Fluid mechanics is relevant to a wide variety of practical applications where fluids (gases or liquids) are used. The fluid
with a linear relationship between shear stress and strain rate is known as a Newtonian fluid, which is a very appropriate
model for air, gases, and water. In this course, we introduce a mathematical description of Newtonian fluid flows and derive
the fundamental equations by applying the conservation laws of mass, momentum, and energy.
The specific purposes of the class are:
1) To provide an understanding of the governing laws of Newtonian fluid motion described by partial differential equations.
2) To develop the ability to use the governing equations in solving fluid motions.
1) To provide an understanding of the governing laws of Newtonian fluid motion described by partial differential equations.
2) To develop the ability to use the governing equations in solving fluid motions.
- Students will be able to explain basic fluid properties such as viscosity and compressibility.
- Students will be able to examine the movement of fluid elements.
- Students will be able to derive the conservation equation of mass and momentum.
- Students will be able to calculate the complex potentials of ideal fluids.
- Students will be able to examine incompressible viscous fluid flows and to calculate velocity profiles and pressure losses in a pipe.
| Homework assignments and quizzes | Term-end examination | Total. | |
|---|---|---|---|
| 1. | 8% | 8% | |
| 2. | 8% | 15% | 23% |
| 3. | 8% | 15% | 23% |
| 4. | 8% | 15% | 23% |
| 5. | 8% | 15% | 23% |
| Total. | 40% | 60% | - |
Your final grade will be calculated according to the following process:
- Assignments and quizzes: 40%
- Term-end examination: 60%
An aggregate score of at least 60% is required to pass the course.
- Assignments and quizzes: 40%
- Term-end examination: 60%
An aggregate score of at least 60% is required to pass the course.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Nature of a fluid and fluid properties - Continuity - Compressibility - Viscosity - Newtonian fluid model (Newton's law of viscosity) |
- Read the textbook pp.1-6 | 90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 2. | Mathematical representations of fluid flow - Lagrangian description, Eulerian description - Streamlines, streamtubes, pathlines, and streaklines |
- Watch the lecture video "Mathematical representations of fluid flow (08:37)" and "Stream line (07:40)" - Submit the assignment #1 - Read the textbook pp.6-9 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 3. | Deformation of a fluid element (1) - Translation, deformation and rotation of fluid elements - Deformation rate tensor, strain rate tensor and rotation tensor - Vorticity |
- Watch the lecture video "Deformation rate of a fluid element (08:04)" - Submit the assignment #2 - Read the textbook pp.9-13 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 4. | Deformation of a fluid element (2) -Stress tensor |
- Watch the lecture video "Stress of viscous fluid -introduction- (12:27)" - Submit the assignment #3 - Read the textbook pp.14-17 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 5. | Fundamental equation (1) - Conservation equation of mass |
- Watch the lecture video "Derivation of continuity equation (08:28)" - Submit the assignment #4 - Read the textbook pp.19-21 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 6. | Fundamental equation (2) - Navier-Stokes equations |
- Watch the lecture video "Equation of motion of a fluid (08:17)" - Submit the assignment #5 - Read the textbook pp.21-23 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 7. | Circulation and Stokes's theorem - Definition of the circulation - Derivation of the Stokes's theorem |
- Watch the lecture video "Circulation (17:24)" - Submit the assignment #6 - Read the textbook pp.13-14 and pp.31-32 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 8. | Potential flows (1) - Velocity potential - Stream function - Cauchy-Riemann equations |
- Watch the lecture video "Stream function (06:05)" - Submit the assignment #7 - Read the textbook pp.31-35 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 9. | Potential flows (2) - Complex potential - Uniform flow - Irrotational vortex - Source and sink |
- Watch the lecture video "Complex potential (12:36)" - Submit the assignment #8 - Read the textbook pp.35-41 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 10. | Potential flows (3) - Complex velocity - Flow past a circular cylinder |
- Watch the lecture video "Doublet (07:39)" - Submit the assignment #9 - Read the textbook pp.42-44 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 11. | Potential flows (4) - Flow past a circular cylinder with circulation - Lift and drag acting on the circular cylinder - Magnus effect - Kutta-Joukowski theorem |
- Watch the lecture video "Flow past a circular cylinder with circulation (05:30)" - Submit the assignment #10 - Read the textbook pp.44-46 and pp51-54 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 12. | Incompressible viscous flow (1) - Steady flow between two parallel flat plates (Couette flow) - Velocity profile for the Couette flow for various pressure gradient |
- Watch the lecture video "A flow between two parallel flat plates (06:42)" - Submit the assignment #11 - Read the textbook pp.55-57 |
90minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 13. | Incompressible viscous flow (2) - Steady flow in a cylindrical pipe (Poiseuille flow) - Pressure drop in a fluid flowing through a cylindrical pipe |
- Watch the lecture video "Viscous flow in the cylindrical pipe (06:33)" - Submit the assignment #12 - Read the textbook pp.58-62 |
120minutes |
| - Review the today's lesson by watching the lecture video | 90minutes | ||
| 14. | Course summary and term-end examination - Comments on the examination - Toward the next step (overview of Fluid Mechanics 2) |
- Review the lesson 1-13 - Review the exercises in chapter 1-4 |
210minutes |
| - Review the term-end examination | 70minutes | ||
| Total. | - | - | 2650minutes |
| ways of feedback | specific contents about "Other" |
|---|---|
| Feedback in the class | 事前課題のフィードバックは，授業内での解説，補足説明，小テストなどによって行う．提出された課題や小テストの答案は，ScombZから返却する． |
Students are expected to be comfortable with the material from the following subjects:
- Hydrodynamics 1
- Hydrodynamics 2
- Complex Function Theory
- Hydrodynamics 1
- Hydrodynamics 2
- Complex Function Theory
- Non-social and professional independence development course
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | N/A |
- 7.AFFORDABLE AND CLEAN ENERGY
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
- 13.CLIMATE ACTION
Last modified : Thu Mar 06 10:07:26 JST 2025