2.14 THE "PIZZA" PROCEDURE FOR PROBLEM SOLVING Now that you have seen a few examples of solved problems, you may have noticed some common features in the solutions. In every problem, we define the system, orga nize information into a schematic, apply governing principles, make assumptions, evaluate properties, and perform calculations. If problems are tackled in this systematic way, errors are avoided and correct solutions achieved. In this section, we give an overview of effective problem-solving technique and offer hints for solving tough problems Many students find "getting started" to be the most difficult part of the problem. As problems become more involved (see, for example, Figure 1-13, which is a schematic of a Rankine cycle power plant used to generate electricity), the tendency of many students is to immediately try to calculate something-anything. This approach can cause problems. First, many students select an equation from the text without thinking about the restrictions on that equation. For example, a student may be trying to calculate temperature and select the ideal gas law simply because it contains temperature even though the substance they are analyzing is a liquid. More subtle errors also occur, such as applying an equation that is only true for adiabatic (insulated) cases to isothermal cases. The correct approach to solving problems involves stepping back, avoiding immediate equation grabbing, and thinking carefully about all aspects of the problem. In other words if you sit on your hands and give some thought to the solution before trying to calculate something, you might make more and faster progress than by an immediate calculation On the other hand, it is not always possible to see a solution procedure clearly from start to finish when beginning a problem. You may need to "play" with the equations to feel your way to a solution. Problems arise when you use equations that do not apply, so you must always be sensitive to the appropriate assumptions and restrictions on equations. Almost all solutions to engineering problems require three tasks. If each of these tasks is handled correctty, a reasonable and/or accurate solution will be obtainable; if one task is not handled well, then the odds are poor that the answer obtained will be correct. We compare the solution procedure to a three-legged stool; remove one leg from the stool, and the stool falls. For engineering problems, the three "legs" are (1) analysis, (2) application of goveming concepts, and (3) evaluation of properties These "legs" are described below, where we discuss a methodology to solve problems We lay out this discussion in the format we use to solve the example problems. Example Problem Statement The problem statement gives much information, either explicitly or implicitly. The information may be described in tems of the value of variables at different locations in the system, a drawing of an assembly of devices working together, descriptions of how a device operates, and so on. The question to be answered is asked. Approach: The analysis of the problem is wrapped up in the approach to the problem solution. This can be broken into about three steps (some problems require more, others less): Read the problem. This seems to be an obvious statement. Nevertheless, many students partially read the problem and then immediately start trying to calculate something. A quick or partial reading often misses crucial pieces of information. It is useful to read the problem statement at least twice Draw a schematic and organize the inforamtion. As noted in Chapter 1, a schematic diagram simply shows the relationship between various pieces of a systcm. Indicate the processes involved Give each location or piece of information a unique symbol consistent with how that information will be used in an equation. Include units with the given information. Also, write down what is being sought-not in words copied from the problem statement, but rather with a symbol you wil use in the equations Think. This is the step some students give little attention to. Now is the time to sit on your hands for a moment or two. Consider what is occurring in the system you have drawn. Does the problem have to be solved as a steady or unsteady process? Is it a closed or an open system? Decide which governing principles (e.g.. conservation of mass, conservation of energy, conservation of momentum, entropy balance, a force balance, a moment balance, etc.) are needed and how you will attack the problem