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Write Equations and Lookup Data

1- Read Carefully

2- Draw a Diagram

3- List Given Information

4- List All Assumptions

Write Equations & Lookup Data

6- Solve Equations

Verify Assumptions

8- Answers

This stairway shows that the solution for a problem is a logical sequence of steps.

5- Write Equations & Lookup Data

n this step, you must write all of the independent equations that describe the process you are analyzing. In this course, most of the equations will be independent, but that is NOT always the case.
An equation is NOT independent if the other equations can be rearranged and
combined algebraically to obtain the same equation.

2 x + y = 11

x - y = 1

x + 2 y = 10

Next, make a list of all of the unknown variables in these equations. Decide which of the unknowns can be determined from reference
data sources, such as the NIST WebBook, and look up their
values. This leaves you with a shorter list of the true
unknowns for the problem.

You may not need to solve ALL of the independent equations for ALL of the unknowns in order
to answer the questions that were posed
in the problem statement.

Lesson
4D Blog

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Lesson 4D: page 7 of 13

Students tend to skip the first four steps in this procedure and jump directly to this step.
On very simple problems, this approach may be effective, but it is a foolish approach to larger more complex problems.
In this step, you write a complete set of independent equations.
Complete and Independent are the key words here.
A complete set of equations describes all of the important aspects of the system.
Independent equations are not redundant.
Only 2 of the three equations shown here are independent. Why ?
If you subtract the 2nd equation from the 1st equation, the result is identical to the 3rd equation.
So, which equation is the redundant one ?
That question doesn’t make sense. Any 2 of the equations can be used to obtain the third one.
So, any two of the equations are independent. Pick any two you want !
It is generally best to keep the simplest equations in your independent set of equations.
The catch is that it sometimes takes experience to easily recognize which equations will be easier to solve.
The good news here is that in this course, most of the equations we will write will be independent, so we won’t have to worry too much about independence.
Next, we list all of the unknown variables that appear in our set of independent equations.
Look up any data you can in a reference book or website like the NIST Web Book.
The remaining unknowns are the ones you may need to determine in order to solve the problem.
Keep in mind that you don’t always need to solve ALL of the equations for all the unknowns.
You might get away with solving a subset of the independent equations for only those unknowns that you need in order to answer the questions that were posed in the problem statement.
Be alert. Don’t do more work than necessary.

Write Equations and Lookup Data

Ch 4, Lesson D, Page 7 - Write Equations and Lookup Data