2016 Fundamentals of Fluid Mechanics

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Academic unit or major
Undergraduate major in Mechanical Engineering
Hanamura Katsunori  Aoki Takayuki  Kyogoku Keiji  Tanahashi Mamoru  Suekane Tetsuya  Xiao Feng 
Class Format
Media-enhanced courses
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Course description and aims

This course focuses on basic concepts in fluid mechanics starting from continuum physics. Topics include fundamentals of ideal fluid, governing equations of fluid motion, Euler's equation of motion, vorticity and circulation, Bernoulli's theorem, streamlines, stream function and velocity potential function. By combining lectures and exercises, the course enables students to understand and acquire the fundamentals of ideal 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. Therefore, this lecture is mandatory in the course of mechanical engineering and treated as minimum requirement to take ‘Practical Fluid Mechanics’ and ‘Advanced Fluid Mechanics’.

Student learning outcomes

By the end of this course, students will be able to:
1) Understand and derive governing equations of ideal fluid.
2) Explain the principal theorems related to circulation and vorticity.
3) Acquire basic aspects of fundamental flow fields using Bernoulli's theorem.
4) Explain definitions of streamlines and stream function, velocity potential and complex velocity potential functions of basic flow field.
5) Explain lift and drag forces for the flow of ideal fluids over bodies.


Ideal fluid, Governing equations, Euler's equation of momentum, Vorticity and circulation, Bernoulli's theorem, Streamlines and stream function, Velocity potential function

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 after the 7th and 14th 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 Continuum physics, Stress, Ideal and viscous fluids, Compressibility Understand basic concept of fluid mechanics based on continuum physics and definition of ideal fluid
Class 2 Physical quantities representing flow, Lagrangian and Eulerian method, Euler's equation of continuity Understand flow quantities and methods which are required to describe flow
Class 3 Euler's equation of motion, Flux of momentum, Equation of state Understand Euler's equation of motion and flux of momentum
Class 4 Streamlines, Pathlines, Streaklines, Motions of fluid elements Understand fundamental methods which describe fluid motion
Class 5 First integral of momentum equation, Bernoulli's theorem Understand first integral of momentum equation and Bernoulli's theorem
Class 6 Applications of Bernoulli's theorem Understand applications of Bernoulli's theorem
Class 7 Theorem of streamline curvature, Lagrangian vortex theorem, Vorticity and circulation, vortex tube Understand several important theorems in fluid mechanics: theorem of streamline curvature and Lagrangian vortex theorem
Class 8 Kelvin's circulation theorem, Helmholtz's vortex theorem Understand several important theorems in fluid mechanics: Kelvin's circulation theorem and Helmholtz's vortex theorem
Class 9 Stream function and velocity potential function Understand stream function and velocity potential function to describe flow field
Class 10 Velocity potential function of a flow around the sphere in an uniform flow Understand velocity potential function of a flow around the sphere in an uniform flow
Class 11 Complex velocity potential Understand definition of complex velocity potential
Class 12 Complex velocity potentials of fundamental flow geometries Understand complex velocity potentials of fundamental flow geometries
Class 13 Applications of complex velocity potential Understand several applications of complex velocity potential
Class 14 Kutta-Joukowski theorem Understand Kutta-Joukowski theorem to predict lift and drag forces
Class 15 Schwarz-Cristoffel theorem Understand Schwarz-Cristoffel theorem to represent flow in a complex geometries


T. Miyauchi, M. Tanahashi, H. Kobayashi, Fundamentals of Fluid Mechanics, Tokyo: Surikougakusya ISBN:978-4-86481-023-4

Reference books, course materials, etc.

I. Imai, Fluid Mechnaics(first part), Tokyo: Shoukabou ISBN: 4-7853-2314-0
M. Hino, Fluid Mechanics, Tokyo: Asakura: ISBN: 4-254-20066-8 C305
JSME textbook series Fuild Mechanics, Tokyo: Maruzen ISBN: 978-4-888898-119-4 C3353

Assessment criteria and methods

Students' knowledge of ideal fluid, and applications will be assessed.
Final exams 80%, exercise problems 20%.

Related courses

  • Practical Fluid Mechanics
  • Advanced Fluid Mechanics

Prerequisites (i.e., required knowledge, skills, courses, etc.)

Partial Differential Equations(MEC.B213.A), Vector Analysis (MEC.B214.A).

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