Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows from edX

This course covers the Navier-Stokes equations for viscous flows: including pipe flows, channel flows and free surface flows, dynamical similarity and dimensional analysis, Stokes flows, similarity solutions and transient responses, lubrication analysis and surface tension. This course features lecture and demo videos, lecture concept checks, practice problems, and extensive problem sets.

This course is the second of a three-course sequence in incompressible fluid mechanics consisting of Advanced Fluid Mechanics 1: Fundamentals; Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows, and Advanced Fluid Mechanics 3: Potential Flows, Lift, Circulation & Boundary Layers. The series is based on material in MIT’s class 2.25 Advanced Fluid Mechanics, one of the most popular first-year graduate classes in MIT’s Mechanical Engineering Department. This series is designed to help people gain the ability to apply the governing equations, the principles of dimensional analysis and scaling theory to develop physically-based, approximate models of complex fluid physics phenomena. People who complete these three consecutive courses will be able to apply their knowledge to analyze and break down complex problems they may encounter in industrial and academic research settings.

The material is of relevance to engineers and scientists across a wide range of mechanical chemical and process industries who must understand, analyze and optimize flow processes and fluids handling problems. Applications are drawn from hydraulics, aero & hydrodynamics as well as the chemical process industries.

What's inside

Learning objectives

The navier-stokes equation and appropriate boundary conditions
The concept of dynamical similarity
Application of dimensional analysis to complex problems

Analysis of complex viscous flows such as stokes flows or transient responses
Lubrication analysis for thin films and free surfaces

The navier-stokes equation and appropriate boundary conditions
The concept of dynamical similarity
Application of dimensional analysis to complex problems
Analysis of complex viscous flows such as stokes flows or transient responses
Lubrication analysis for thin films and free surfaces

Syllabus

The Navier-Stokes equation and viscous flow

Pipe flows, channel flows and free surface flows

Dynamical Similarity and dimensional analysis

More Complex Viscous Flows; Stokes Flows, Similarity Solutions and Transient Responses

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Read about what's good

what should give you pause

and possible dealbreakers

Builds a strong foundation for beginners in incompressible fluid mechanics

Strengths an existing foundation in fluid mechanics for intermediate learners

Develops professional skills in advanced fluid mechanics

Covers unique perspectives and ideas in fluid mechanics

Takes a creative approach to an established topic in fluid mechanics

Offers a comprehensive study of one aspect of fluid mechanics

Reviews summary

Rigorous navier-stokes mastery

According to learners, Advanced Fluid Mechanics 2 is a highly rigorous and challenging course that provides an exceptional deep dive into the Navier-Stokes equations and viscous flows. Students frequently praise the instructor's remarkable clarity in explaining complex concepts like lubrication analysis and dimensional analysis. The problem sets are consistently highlighted as challenging yet essential for solidifying understanding and applying theory. While the course demands significant prior knowledge and dedication, particularly in advanced mathematics, many find it incredibly rewarding. Some feedback suggests a desire for more practical, industry-specific examples, although the course is largely seen as preparing students for academic and research settings. Recent reviews indicate noticeable improvements in clarity and updated material, suggesting the course continues to evolve.

This course is highly rigorous, requiring significant effort and strong prerequisites.

"The course material is rigorous, preparing me for graduate-level work."

"I found this course quite difficult to follow without prior exposure to some of the concepts."

"It requires significant effort, but it's worth it for the depth of understanding I gained."

"It assumes a very high level of prior knowledge; I had to supplement heavily with textbooks."

"A strong background in vector calculus and differential equations is essential for this course."

Recent reviews indicate positive updates and enhanced clarity in the course material.

"The updated material and clarity in recent lectures are noticeable improvements. This course has clearly evolved."

Problem sets are crucial for applying theory and solidifying understanding.

"The practice problems truly solidify my understanding."

"The problem sets are challenging but fair."

"The problem sets are key to learning this material."

"The rigor of the problem sets is perfectly balanced for deep learning."

"The problem sets are fantastic for applying the theory."

The instructor excels at simplifying complex fluid mechanics concepts.

"The instructor, Professor Tribuchet, makes incredibly complex topics like the Navier-Stokes equations and lubrication analysis remarkably clear."

"Professor Tribuchet's explanations are superb."

