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Problem Solving in Engineering


One of the primary tasks for engineers is often solving problems. It is what they are, or should be, good at. Solving engineering problems requires more than just learning new terms, ideas and concepts, and using rules and laws.


To find out what engineering is really about, we must learn how to apply these concepts and laws to real or hypothetical situations. Experience has shown that this kind of learning cannot occur without practice. This means spending more time working problems than reading the text.


Problem solving is more than merely substituting numbers in a mathematical formula. We should begin by studying the ideas, the concepts, and their relationships first. Then we should attempt the problems as a way to find out whether or not we understand the subject.


Problem Solving Process



In order to build a model and solve the problem, the following steps may be followed:


     1.   Carefully identify what is given in the problem. This is an important step because it makes things clear before attacking the problem. Read the entire problem carefully. You may need to briefly write down the question using symbols, make lists or tables of known and unknown information, and draw a diagram of the physical situation.


     2.   Carefully identify the objective of the problem. This could be the most important step, because it becomes the foundation for all the rest of the steps. What is the problem asking you to solve or find? Sometimes the objective of the problem is clear; some other times you need to lists the unknown information in order to identify the objective.


     3.   Decide which mathematical tool best suits the problem. What are the possible paths of solution to be followed? What are the processes involved? What are the relationships involved? And, determine which path and process promise the greatest likelihood of success. This step will help you build a collection of analytical methods, many of them will work to solve the problem, and however, many others may not work. Also, one method may produce fewer equations to be solved than another, or it may require less mathematics than other methods.


     4.   Write equations and develop a model. After you decide on the method, document the process very well by writing the equations to actually start solving the problem.


     5.   Attempt a solution. Present detailed solution before putting real numbers into equations. Paper-and pencil, calculator, and computer tools are all available to pursue the solution.


     6.   Verify the solution. Is it realistic, expected, or not at all? Ask yourself whether the solution you have obtained makes sense. Does the magnitude of the answer seem realistic? You may want to rework the problem via an alternative method to test the validity of your original answer. By doing so, you develop your perception about the most efficient methods to solve the problem. In real life, any design is checked by several independent means. Acquiring the habit of verifying the answer will help you as a student and as an engineer in the future.


     7.   Finally, if the solution is realistic, present the solution to your professor, boss, or team members. If not, then return to step 3 and continue through the process again.


It is important to know that although the above steps have been organized to apply to engineering foundations types of problems, the problems to be solved during one’s career will vary in complexity and magnitude.



Working Example


As an example of the general guidelines for problem solving, let us work a sample problem.




Consider a tank that is used to store a liquid. Liquid can be let into the tank through an inlet pipe at the top, and it discharges from the tank through an orifice near the base. Such a situation occurs frequently in mechanical and chemical engineering applications. Consider two cases for the flow through the orifice: laminar and turbulent. What is the rate of outflow from the tank if the height of the liquid is 0.5 m and the discharge coefficient is 0.7.




By reading the problem carefully and drawing a diagram similar to the following Figure, we will have covered steps 1 and 2.


A liquid storage system.


The basis of this approach to model building is that the equations which constitute a model are not arbitrary mathematical entities, but have a consistent physical basis. There are certain types of equation which describe different aspects of a model.


A knowledge of this helps to ensure that all equations are written down. For step 3 recall the relationship between the volumetric rate of outflow Q measured in (m3/s) and the height of the liquid h measured in (m).





where Cd is a constant of proportionality called the discharge coefficient. The discharge coefficient is constant that depend on the shape of the orifice.


It could be a sharp-edged, a short flush-mounted tube, or a rounded orifice. In this example, we have assumed that the volumetric flow rate of the liquid is proportional to the height only, however, in practice the flow rate depends on the pressure drop across the orifice, orifice cross-sectional area, and fluid density.


The dependent variable Q is a function of the independent variable h. Therefore, the input function is the head h, the function rule is “multiply the input by Cd”, and the resulting output is the flow rate Q. A graph of Q against h is shown in the following Figure.


A graph of Q and h relationship for a laminar flow.


If the flow through the orifice is turbulent then a different functional relationship will exist between Q and h





A graph of Q against h

A graph of Q against h


Now in accord with step 5, we substitute the values and the units for the algebraic symbols. For laminar flow



For turbulent flow