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.
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
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
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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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 | |
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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 |
M. Hino, Fluid Mechanics, Tokyo: Asakura: ISBN: 4-254-20066-8 C305
I. Imai, Fluid Mechnaics(first part), Tokyo: Shoukabou ISBN: 4-7853-2314-0
Students' knowledge of visous fluid and compressible flows, and applications will be assessed.
Final exams 70%, exercise problems 30%.
Partial Differential Equations (MEC.B213.A), Vector Analysis (MEC.B214.A), Fundamenals of Fluid Mechanics (MEC.F201.R)