Welcome to Week 1 of
Mathematics for Engineers, the capstone course.
In this week, we'll learn
the governing equations for our flow.
We'll begin with the Navier-Stokes equations
for the velocity field.
Then we'll define the vorticity field,
and derive its governing equation.
To solve for the flow around the cylinder,
we'll need to consider the geometry.
We'll look for a two-dimensional solution,
and define a scalar vorticity and a stream function.
The equations will contain
a single dimensionless parameter
called the Reynolds number.
Finally, we'll introduce log-polar coordinates,
which is a modified polar coordinate system
that simplifies the governing equations.
Please join me in this first week of
Mathematics for Engineers, the capstone course.