Problem Solving Techniques

In this section, different topics are introduced that should be kept in the back of your mind as you are working problems. These ideas are not things which you can sit down and memorize easily. They come out of solving many, many problems over time until the information becomes internalized. Here is a brief table of the important points:

Technique What? Examples
Definitions What do words mean? density, volume
Terminology What are things? distillation column, stripper
Keeping Track What do I know? flowrates, temperatures
Equations What can I do mass balances, energy balances
Formulas What am I supposed to do? use ideal gas law, use Raoult's law
Units What are the things I know? Btu/hr, grams/liter, pound-force
Interrelationships What gets me from here to there? density = 1/specific volume

Definitions are what you'll spend a lot of time learning when you first start taking your chemical engineering courses. Some of the terms, like density, will be familiar to you, while others, like Raschig rings (encountered in Mass Transfer and Separations) will not. As you encounter the new terms it is a good idea to spend some time trying to memorize what they mean and what units may be associated with them.

Terminology is very similar to definitions. Terminology, as I refer to it, deals with how language is used and what the problem statement is telling you. Students often have a difficult time figuring out how to draw a sketch of a problem because they simply haven't learned what the pieces of equipment look like. For example, distillation columns generally have one inlet, or feed stream, and two oulets, one is called the bottoms and one is called the overhead. Once you know that, you can draw almost any distillation column and know how it needs to connect to other things in your flowsheet. So, terminology deals with not only definitions, but with how things are connected.

Keeping track of information is a big part of being a good problem solver. When you have 5 pieces of equipment and 5 components and 12 streams, that give you a lot of numbers to keep track of in your mind all at once. It's very easy in cases like this to forget what you already know, or to try to solve for something that you'll never need. The problems you'll start out doing normally don't have so many streams or things to keep track of. Soon, though, it becomes impossible to juggle all those numbers and units without organizing it in some way that allows you to quickly and easily know whether you already found a certain number. The method I developed involves making tables of information and will be covered in detail here.

 Equations  are what enable you to solve the problem. Without being able to write good equations you'll almost never be able to get to the right answer. If you are able to get to the right answer it will most certainly have taken you much, much longer to get there than if you wrote true equations. Being able to write equations is also what makes you an engineer and not just a human calculator. This is also one of the major differences you'll find between high school, freshman level courses, and your core classes in engineering. A good engineer will know where things come from and how to create new equations for a new situation. In high school, you probably learned something, were assigned homework on it, did the homework by finding the right formula in the book and plugging numbers into it, and then quickly forgetting what it all meant. This is mostly true for the freshman level physics and chemistry classes that you have taken. But then you get to your introductory engineering courses and run into a problem. You can search the book for hours and never find the right equation for your problem. So, it's important to realize early on in your education that you are going to have to be able to write your own equations (hopefully correctly) to solve problems.

Formulas are different from equations. I use the term equations to refer to relationships that you, the engineer, have made in mathematical terms. Formulas are something you would use that someone else has come up with and that seem to work. An example of a formula is the ideal gas law: PV = nRT. You have probably already used this one many times in the past. You didn't rederive it each time (in fact, you probably aren't even sure where it comes from). You just know it works in many situations and you know what variables must go into it to get a good result back out. Being a good engineer requires you to remember when you can use certain formulas and when it would be a bad idea to do so. You also need to be able to remember what all the variables are and how to manipulate units to get a meaningful answer.

Units are probably one of the biggest problems that people run into when they are first starting out as an engineer. They are what can turn a completely correct answer into the completely wrong one. One of the tricks that we (professors and authors) like to pull on you is to give you a problem statement with more than one type of unit in it. For instance, we like to give youa problem where some of the masses are in pounds and some of them are in kilograms. This helps us make sure that you are paying attention and know what you are doing. If you don't convert one of the units into the other with the right conversion factor, you'll never get the right answer.

And finally, interrelationships between one variable and another are often what enables you to get from point A to point B when solving a problem. For instance, you will often end up using the fact that the specific volume is equal to one over the density, i.e., Specific Volume = 1/density. If you know this, you can often move from one part of the problem to the next. Being a successful engineer means that you probably know a lot of standard relationships between things without having to go look them up.

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