# CBE 30355 - Lecture Notes - Nov. 15, 2022

## Announcements

## Class notes

Read through pages 270-282 of the notes and view the online narration below. Don't forget to complete the quiz in Canvas!

The main points of the lecture were

## Goals:

After this class you should be able to:
- Apply Morgan's Theorem to obtain similarity solutions to boundary layer problems.

## Reading

- The class notes.
- BS&L, chapter 4

## Additional Readings:

It may be getting a bit chilly outside, but soon it will be warm again (OK, I'm an
optimist)! An interesting application of Bernoulli's equation to summer activities is the
air-powered squirt gun, AKA the Super Soaker. To see detailed information on how
such squirt guns work, check out the link given
here.

## Demonstration:

## Computer Example:

Boundary layer problems such as the Blasius Equation for flow past a flat plate yield non-linear ODE's once we've applied Morgan's Theorem. While these equations don't typically have analytic solutions, they are extremely simple to solve using ODE solvers as a system of first order differential equations. Because they usually have boundary conditions (rather than all the necessary initial conditions), you can "guess" the missing initial conditions, integrate the equations, and adjust the initial condition until the boundary condition is satisfied (called the shooting method, as it is analogous to doing artillery ranging shots). Such a program for the Blasius problem is given in the file miss.m. If you call this using a root solver it will yield the unknown initial condition (the dimensionless scaled shear stress at the plate). I've also tracked out the displacement thickness as an extra first order equation. This isn't necessary, but is far more convenient than integrating it later after the velocity profile is already solved.

David.T.Leighton.1@nd.edu