Nondimensional
What is the rule of thumb for nondimensionalization?
Order of Magnitude 1
Classify the following Equation:
x2y''+xy' = ln(x)
2nd Order Linear Variable Coefficient Inhomogeneous ODE (Euler Cauchy)
What is the generic balance equation?
How would you solve the following for yp?
g(x) = ln(x)
Variation of Parameters
What is the name of the tower on campus?
Hoover
What is the Buckingham II equation? What does it tell you?
# of dimensionless groups = # variables/parameters - #fundamental dimensions
How would you solve the following?
y'' + 2y' = x2 + 4
characteristic equation + method of undetermined coefficents
What assumption results in the following?
dC/dt = 0
steady-state
How would you solve the following?
y' + 3y = ex
Integrating Factor
What cartoon character was seen in Lecture 22?
Spongebob
How do we typically nondimensionalize our dependent variable?
current change / total change
What is rule #2 for method of undetermined coefficients?
Your yp,guess cannot match your yH solution, if it does multiply by x
What is the assumption for the concentration leaving a CSTR?
well-mixed (e.g., concentration within the tank)
How would you solve the following?
y'' + 2y = sin(2x)
characteristic equation + method of undetermined coefficents
There is a couch in Dr. Kat's office, what color is it?
Orange
What does the Da number represent?
kinetics compared to diffusion
What would your yp, guess be?
y'' + y = 3x2ex
(Ax2 + Bx + C)(Dex)
How would you write the GEN term for a compound B being generated via a second order reaction (k) in a batch reactor?
A --> B
kCA2V
What is the integrating factor for the following equation?
2y''-3y=2x2
You would not use integrating factor
What animal was used as an example in Lecture 14?
JackRabbit
What is the Biot (Bi) number represent?
Bi = hLc / k
convection compared to conduction heat transfer
What is the Laplacian expansion for the r-direction in spherical coordinates?
1/r2 d/dr(r2 d/dr)
Where did Dr. Kat do her undergrad?
Cal Poly Pomona