Thermodynamics

Chapter 1 | 27Solution The reading of a manometer attached to a tank and the atmosphericP atm = 96 kPapressure are given. The absolute pressure in the tank is to be deter-mined.Assumptions The fluid in the tank is a gas whose density is much lowerP = ?than the density of manometer fluid.h = 55 cmProperties The specific gravity of the manometer fluid is given to be 0.85.We take the standard density of water to be 1000 kg/m 3 .Analysis The density of the fluid is obtained by multiplying its specificgravity by the density of water, which is taken to be 1000 kg/m 3 :SG = 0.85r SG 1r H2 O2 10.852 11000 kg>m 3 2 850 kg>m 3Then from Eq. 1–23,FIGURE 1–46P P atm rghSchematic for Example 1–6.1 N 96 kPa 1850 kg>m 3 219.81 m>s 2 210.55 m2 a1 kg # ba 1 kPam>s21000 N>m b 2 P atmFluid 1 100.6 kPah 1Discussion Note that the gage pressure in the tank is 4.6 kPa.Fluid 2h 2Fluid 3Many engineering problems and some manometers involve multiple immisciblefluids of different densities stacked on top of each other. Such systems1h 3can be analyzed easily by remembering that (1) the pressure change across afluid column of height h is P rgh, (2) pressure increases downward in agiven fluid and decreases upward (i.e., P bottom P top ), and (3) two points atthe same elevation in a continuous fluid at rest are at the same pressure.The last principle, which is a result of Pascal’s law, allows us to “jump”FIGURE 1–47In stacked-up fluid layers, the pressurechange across a fluid layer of densityr and height h is rgh.from one fluid column to the next in manometers without worrying aboutpressure change as long as we don’t jump over a different fluid, and theA flow sectionfluid is at rest. Then the pressure at any point can be determined by startingor flow devicewith a point of known pressure and adding or subtracting rgh terms as weadvance toward the point of interest. For example, the pressure at thebottom of the tank in Fig. 1–47 can be determined by starting at the freeFluidsurface where the pressure is P atm , moving downward until we reach point 1at the bottom, and setting the result equal to P 1 . It gives1 2In the special case of all fluids having the same density, this relation reducesto Eq. 1–23, as expected.Manometers are particularly well-suited to measure pressure drops acrossa horizontal flow section between two specified points due to the presenceof a device such as a valve or heat exchanger or any resistance to flow. Thisis done by connecting the two legs of the manometer to these two points, asshown in Fig. 1–48. The working fluid can be either a gas or a liquid whosedensity is r 1 . The density of the manometer fluid is r 2 , and the differentialfluid height is h.hr 1A BFIGURE 1–48Measuring the pressure drop across aflow section or a flow device by adifferential manometer.r 2a