Thermodynamics

Chapter 1 | 37which is an exact mathematical expression of the problem statement with xand y denoting the unknown numbers. The solution to this system of twononlinear equations with two unknowns is obtained by a single click on the“calculator” icon on the taskbar. It givesx5andy1Discussion Note that all we did is formulate the problem as we would onpaper; EES took care of all the mathematical details of solution. Also notethat equations can be linear or nonlinear, and they can be entered in anyorder with unknowns on either side. Friendly equation solvers such as EESallow the user to concentrate on the physics of the problem without worryingabout the mathematical complexities associated with the solution of theresulting system of equations.EXAMPLE 1–12Analyzing a Multifluid Manometer with EESReconsider the multifluid manometer discussed in Example 1–7 and replottedin Fig. 1–61. Determine the air pressure in the tank using EES. Alsodetermine what the differential fluid height h 3 would be for the same airpressure if the mercury in the last column were replaced by seawater with adensity of 1030 kg/m 3 .AIR1WATEROilh 1h 2h 32Solution The pressure in a water tank is measured by a multifluidmanometer. The air pressure in the tank and the differential fluid height h 3if mercury is replaced by seawater are to be determined using EES.Analysis We start the EES program by double-clicking on its icon, open anew file, and type the following on the blank screen that appears (we expressthe atmospheric pressure in Pa for unit consistency):g=9.81Patm=85600h1=0.1; h2=0.2; h3=0.35rw=1000; roil=850; rm=13600P1+rw*g*h1+roil*g*h2-rm*g*h3=PatmMercuryFIGURE 1–61Schematic for Example 1–12.Here P 1 is the only unknown, and it is determined by EES to beP 1 129647 Pa 130 kPawhich is identical to the result obtained before. The height of the fluid columnh 3 when mercury is replaced by seawater is determined easily byreplacing “h30.35” by “P1129647” and “r m13600” by “r m1030,”and clicking on the calculator symbol. It givesh 3 4.62 mDiscussion Note that we used the screen like a paper pad and wrote downthe relevant information together with the applicable relations in an organizedmanner. EES did the rest. Equations can be written on separate linesor on the same line by separating them by semicolons, and blank or commentlines can be inserted for readability. EES makes it very easy to ask“what if” questions, and to perform parametric studies, as explained inAppendix 3 on the DVD.EES also has the capability to check the equations for unit consistency ifunits are supplied together with numerical values. Units can be specified