Thermodynamics

Chapter 17 | 831TABLE 17–1Variation of fluid properties in flow direction in duct described inExample 17–3 for m . 3 kg/s constantP, kPa T, K V, m/s r, kg/m 3 c, m/s A, cm 2 Ma1400 473 0 15.7 339.4 ∞ 01200 457 164.5 13.9 333.6 13.1 0.4931000 439 240.7 12.1 326.9 10.3 0.736800 417 306.6 10.1 318.8 9.64 0.962767* 413 317.2 9.82 317.2 9.63 1.000600 391 371.4 8.12 308.7 10.0 1.203400 357 441.9 5.93 295.0 11.5 1.498200 306 530.9 3.46 272.9 16.3 1.946* 767 kPa is the critical pressure where the local Mach number is unity.Flow directionAA, Ma, r, T, VTrMa1400V12001000800P, kPa600400200FIGURE 17–13Variation of normalized fluidproperties and cross-sectional areaalong a duct as the pressure dropsfrom 1400 to 200 kPa.We note from Example 17–3 that the flow area decreases with decreasingpressure up to a critical-pressure value where the Mach number is unity, andthen it begins to increase with further reductions in pressure. The Machnumber is unity at the location of smallest flow area, called the throat (Fig.17–14). Note that the velocity of the fluid keeps increasing after passing thethroat although the flow area increases rapidly in that region. This increasein velocity past the throat is due to the rapid decrease in the fluid density.The flow area of the duct considered in this example first decreases andthen increases. Such ducts are called converging–diverging nozzles. Thesenozzles are used to accelerate gases to supersonic speeds and should not beconfused with Venturi nozzles, which are used strictly for incompressibleflow. The first use of such a nozzle occurred in 1893 in a steam turbine