Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows
Learn how to apply the Navier-Stokes equations to viscous flows. Analyze pipe, channel and Stokes flows, and use dynamical similarity, dimensional analysis, and lubrication theory to model fluid optimization and handling problems in industrial and academic settings.
Course Information
Certificate Track
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About this Course
In this graduate-level online course from the MIT Department of Mechanical Engineering, you will learn how to use the Navier-Stokes equations and techniques like dimensional analysis to understand complex fluid mechanics problems.
The second in a three-course sequence covering incompressible fluid mechanics, this course focuses on viscous flows. It covers the following topics: 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.
Based on material from 2.25 Advanced Fluid Mechanics – one of the most popular first-year graduate classes in MIT’s Mechanical Engineering Department – this series consists of the following three modules:
- Advanced Fluid Mechanics 1: Fundamentals
- Advanced Fluid Mechanics 2: The Navier-Stokes Equations for Viscous Flows
- Advanced Fluid Mechanics 3: Potential Flows, Lift, Circulation & Boundary Layers
Through lecture and demo videos, lecture concept checks, practice problems, and extensive problem sets, this series is designed to help you 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.
Learners 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 and hydrodynamics, as well as the chemical process industries.
What you'll learn
- 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 flow or transient responses
- Lubrication Analysis for thin films and free surfaces
Prerequisites
Comfort with undergraduate-level fluid mechanics, multivariable calculus and undergraduate differential equations: elementary vector and tensor manipulation, Fourier transforms, solving second order linear ODEs and PDEs. Students without this background will find there is a steep learning curve and may have to put in more than the estimated time effort.
Note: this module (2.25.2x) is designed to be stand-alone. You do not need to take the first module (2.25.1x) to successfully complete this module.
Meet your instructors
Gareth McKinley
Professor, Mechanical Engineering
Gareth McKinley is the School of Engineering Professor of Teaching Innovation within the Department of Mechanical Engineering at MIT. He received his BA and M.Eng. degrees from the University of Cambridge and his Ph.D (1991) from the Chemical Engineering department at MIT. He taught in the Division of Engineering and Applied Sciences at Harvard from 1991-1997 and was an NSF Presidential Faculty Fellow from 1995-1997. He served as Executive Editor of the Journal of Non-Newtonian Fluid Mechanics from 2001 to 2009 and as Associate Editor of Journal of Fluid Mechanics from 2007-2009. He most recently served as the Associate Dept. Head for Research of the Mechanical Engineering Department at MIT from 2008-2013. He is also a co-founder of Cambridge Polymer Group. He is the author of over 300 technical publications and was one of the winners of the 2007 Publication Award of the Society of Rheology. He is a Fellow of the American Physical Society. He was the recipient of the 2013 Bingham Medal of the Society of Rheology and in 2014 he was awarded the Gold Medal of the British Society of Rheology. He served as President of the Society of Rheology from 2015-2017 and is also the past chair of the US National Committee of Theoretical and Applied Mechanics (USNC/TAM). In 2019 he was elected to the National Academy of Engineering and also inducted as a Fellow of the Royal Society of London.)
Gareth McKinley’s research interests include extensional rheology of complex fluids, non-Newtonian fluid dynamics, microrheology & microfluidics, field-responsive fluids, super-hydrophobicity, wetting of nanostructured surfaces and the development of nanocomposite materials.
Areas of Expertise
- Non-Newtonian Fluid Mechanics
- Rheology
Major Works:
- Keshavarz, B., Divoux, T., Manneville, S., McKinley G.H., Nonlinear Viscoelasticity and Generalized Failure Criteria for Biopolymer Gels, ACS Macro Letters , (2017), 6 663-667; DOI: http://10.1021/acsmacrolett.7b00213
- Hyun, K., Wilhelm, M., Klein, C.O., Cho, K.S., Nam, J.G., Ahn, K.H., Lee, S.J., Ewoldt, R.H. and McKinley, G.H., A Review of Nonlinear Oscillatory Shear Tests: Analysis and Application of Large Amplitude Oscillatory Shear (LAOS), Prog. Poly. Sci , (2011) 36 , 1697
- Pipe, C.J. and McKinley, G.H., Microfluidic Rheometry, Mech. Research Comm. , (2009), 36 110-120.
- Tuteja, A., Choi, W., Ma, M., Mabry, J.M., Mazzella, S.A., Rutledge, G.C., Cohen, R.E. and McKinley, G.H., Designing Superoleophobic Surfaces, Science , 318 (2007), 1618-1622.
- Sridhar, T. and McKinley, G.H., "Filament Stretching Rheometry of Complex Fluids”, Annual Reviews of Fluid Mechanics, Annual Reviews Press, 34 , pp. 375-415, (2002).
