Viscous Fluid Dynamics

Course title

A0016000

Middle-level Diploma Policy (mDP)

Program / Major	mDP	Goals	Courses
Fundamental Mechanical Engineering	D	自然科学の法則に基づいて機械の運動機構や動特性、構造や強度、物質・運動量・エネルギーの流れなど機械工学の基盤技術に関わる物理現象を理解し、現象の予測や解析を行うことができる。	Main
Advanced Mechanical Engineering	F	産業界や社会の要請を把握して解決するべき課題を設定し、機械工学の学理を応用して異分野を含む融合分野で革新的な機能を創成することができる。	Sub
Environment and Materials Engineering	B	地球環境や地域社会との調和を見据えて、さまざまな工学分野に関わる問題を解決することができる。	Sub
Chemistry and Biotechnology	B	地球環境や地域社会との調和を見据えて、さまざまな工学分野に関わる問題を解決することができる。	Sub
Electrical Engineering and Robotics	D	電気工学や関連する工学の技術分野を課題に適用し、社会の要求を解決するために応用することができる。	Sub
Advanced Electronic Engineering	E	専門的デザイン課題について解決する能力を身に付けることができる。	Sub
Information and Communications Engineering	F	社会のニーズに対して技術課題を主体的に発見し、工学分野における分野横断的な知識も活用しつつ、計画的・継続的に取り組んで課題を達成することができる。	Sub
Computer Science and Engineering	G	技術的課題に対してさまざまな工学分野の知識を関連付けながら主体的に取り組み、継続的に学修する能力を身に付けることができる。	Sub

Purpose of class

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.

Course description

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.

Goals and objectives

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.

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	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%	-

Evaluation method and criteria

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.

Language

Japanese

Class schedule

	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
1.		- 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
2.		- 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
3.		- 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
4.	Deformation of a fluid element (2) -Stress tensor	- 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
5.	Fundamental equation (1) - Conservation equation of mass	- 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
6.	Fundamental equation (2) - Navier-Stokes equations	- 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
7.		- 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
8.		- 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
9.		- 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
10.		- 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
11.		- 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
12.		- 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
13.		- 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
14.		- Review the term-end examination	70minutes
Total.	-	-	2650minutes

Feedback on exams, assignments, etc.

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．

Textbooks and reference materials

Will be introduced in the class.

Prerequisites

Students are expected to be comfortable with the material from the following subjects:
- Hydrodynamics 1
- Hydrodynamics 2
- Complex Function Theory

Office hours and How to contact professors for questions