Engineering Problem Solving
Good problem solving ability is an essential skill for all engineers. There is no universally accepted methodology for solving engineering problems. Problem solving skills are attained through practice. The problem sets assigned as homework in your engineering courses are the mechanisms for mastering the concepts learned in the lecture and in the reading material. It is important that you spend time trying to do the problems on your own before seeking help, because the process of thinking about and strategizing a solution procedure is extremely important in assimilating the concepts.
The computer-based problem sets designed for this course are intended to build up your problem solving skills. They are not different from chapter end problems in a good text book, except that we have tried to give you guidance and feedback during the problem solving process so you know you are on the right track. Hint and help files are provided to guide you towards a solution. In case you are unable to get the right answer, you can take a look at how the solution was arrived at. Where possible we have provided references to text readings and examples that are relevant to the problem at hand.
Even though there are no general procedures for problem solving, several techniques can help. Resist the urge to write formulas and substitute numbers into them. This usually leads to errors and mistakes besides making it harder for some one else to check your solution. Some suggested steps are given below. At first these steps may seem superfluous and unnecessary, but being systematic is the hallmark of a good engineer. It will also help you develop good written communication skills which are essential to function as an effective engineer. Not all problems will require you to go through all the steps, so use your judgment and intuition.
Step 1. Abstract the Problem
Remind yourself that you can do the problem with the information given. While some problems appear to be difficult at first, rest assured that after reading it a few times, you will be able to tackle it. Write an abstract of the problem statement listing all of the information given and defining some variables and constants along the way. Ask the question: what exactly is being asked in this particular problem? Do not repeat the problem statement, rather try to restate it in terms of how you interpreted it. One good way to abstract the problem statement is to draw an engineering sketch. This means if the problem is about a compressor you would draw a sketch and supply appropriate information. Use engineering symbols where possible as shown in your reading assignments. You are defining and planning. Include the specified constraints. If it is useful, write down given information at appropriate locations in the sketch.
Drawing a sketch, even if it is given in the problem statement, allows you to concentrate and focus your attention on the problem. This is good practice even in tests. When you are drawing a sketch you are translating from a verbal to a graphical interpretation of the problem statement. The sketch may be of the equipment or of the events taking place as verbally described in the problem. Use engineering paper if it helps you to draw better sketches. This paper has vertical and horizontal ruling that allows better sketches.
Step 2. Make a list of Variables
List all the variables/unknowns associated with the problem. Make a list of known quantities. Pay close attention to dimensional units. Each number (variable) must be accompanied by units. Do not assume that you have to use all the data given in the problem statement to solve the problem. On the other hand, data given may not be sufficient and in that case you may need to make certain assumptions as stated below.
Step 3. State the Basis for your calculations.
In many problems, the statement may include a base flow rate or volume or production capacity. If it is given in the problem, restate it. If it is necessary to assume one (e.g. you can do the problem assuming 100 kg of feed) do so and state your basis clearly.
Step 4. Make and State your Assumptions.
Most problems require assumptions to arrive at an answer. Sometimes these assumptions are given in the problem statement. Sometimes you may need to make them yourself. If you do, you must state it, and if possible, justify why you made that assumption. Any assumptions you make in arriving at your mathematical model should be clearly stated. Do not oversimplify the problem because in that case your answer may not apply.
Step 5. List your References.
Often, you need to get additional data to solve the problem. The source of all data and information used in your solution, except that contained in the problem statement, should be referenced. References must contain enough information so that your supervisor could easily look up your referenced data.
Step 6. Develop Model Equations.
Write down all the governing equations using the algebraic symbols to represent the unknowns. Remember the acronym: KISS ( Keep it Simple and Solvable). If necessary make more assumptions to simplify the problem. You may need to add more variables to define the model. Check for consistency of units used, eg. Both sides of an equation must have the same set of units. All terms being added or subtracted must have the same units. Terms within exponentials or logarithms must be dimensionless. Each equation must be preceded by a line stating what it is or how it is obtained. All variables should be clearly identified and defined with appropriate units. The most common mistake is using inconsistent sets of units. Try to use conventional symbols where possible (e.g. x i for liquid mole fractions, L for liquid flow rates, etc.). Graphical correlations would be included here if they are required to solve the problem.
You will need one equation for every unknown variable in the problem. If you do not have enough equations, you may need to think about other possible relationships among the variables you have overlooked. If you have more equations than variables, some of the equations may be redundant in nature. Go back and check your assumptions and model if there is an inconsistency. Later on, you will be introduced formal methods of analyzing a model to determine if there are enough degrees of freedom to solve the problem (called degrees of freedom analysis).
Step 7. Solve the Equations.
Equations may be algebraic in nature or they may be in the form of differential equations if there is a time or distance variable involved in the problem. There are powerful software available for solving such equations. TKSolver® is great for solving collections of linear and nonlinear equations. Mathcad®, Matlab® and Maple® are great for differential equation systems. Simulink® is great for ordinary differential equation models. Femlab® is great for solving partial differential equations. Maple® and Mathematica® are great for solving symbolic equations. You should get familiar with these tools in the course of your engineering education. Use the right tool for the problem.
Choose a method of solving the mathematical model for the unknowns and execute the solution. You should label each equation when you write it down. Round off answers to reasonable significant digits because calculators and computers report 7 or more digits and typically you do not have that kind of accuracy in the data or the model used.
Remember the principle “GIGO: Garbage in; Garbage Out” as it applies to computer based solutions. Your answer is only as good as what you put in. Which is why the next step is important.
Step 8. Interpret the Solution and make Conclusions
Look at the solution to the equation and interpret the numbers in light of the problem statement. Check if it makes sense physically. For example, if the answer is a fluid velocity, then compare against normally expected velocities in the problem context. If it is a temperature, then check if it is very high or very low. Use your intuition and common sense to validate your answer.
If the answer is unreasonable, then may be you need to check your assumptions and/or model equations. Using computers and calculators you can avoid errors in arithmetic.
Engineering design problems are a different breed. These are typically stated with minimal information and often have multiple answers or solutions. The problem statements are often vague. Eg. Design a bridge to cross the river. You as the engineer must choose the location, the length, width, material of construction, structure etc., taking into account the requirements of the bridge and constraints imposed by social, economic, safety and political considerations. By the time you graduate, you are expected to pick up the necessary skills to tackle such open ended problems.