2023 Hydraulics I

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Academic unit or major
Undergraduate major in Civil and Environmental Engineering
Fujii Manabu  Utsumi Nobuyuki 
Class Format
Lecture    (Face-to-face)
Media-enhanced courses
Day/Period(Room No.)
Tue3-4(MI1-107(M114))  Fri3-4(MI1-107(M114))  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

Course description and aims

This course focuses on the hydraulics, especially the its fundamental concept and physical laws. First, the basic equation to describe the fluid dynamics and continuous equation are derived and the several fundamental water flows with/without viscosity are introduced. After learn the surface wave on a water surface, the conservation laws of the energy and momentum are derived. Based on the conservation lows, the fundamental hydraulic phenomena are discussed.
In the human society of today, civil engineering is demanded to create and retain the safe and health water environments. The understanding of the water flow should provide a foundation to achieve the mission. By learning the fundamental physical law and basic phenomena of the water flow, you will be able to acquire a skill to understand the complex water flow and its effects in the actual water environment such as the river, lake and ocean.

Student learning outcomes

By the end of this course, students will be able to:
I. Describe the water flow using the basic equations and understand its physical meaning.
II. Understand the fundamental and important concepts and parameters to represent the water flow, and explain their physical meanings.
III. Understand the fundamental law of the surface wave of the water, and explain its physical features.
IV. Understand the energy and momentum conservation law for the water flow, and apply them to several fundamental cases of the water flow.


Description of flow field, Navier-Stokes equation, vorticity/circulation and viscosity, surface wave of water, small amplitude wave, Bernoulli’s law, conservation law of momentum, specific energy, flownet

Competencies that will be developed

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

Class flow

At the each class, solutions to exercise problems are requested. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Concept of "Fluid" - description of water flow Understand a concept of "Flow", and method to describe the water flow using mathematical expression.
Class 2 Basic equation of water flow - derivation of the equation of motion and conservation equation Understand the Navier-Stokes equation and conservative equation
Class 3 Features of basic equation of water flow - Solution of fundamental flow field (Hydrostatic pressure and two-dimensional Poiseuille Flow) Solve the basic equation of water flow and understand the physical features of several fundamental flow field
Class 4 Deformation of water and stress Understand how to describe the water's deformation. Understand the relation between the deformation and stress.
Class 5 Representaion of water flow pattern with the volticity and circulation Understand the stream function, volticity and circulation
Class 6 Advection and diffusion process - Advection equation, production of volticity, impact of viscosity and boundary layer Understand the fundamental aspect of the turbulent flow. Understand relation between diffusion/ stress and turbulence
Class 7 Surface wave of water - theory of small amplitude wave, phase velocity and dispersion, trajectory of water particle, energy transportation by the wave and shoaling Understand the theory of small amplitude wave and dispersioness of the wave, the motion of water particle in the wave, propagation of a group of waves and shoaling effect
Class 8 Fundamental principle of water flow I - derivation of energy conservation law (Bernoulli's principle) Derive Bernoulli's principle and understand it
Class 9 Fundamental principle of water flow II - application of energy conservation law (Bernoulli's principle) Apply Bernoulli's principle to the flow in simple container
Class 10 Fundamental principle of water flow III - derivation of momentum conservation law Understand the transportation of momentum in water flow and derive the conservation law of the momentum
Class 11 Fundamental principle of water flow IV - application of momentum conservation law Apply the momentum conservation law and evaluate a drag force caused by water flow.
Class 12 Application of the conservation laws to open-channel flow Understand the relationship between water depth and specific energy in a open-channel flow
Class 13 Evalution of the flow using "flownet" Understand a method to evaluate flow using "flownet"
Class 14 Final examination

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


Hino Mikio, Hydraulics "Meikai Suirigaku", Maruzen (1983/01), ISBN-13: 978-4621027783 (Japanese)

Reference books, course materials, etc.

Ikeda Shunsuke, Hydraulics "Shoujutu Suirigaku", Gihodo (1999/01), ISBN-13: 978-4765515993 (Japanese)
Other references in Japanese

Assessment criteria and methods

Students' knowledge of "description of water flow with mathematical equation" and "fundamental concept and laws to evaluate wate flow" will be assessed.
Final exams 80% (in classroom), exercise problems 20%.

Related courses

  • CVE.B202 : Hydraulics II
  • CVE.B311 : River Engineering
  • CVE.B310 : Coastal Engineering and Oceanography
  • CVE.G310 : Water Environmental Engineering

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


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