"The way Professor Tribuchet breaks down the Navier-Stokes equations is unparalleled."

"Professor Tribuchet makes a very difficult subject understandable."

Some learners find the course pace quick and suggest a need for more visual aids or detailed derivations.

"Sometimes I found the pace a bit fast, and having a strong background in vector calculus... is essential."

"The instructor is knowledgeable, but sometimes rushes through complex derivations without sufficient step-by-step explanation."

"Some topics like free surface flows could have used more visual aids."

"My only minor critique is that some explanations could use more visual aids."

While valuable, some learners desired more real-world industrial applications.

"It felt too theoretical. I was hoping for more applied examples relevant to industrial problems..."

"I found the problem sets overly mathematical and less about real-world scenarios."

"While the theoretical depth is commendable, I think more emphasis on practical applications or industry-specific case studies would benefit professionals."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows with these activities:

Connect with fluid mechanics researchers

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Expand your network and gain insights by reaching out to researchers actively working in the field of fluid mechanics.

Browse courses on Fluid Mechanics

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Identify potential mentors through university websites, research databases, and professional organizations
Craft a personalized email introducing yourself and expressing your interest in their work
Follow up with potential mentors who respond positively

Review differential equations

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Practice solving differential equations to solidify your understanding of this topic before the course begins.

Browse courses on Differential Equations

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Solve 10-15 differential equations of varying types

Write notes on Navier-Stokes Equation

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Enhance your understanding of this fundamental equation by creating detailed notes summarizing key concepts and derivations.

Browse courses on Fluid Mechanics

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Gather relevant course materials, including lecture notes and textbook chapters
Summarize the key concepts of the Navier-Stokes Equation, including its derivation and physical significance
Provide examples of how the Navier-Stokes Equation is used to solve problems in fluid mechanics

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Solve Navier-Stokes Equation practice problems

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Reinforce your problem-solving skills and deepen your understanding of the Navier-Stokes Equation by working through practice problems.

Browse courses on Fluid Mechanics

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Collect a set of practice problems from textbooks, online resources, or the course instructor
Attempt to solve the problems independently
Review your solutions and identify areas where you need further clarification
Seek assistance from the instructor or a tutor if needed

Tutor students in introductory fluid mechanics

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Enhance your understanding by helping others grasp the fundamental concepts of fluid mechanics.

Browse courses on Fluid Mechanics

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Identify opportunities to tutor other students, either through university programs or private arrangements
Prepare lesson plans and materials to effectively convey the concepts
Provide individualized support and guidance to students

Design a fluid system using the Navier-Stokes Equation

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Apply your knowledge of the Navier-Stokes Equation to design a functional fluid system, such as a pipe network or a hydraulic circuit.

Browse courses on Fluid Mechanics

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Define the specifications and requirements of the fluid system
Apply the Navier-Stokes Equation to model the fluid flow through the system
Optimize the design of the system to meet the desired performance criteria
Create a detailed report or presentation documenting the design process and results

Contribute to an open-source fluid mechanics project

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Gain practical experience and contribute to the fluid mechanics community by working on open-source projects.

Browse courses on Fluid Mechanics

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Identify open-source fluid mechanics projects on platforms like GitHub
Select a project that aligns with your interests and skills
Contribute to the project by fixing bugs, adding features, or improving documentation

Participate in a fluid mechanics competition

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Test your skills and knowledge by participating in fluid mechanics competitions, such as design challenges or research presentations.

Browse courses on Fluid Mechanics

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Research fluid mechanics competitions and identify those that align with your interests
Form a team or work independently to develop a solution to the competition's challenge
Submit your solution and present it to a panel of judges

Career center

Learners who complete Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows will develop knowledge and skills that may be useful to these careers:

Computational Fluid Dynamics Engineer

Computational Fluid Dynamics Engineers use computer simulations to study fluid flow and heat transfer. This course provides a strong foundation in the fundamentals of fluid mechanics, which is essential for Computational Fluid Dynamics Engineers to develop and validate their models.

See salaries and explore the career path for Computational Fluid Dynamics Engineer

Hydraulic Engineer

Hydraulic Engineers design and maintain systems that control water flow. These systems are important in areas such as flood prevention, water supply, and irrigation. The material in this course, especially relating to pipe flow, channel flow, and free surface flow, is a very good fit for the work done by Hydraulic Engineers.

