23 - Exam 2 Review#

This is a short writeup of some of the key points that we have covered in the course since the last exam. You should be familiar with these points for Excel, Aspen, Ansys, Cantera, SolidWorks.

Excel Functions#

  • How to use the functions in Excel such as max, average, count, countif, vlookup, etc.

Equations#

  • Understand how to solve equations using linear algebra (Ax = b) with MINVERSE, MMULT, etc.

  • Understand how to solve equations using root finding like solver (f(x) = 0)

For example, the following system of equations can be solved any number of ways.

\[\begin{split} 2x + y + q = 4 \\ x + z = 5 \\ y + z = 6 \\ q + x + y = 10 \end{split}\]

How would you go about solving the above using linear algebra?

ODE’s and Derivatives#

  • Understand how to solve derivatives using rows and columns in Excel using Euler’s method

For example if you have the following differential equation (typical of a second order reaction), how would you solve it?

\[ \frac{dx}{dt} = -kx^2 \]

Excel VBA Loops#

  • Understand how to use VBA do and do while loops

For example, the sequence of triangular numbers is generated by the following formula:

\[ T_n = \frac{n(n+1)}{2} \]

Lets say you have an existing array of T = (0,1,3,6) and you want to add the next 10 triangular numbers to the array. How would you do that? The sum of the inverse of the Triangular array is a converging series, what is your estimate of the value of that converging series based on the 14 numbers in your array?

Regression#

  • Understand how to use regression to fit a curve to data using trendline

  • Understand how to use regression by minimizing the sum of square errors given an equation

How would you use solver to fit a parabolic curve to the following data?

\[\begin{split} x = [1,2,3,3,4,5,5] \\ y = [1.23,3.9,9.3,9.1,16.3,25.5,26] \end{split}\]

How would you use trendline to do the same thing?

Cantera#

  • Understand how to use the property data functions with Cantera including finding the enthalpy and other state variables for a given temperature and pressure.

  • Understand how to determine the adiabatic flame temperature of a given gas with a given stoichiometric ratio.

SolidWorks#

Understand how to make a basic drawing in SolidWorks

Ansys Workbench#

Understand how to do steady state and transient heat transfer in Ansys using drawings from SolidWorks

Aspen Plus#

Understand how to do basic simulations of chemicals and flash processes.