### 2018　Practical Fluid Mechanics B

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Instructor(s)
Aoki Takayuki  Oshima Shuzo  Horiuti Kiyosi  Shimura Masayasu
Class Format
Lecture / Exercise
Media-enhanced courses
Day/Period(Room No.)
Mon5-8(W541)
Group
B
Course number
MEC.F211
Credits
2
2018
Offered quarter
4Q
Syllabus updated
2018/3/20
Lecture notes updated
-
Language used
Japanese
Access Index

### Course description and aims

This course focuses on basic concepts of viscous flow and its applications. Topics include fundamentals of viscous fluid, Navier-Stokes equations, Reynolds number, exact solutions of Navier-Stokes equations for parallel flows such as Couette-Poiseuille flow and Hagen-Poiseuille flow, Stokes's approximation, Oseen's approximation, boundary layer, Compressible flows. By combining lectures and exercises, the course enables students to understand and acquire the fundamentals of viscous fluid which are important for developments of real applications in mechanical engineering.

Fluid mechanics is one of the most important basic science in mechanical engineering. Following to ‘Fundamentals of Fluid Mechanics’, this lecture focuses on viscous fluids which appears in real worlds. By combining lectures and exercises, the course enables students to understand and acquire the fundamentals of viscous flow.

### Student learning outcomes

By the end of this course, students will be able to:
1) Understand and derive governing equations of viscous fluid.
2) Acquire exact solutions of Navier-Stokes equations for several parallel flows.
3) Explain basic aspects of boundary layer
4) Explain Stokes's and Oseen's approximations and derive friction and pressure drags for viscous fluids over bodies.
5) Explain basic aspects of compressible flows

### Keywords

Viscous fluid, Navier-Stokes equations, Reynolds number, Parallel flows, Couette-Poiseuille flow, Hagen-Poiseuille flow, Boundary layer, Stokes's approximation, Oseen's approximation, Compressible flows

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

### Class flow

The course is taught in lecture style. Exercise problems will be assigned every 2 or 3 classes. Required learning should be completed outside of the classroom for preparation and review purposes.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Viscosity, Strain tensor, Rate of deformation Understand basic concept of viscous fluid and characteristics of strain tensor and rate of deformation
Class 2 Navier-Stokes equations, Couette flow, Reynolds number Derive Navier-Stokes equations and understand basics of Couette flow and Reynolds number
Class 3 Parallel flow, Couette-Poiseuille flow, Hagen--Poiseuille flow Understand several parallel flows as exact solutions of Navier-Stokes equations
Class 4 Rayleigh's problem and flows induced by oscillating walls Understand exact solutions of Navier-Stokes equations for flows induced by oscillating walls
Class 5 Concept of boundary layer, Prandtl's boundary layer equation Understand concept of boundary layer and derive boundary layer equation
Class 6 Blasius solution of boundary layer equation Understand Blasius solution of boundary layer equation
Class 7 Numerical solution of boundary layer equation Obtain numerical solution of boundary layer equation
Class 8 Momentum-integral equation of boundary layer Understand Momentum-integral equation of boundary layer
Class 9 Separation of boundary layer Understand separation boundary layer and its effects
Class 10 Stokes's approximation Understand Stokes's approximation of Navier-Stokes equations
Class 11 Stokes's approximation of a flow around the sphere in an uniform flow Understand Stokes's approximation of a flow around the sphere in an uniform flow
Class 12 Oseen's approximation Understand Oseen's approximation of Navier-Stokes equations
Class 13 Oseen's approximation of a flow around the sphere in an uniform flow Understand Oseen's approximation of a flow around the sphere in an uniform flow
Class 14 Fundamental concepts of compressible flows, Mach number, Shock Understand fundamental concepts of compressible flows with Mach number and shock
Class 15 Governing equations of compressible flow Derive governing equations of compressible flow and understand basic aspects of compressibility

### Textbook(s)

M. Hino, Fluid Mechanics, Tokyo: Asakura: ISBN: 4-254-20066-8 C305

### Reference books, course materials, etc.

I. Imai, Fluid Mechnaics(first part), Tokyo: Shoukabou ISBN: 4-7853-2314-0

### Assessment criteria and methods

Students' knowledge of visous fluid and compressible flows, and applications will be assessed.
Final exams 70%, exercise problems 30%.