See salaries and explore the career path for Hydraulic Engineer

Fluid Power Engineer

Fluid Power Engineers design and maintain hydraulic and pneumatic systems. This course may be useful for Fluid Power Engineers interested in developing a strong foundation in fluid dynamics, which is essential for understanding how these systems operate.

See salaries and explore the career path for Fluid Power Engineer

Aerospace Engineer

Aerospace Engineers design, develop, test, and operate aircraft, spacecraft, and other related systems. This course provides a solid foundation in the fundamentals of fluid mechanics, which are essential for Aerospace Engineers working on aerodynamics, propulsion, and other fluid-related systems.

See salaries and explore the career path for Aerospace Engineer

Geotechnical Engineer

Geotechnical Engineers study the behavior of soil and rock, and design foundations for buildings and other structures. This course may be useful for Geotechnical Engineers who work with soil liquefaction, seepage, and other fluid-related phenomena.

See salaries and explore the career path for Geotechnical Engineer

Civil Engineer

Civil Engineers design and construct buildings, bridges, roads, and other infrastructure projects. Although not all Civil Engineers work with fluid mechanics, this course can help build a foundation for those who do, especially in areas relating to hydraulic structures and water resources.

See salaries and explore the career path for Civil Engineer

Chemical Process Engineer

Chemical Process Engineers design processes and equipment to refine raw materials into useful products. This course covers concepts that Chemical Process Engineers use and can help someone interested in the field build a foundation in fluid mechanics.

See salaries and explore the career path for Chemical Process Engineer

Manufacturing Engineer

Manufacturing Engineers plan and oversee production processes in factories and other manufacturing facilities. The concepts of lubrication analysis and surface tension covered in this course may be useful for Manufacturing Engineers who work with fluids, such as in the production of paints, coatings, and adhesives.

See salaries and explore the career path for Manufacturing Engineer

Environmental Engineer

Environmental Engineers design and implement solutions to environmental problems, such as air pollution, water pollution, and waste management. The concepts of dynamical similarity and dimensional analysis covered in this course may be useful in modeling environmental systems, as they provide tools for studying complex phenomena with many variables.

See salaries and explore the career path for Environmental Engineer

Acoustical Engineer

Acoustical Engineers design and implement solutions to noise and vibration problems. This course may be полезно for Acoustical Engineers interested in understanding the fluid dynamics of sound propagation and absorption.

See salaries and explore the career path for Acoustical Engineer

Nuclear Engineer

Nuclear Engineers research, design, develop, and operate nuclear power plants and other nuclear facilities. While not all Nuclear Engineers work with fluid mechanics, this course may be a good fit for those interested in areas related to reactor cooling, fuel processing, and waste management.

See salaries and explore the career path for Nuclear Engineer

Mechanical Engineer

Mechanical Engineers are responsible for designing and building a wide range of machines and devices, from cars to robots. This course may be useful for Mechanical Engineers who wish to enter a subfield involving fluid dynamics by providing a foundation in fundamental concepts in the field.

See salaries and explore the career path for Mechanical Engineer

Petroleum Engineer

Petroleum Engineers plan and direct exploration and production of oil and gas. Their work helps provide energy resources that power modern society. Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows may be useful for this role in that it provides insight into complex fluid dynamics that may arise when exploring for oil and gas.

See salaries and explore the career path for Petroleum Engineer

Biomedical Engineer

Biomedical Engineers apply engineering principles to solve problems in the medical and health care fields. Some Biomedical Engineers work with fluid dynamics, so this course may be of interest in helping students learn about a complex field.

See salaries and explore the career path for Biomedical Engineer

Materials Scientist

Materials Scientists study the properties of materials that can be used in a wide variety of products, including electronics, aerospace components, and medical devices. Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows may be useful for a small portion of Materials Scientists who study liquids and polymers, as it provides a foundation in the modeling of fluid dynamics.

See salaries and explore the career path for Materials Scientist

Advanced Fluid Mechanics 2

The Navier-Stokes Equations for Viscous Flows

What's inside

Learning objectives

Syllabus

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Reviews summary

Rigorous navier-stokes mastery

Activities

Career center

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