 Boundary layers 17 Bernoulli; incompressible | 18 Manometry; compressible 19 Drag force; compressible 20 Boundary layer; compressible 21 Boundary layer; incompressible 22 Continuity; incompressible 23 Continuity/Bernoulli; incompressible 24 Boundary layer; compressible 25 Impulse-momentum; incompressible 26 Boundary layer; compressible 27 Continuity/Bernoulli; incompressible 28 Drag force; compressible 29 Drag force; compressible 30 Pressure measurement; compressible 31 Continuity/Temperature variations; compressible 32 Fluid properties (viscosity) |

Targeted Concepts | |
---|---|

3 Continuity; compressible 4 Bernoulli; incompressible 5 Boundary conditions for boundary layer 6 Momentum; incompressible, Euler 7 Pressure definition, statics 8 Viscous flow between flat-plates; incompressible 9 Pascal’s Law, statics 10 Manometry; compressible, Bernoulli 11 generalized Bernoulli; pressure loss in pipes 12 Forces on submerged surface 13 Ideal Gas Law 14 Manometry; statics 15 Shear stress 16 Flow between two flat-plates, velocity profile 17 Bernoulli; flow in a horizontal diffuser 18 Manometry; compressible, statics | 19 Laminar drag force over a flat-plate 20 Boundary layer; control volume approach 21 Flow between two moving flate-plates, velocity profile 22 Continuity; incompressible 23 Continuity/Bernoulli; vertical diffuser, incompressible 24 Boundary layer; velocity profile 25 Impulse-momentum; incompressible 26 Boundary layer and wall stress profile 27 Continuity/Bernoulli; vertical contraction, incompressible 28 Drag force of different profiles in air 29 Drag force; viscous drag 30 Pressure measurement; Prandtl/Pitot tube 31 Continuity/Temperature variations; compressible flow through a diffuser 32 Fluid properties (viscosity) |

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**MDPI and ACS Style**

Huilier, D.G.F. Forty Years’ Experience in Teaching Fluid Mechanics at Strasbourg University. *Fluids* **2019**, *4*, 199.
https://doi.org/10.3390/fluids4040199

**AMA Style**

Huilier DGF. Forty Years’ Experience in Teaching Fluid Mechanics at Strasbourg University. *Fluids*. 2019; 4(4):199.
https://doi.org/10.3390/fluids4040199

**Chicago/Turabian Style**

Huilier, Daniel G. F. 2019. "Forty Years’ Experience in Teaching Fluid Mechanics at Strasbourg University" *Fluids* 4, no. 4: 199.
https://doi.org/10.3390/fluids4040199