Advanced Fluid Mechanics: Fundamentals

Course Description

Welcome to the exciting world of Advanced Fluid Mechanics: Fundamentals! This cutting-edge course, offered by the prestigious MITx, is designed to take your understanding of fluid mechanics to the next level. As the first installment in a three-course sequence, this program lays the groundwork for mastering complex fluid flow problems that are essential in various engineering and scientific fields.

What You'll Learn

In this comprehensive course, you'll dive deep into the fascinating realm of advanced fluid mechanics. You'll explore:

• The intricate connections between fluid mechanics and continuum mechanics
• The mysteries of hydrostatics
• Concepts of buoyancy and rigid body accelerations
• Inviscid flow and the application of Bernoulli's theorems
• Complex fluid flow problems using control volume analysis

Prerequisites

To make the most of this advanced course, you should be comfortable with:

• Undergraduate-level fluid mechanics
• Multivariable calculus
• Undergraduate differential equations
• Elementary vector and tensor manipulation
• Fourier transforms
• Solving second-order linear ODEs and PDEs

Course Content

• Continuum mechanics and its relationship to fluid dynamics
• Hydrostatics and fluid equilibrium
• Buoyancy principles and rigid body accelerations
• Inviscid flow theory and applications
• Bernoulli's theorems and their practical use
• Control volume analysis for complex engineering problems
• Euler's equation and its significance in fluid mechanics
• The Mechanical Energy Equation and its applications
• Mass conservation, linear and angular momentum theorems
• First and second laws of thermodynamics in fluid systems

Who Should Take This Course

This course is ideal for:

• Engineers and scientists working in mechanical, chemical, and process industries
• Professionals in hydraulics, aero & hydrodynamics, and chemical process industries
• Graduate students and advanced undergraduates looking to enhance their fluid mechanics knowledge

Real-World Applications

The skills acquired in this course have wide-ranging applications, including:

• Analyzing and solving complex fluid flow problems in industrial and academic research settings
• Designing more efficient hydraulic systems
• Optimizing chemical processes
• Working on cutting-edge aerospace projects

Syllabus

1. Continuum viewpoint and the equations of motion
2. Hydrostatic analysis of fluids in static equilibrium, buoyancy
3. Inviscid flow (differential approach): Euler's equation, Bernoulli's integral, and the effects of streamline curvature. The Mechanical Energy Equation
4. Control volume theorems (integral approach): Mass conservation, linear momentum theorem, angular momentum theorem, first and second laws of thermodynamics
5. Application to increasingly complex systems