# Hydrodynamics

## Summary

Nondimensionalized Navier-Stokes equations result in a great variety of models (Stokes, Lubrication, Euler, Potential) depending on the Reynolds number. The concept of boundary layer enables us then to identify the different components of the hydrodynamic drag. Wave drag is finally introduced.

## Content

The objective of this class is to describe and understand hydrodynamic flows by means of physical modeling. With help of dimensional analysis of the Navier-Stokes equations, several fluid models are introduced depending on the dominant physical effects: hydrostatics, capillarity, dissipation or inertia. This approach allows to describe important concepts like lift or wave dispersion and naturally leads to the concept of boundary layer so as to understand the appearance of drag. Wave drag is also introduced and its origin discussed.

## Keywords

Waves, drag, lift, lubrication, boundary layer

## Learning Prerequisites

## Required courses

Having followed an introductory class on Fluid dynamics is expected

## Recommended courses

Fluid mechanics

## Learning Outcomes

By the end of the course, the student must be able to:

- Explain in scientific terms the basic concepts of continuum mechanics (e.g. kinematics, dynamics, conservation equations, Eulerian/Lagrangian approach, stress and strain tensors, constitutive laws, linear elasticity, Newtonian fluid) and apply them to model and analytically resolve simple problems, AH42
- Link flow behaviour with non-dimensional parameters (e.g. Reynolds and Mach numbers), AH2
- Resolve analytically or numerically the potential flow around an airfoil, AH25
- Describe flow in simple geometries, such as over a flat plate, in a tube, or around a sphere or airfoil, AH11
- State the conserved quantities in a given flow and link them to a physical-mathematical description, AH16
- Define, describe and apply the basic flow equations, such as the Navier-Stokes equations, AH17
- Describe simplified governing equations, such as the Bernoulli or potential equations, their domain of validity and apply them in appropriate situations, AH19
- Obtain by an order of magnitude analysis, the simplified equations describing lubrication and boundary layers, AH22
- Describe in detail the physical phenomena associated with the interaction of a flow with a solid wall (as a function of its characteristics, e.g. roughness), AH5
- Describe in detail the physical phenomena associated with the interaction of a flow with a solid wall (as a function of its characteristics, e.g. roughness), AH5
- Apply by an order of magnitude analysis, the simplified equations describing lubrication and boundary layers, AH17
- Describe simplified governing equations, such as the Bernoulli or potential equations, their domain of validity and apply them in appropriate situations, AH15
- Define ,describe and apply the basic flow equations, such as the Navier-Stokes equations, AH14
- State the conserved quantities in a given flow and link them to a physical-mathematical description, AH13
- Describe flow in simple geometries, such as over a flat plate, in a tube, or around a sphere or airfoil, AH9
- Solve analytically or numerically the potential flow around an airfoil, AH19
- Explain in scientific terms the basic concepts of continuum mechanics (e.g. kinematics, dynamics, conservation equations, Eulerian/Lagrangian approach, stress and strain tensors, constitutive laws, linear elasticity, Newtonian fluid) and apply them to model and analytically resolve simple problems.
- Link flow behaviour with non-dimensional parameters (e.g. Reynolds and Mach numbers), AH2

## Transversal skills

- Summarize an article or a technical report.
- Continue to work through difficulties or initial failure to find optimal solutions.

## Teaching methods

Lectures and exercise sessions

## Assessment methods

written exam and two graded homeworks counting each for 10% of the final grade.

## Supervision

Office hours | No |

Assistants | Yes |

Forum | No |

## Resources

## Bibliography

Physical Hydrodynamics, Guyon, Hulin, Petit & Mitescu, Oxford,

2001.

## Ressources en bibliothèque

## Moodle Link

## In the programs

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Hydrodynamics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks**Type:**optional

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Hydrodynamics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks**Type:**optional

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Hydrodynamics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks**Type:**optional

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Hydrodynamics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks**Type:**optional

**Semester:**Spring**Exam form:**Written (summer session)**Subject examined:**Hydrodynamics**Lecture:**2 Hour(s) per week x 14 weeks**Exercises:**2 Hour(s) per week x 14 weeks**Type:**optional

## Reference week

Mo | Tu | We | Th | Fr | |

8-9 | |||||

9-10 | |||||

10-11 | |||||

11-12 | |||||

12-13 | |||||

13-14 | |||||

14-15 | |||||

15-16 | |||||

16-17 | |||||

17-18 | |||||

18-19 | |||||

19-20 | |||||

20-21 | |||||

21-22 |