Thermodynamics

Chapter 1 | 33Performing the integration gives the variation of gage pressure in the gradientzone to beP P 1 r 0 g 4H p sinh1 a tan p 4Then the pressure at the bottom of the gradient zone (z H 4 m)becomes sinh 1 a tan p 4 54.0 kPa 1gage2zH b4 14 m2P 2 8.16 kPa 11040 kg>m 3 219.81 m>s 2 2p44 ba 1 kN1000 kg # b m>s2Discussion The variation of gage pressure in the gradient zone with depth isplotted in Fig. 1–56. The dashed line indicates the hydrostatic pressure forthe case of constant density at 1040 kg/m 3 and is given for reference. Notethat the variation of pressure with depth is not linear when density varieswith depth.z, m43.532.521.510.500 10 20 30P, kPa40 50 60FIGURE 1–56The variation of gage pressure withdepth in the gradient zone of the solarpond.1–12 ■ PROBLEM-SOLVING TECHNIQUEThe first step in learning any science is to grasp the fundamentals and to gaina sound knowledge of it. The next step is to master the fundamentals by testingthis knowledge. This is done by solving significant real-world problems.Solving such problems, especially complicated ones, require a systematicapproach. By using a step-by-step approach, an engineer can reduce the solutionof a complicated problem into the solution of a series of simple problems(Fig. 1–57). When you are solving a problem, we recommend that youuse the following steps zealously as applicable. This will help you avoidsome of the common pitfalls associated with problem solving.Step 1: Problem StatementIn your own words, briefly state the problem, the key information given,and the quantities to be found. This is to make sure that you understand theproblem and the objectives before you attempt to solve the problem.Step 2: SchematicDraw a realistic sketch of the physical system involved, and list the relevantinformation on the figure. The sketch does not have to be somethingelaborate, but it should resemble the actual system and show the key features.Indicate any energy and mass interactions with the surroundings.Listing the given information on the sketch helps one to see the entireproblem at once. Also, check for properties that remain constant during aprocess (such as temperature during an isothermal process), and indicatethem on the sketch.EASY WAYINTERACTIVETUTORIALSEE TUTORIAL CH. 1, SEC. 12 ON THE DVD.PROBLEMSOLUTIONHARD WAYFIGURE 1–57A step-by-step approach can greatlysimplify problem solving.