Thermodynamics

34 | ThermodynamicsGiven: Air temperature in DenverTo be found: Density of airMissing information: AtmosphericpressureAssumption #1: Take P = 1 atm(Inappropriate. Ignores effect ofaltitude. Will cause more than15% error.)Assumption #2: Take P = 0.83 atm(Appropriate. Ignores only minoreffects such as weather.)FIGURE 1–58The assumptions made while solvingan engineering problem must bereasonable and justifiable.Energy use:Energy savedby insulation:IMPOSSIBLE!$80/yr$200/yrFIGURE 1–59The results obtained from anengineering analysis must be checkedfor reasonableness.Step 3: Assumptions and ApproximationsState any appropriate assumptions and approximations made to simplify theproblem to make it possible to obtain a solution. Justify the questionableassumptions. Assume reasonable values for missing quantities that are necessary.For example, in the absence of specific data for atmospheric pressure,it can be taken to be 1 atm. However, it should be noted in the analysisthat the atmospheric pressure decreases with increasing elevation. For example,it drops to 0.83 atm in Denver (elevation 1610 m) (Fig. 1–58).Step 4: Physical LawsApply all the relevant basic physical laws and principles (such as the conservationof mass), and reduce them to their simplest form by utilizing theassumptions made. However, the region to which a physical law is appliedmust be clearly identified first. For example, the increase in speed of waterflowing through a nozzle is analyzed by applying conservation of massbetween the inlet and outlet of the nozzle.Step 5: PropertiesDetermine the unknown properties at known states necessary to solve theproblem from property relations or tables. List the properties separately, andindicate their source, if applicable.Step 6: CalculationsSubstitute the known quantities into the simplified relations and perform thecalculations to determine the unknowns. Pay particular attention to the unitsand unit cancellations, and remember that a dimensional quantity without aunit is meaningless. Also, don’t give a false implication of high precision bycopying all the digits from the screen of the calculator—round the results toan appropriate number of significant digits (see p. 38).Step 7: Reasoning, Verification, and DiscussionCheck to make sure that the results obtained are reasonable and intuitive,and verify the validity of the questionable assumptions. Repeat the calculationsthat resulted in unreasonable values. For example, insulating a waterheater that uses $80 worth of natural gas a year cannot result in savings of$200 a year (Fig. 1–59).Also, point out the significance of the results, and discuss their implications.State the conclusions that can be drawn from the results, and any recommendationsthat can be made from them. Emphasize the limitationsunder which the results are applicable, and caution against any possible misunderstandingsand using the results in situations where the underlyingassumptions do not apply. For example, if you determined that wrapping awater heater with a $20 insulation jacket will reduce the energy cost by $30a year, indicate that the insulation will pay for itself from the energy it savesin less than a year. However, also indicate that the analysis does not considerlabor costs, and that this will be the case if you install the insulationyourself.