Page 54 - Separation process engineering

subproblems may arise; you may find there are not enough data to solve the problem. Recycle through the
problem-solving sequence to solve these subproblems.

Step 4, do it, is often the first step that inexperienced problem solvers try. In this step the mathematical
manipulations are done, the numbers are plugged in, and an answer is generated. If your plan was
incomplete, you may be unable to carry out this step. In that case, return to step 2 or step 3, the explore or
plan steps, and recycle through the process.
In step 5, check your answer. Is it the right order of magnitude? For instance, commercial distillation

columns are neither 12 centimeters nor 12 kilometers high. Does the answer seem reasonable? Have you
avoided blunders such as plugging in the wrong number or incorrectly punching the calculator? Is there an
alternative solution method that can serve as an independent check on the answer? If you find errors or
inconsistencies, recycle to the appropriate step and solve the problem again.
The last step, generalize, is important but is usually neglected. In this step you try to learn as much as
possible from the problem. What have you learned about the physical situation? Did including a particular
phenomenon have an important effect, or could you have ignored it? Generalizing allows you to learn and
become a better problem solver.

At first these steps will not “feel” right. You will want to get on with it and start calculating instead of
carefully defining the problem and working your way through the procedure. Stick with a systematic
approach. It works much better on difficult problems than a “start calculating, maybe something will
work” method. The more you use this or any other strategy, the more familiar and less artificial it will
become.

In this book, example problems are solved using this strategy. To avoid repeating myself, I will not list
step 0, but it is always there. The other six steps will usually be explicitly listed and developed. On the
simpler examples some of the steps may be very short, but they are always present.

I strongly encourage you to use this strategy and write down each step as you do homework problems. In
the long run this method will improve your problem-solving ability.

A problem-solving strategy is useful, but what do you do when you get stuck? In this case heuristics or
rules of thumb are useful. A heuristic is a method that is often helpful but is not guaranteed to help. A
large number of problem-solving heuristics have been developed. I have listed ten (Wankat and Oreovicz,
1993) that are often helpful to students.
Problem-Solving Heuristics:

1. Try solving simplified, limiting cases.
2. Relate the problem to one you know how to solve. This heuristic encapsulates one of the major
reasons for doing homework.

3. Generalize the problem.
4. Try putting in specific numbers. Heuristics 3 and 4 are the opposite of each other. Sometimes it is
easier to see a solution path without all the details, and sometimes the details help.

5. Solve for ratios. Often problems can be solved for ratios, but there is not enough information to solve
for individual values.

6. Do the solvable parts of the problem. This approach may provide information that allows you to solve
previously unsolvable parts.
7. Look for information that you haven’t used.

8. Try to guess and check. If you have a strong hunch, this may lead to an answer, but you must check
your guess.