
Examine the velocity field as functions of x, y, z and time, use unit vectors i j k, and derive acceleration via the material derivative with local and convective terms.
Explore mass conservation under steady, incompressible flow, deriving simplified continuity equations in Cartesian and cylindrical coordinates, and using density constancy and Mach number to justify incompressible modeling.
Derive cylindrical continuity for steady incompressible flow with v_z = B z, solving for v_r to satisfy mass conservation, yielding v_r = - (B/2) r^2 + C/r.
Plot four streamlines from a psi equation by solving for y, then compute velocity components u and v from psi, and compare with MATLAB contour and quiver visuals.
Evaluate the gradient squared of the velocity potential, confirm it equals zero, derive the stream function from phi, and find the streamline value at (1,1).
From continuity, derive the y-velocity as v(y) = -6y for a 2d steady flow, then verify irrotationality and use Bernoulli's equation to compute the pressure difference.
Are you tired of struggling in your Fluids class?
If you answered yes, then this course is for you! Here you'll find easy to understand lectures and plenty of fully-worked examples to help you learn the challenging subject of Fluid Mechanics.
This course is the third in a 3-course series designed to teach the fundamentals of Fluid Mechanics. In this section, we continue learning about fluid in motion and we will introduce the concept of dimensional analysis.
Here's what we'll cover
This course covers the following topics that are generally found in a university-level Intro to Fluids class:
Lagrangian and Eulerian Descriptions
Velocity and Acceleration Fields
Continuity Equation
Navier Stokes
Stream Function
Vorticity and Irrotationality
Velocity Potential
Dimensional Analysis & Buckingham Pi Theorem
Intro to Laminar and Turbulent Flow
And more!
Here's what you get when you enroll
Lifetime access to the course
Easy to follow, on-demand lecture videos
Plenty of fully-worked examples in a variety of difficulty levels
Downloadable outline of notes to help you create an organized set of notes and to help you follow along
What's the format of the course?
Let me just say that I hate engineering courses taught with PowerPoint slides. Due to this, you will not find slides here.
I think people learn better when they have to write the material. That means the majority of my lectures are handwritten. I give you a brief outline of notes to help you follow along and to help minimize the length of the videos.
Speaking of video length... am I the only one who doesn't like watching hour-long lecture videos? I didn't think so.
To eliminate that frustration my lectures are broken up into shorter segments, typically 12-15 minutes.
And if you are here for examples, I made them easy to find. Almost all the examples are in their own videos, that way you can look through the notes and pick and choose which ones you want to watch.