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Problem Solving
This page lists the requirements of a systematic problem solving approach. It is an
acquired skill which takes some time to master. However if you follow this thought
pattern, you will soon feel very comfortable working with these steps.
Suppose you are given a problem in a test or a quiz. Problem solving in a test is a
skill that lets you organize your thoughts and constantly keep focus on relevant
procedures that will yield the correct solution. Therefore it is recommended that
you note the following steps:
1. Statement of the Problem.
This section has two parts - a) Given b) To find. As you read the problem
thoroughly, you would recognize that the problem has supplied some fluid
properties, configurations, variables, equations, etc. for you to make a note of. Write
these down in the Given category using a set of conventional symbols that you would
use in the problem solution. Do not write the whole problem statement. Write down
what you realized as the supplied information, using a standard set of engineering
symbols. Then under b) To find category, list what the problem is asking you to
solve (again, using symbols).
The above section is critical. It takes a little practice to recognize and jot down
correctly what the wording in the problem implies. As you solve more problems, you
will learn more to recognize what the language in technical problem statements are
designed for.
2. System Diagram.
This section is not necessary in all problems. Some problems will supply you the
system configuration. The others will require you to sketch one for your own
understanding. For example, if you are applying a control volume analysis, you need
to identify the system and sketch a control volume with clearly identifiable control
surfaces. In problems of statics and dynamics, this step is like sketching the free
body diagram. Sketch one if it is necessary to apply the governing equations
correctly. Sometimes the problem will not ask you to sketch one explicitly. However
you realize that sketching one will make the solution much easier to solve and
demonstrate your understanding of the whole solution process. Then you should
sketch it even if the problem did not ask for it.
3. Assumptions.
This is a critical step in engineering problem solving. As you apply the engineering
principles, you will realize some principles have limitations in their use. Thus your
analysis becomes limited in applicability. It is important to note these limitations for
successful problem solving. Sometimes the problem statements provide some of the
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assumptions. But many problems will require you to make these assumptions since
it is an important step for engineers learn. Sometimes assumptions are made to
simplify governing equations also. Any assumptions listed in this section, should be
verified in the section on Critical Assessments given below.
4. Governing Equations.
Write the names of the governing equations that are applicable to solve the problem.
This step may be detailed as you reach specific parts of the solution. In other words,
actual equations may be presented in the body of the solution. But it is important to
recognize which equations you need to solve the problem.
5. Detailed Solution.
This is the actual body of the solution. Very often students read the problem and
start working out the detailed solution without realizing the importance of the
previous four steps. This is a bad habit. Soon you will realize that the previous steps
give you a direction to follow a step-by-step approach from the beginning to the end
of the problem. You should write all the details that are necessary for the examiner
to assess your knowledge. However, remember that you are not writing an essay in
English. In technical writing, short and direct answers are credited more than
esoteric use of language and roundabout answers.
6. Critical Assessment.
Once you arrive at your solution and it matches exactly what the problem asked you
to obtain, you may not think about this step at all. However if you had to make
certain assumptions and simplifications in step 3 and did not verify them, you
should verify them here. For example, suppose you assumed laminar flow to solve
the problem. You should verify that the calculated velocity of the flow does indeed
give you a Reynolds number less than the critical Reynolds number.
For design problems, there are several assumptions often necessary. It is important
to assess how good is the solution based upon these assumptions. If the assumptions
do not yield a good solution, you may have to return to step 3 and make different or,
new assumptions. This is a cyclic process in engineering design.