Thermodynamics

at constant velocity in still air may be different at different locations(Fig. 17–10).Fluid flow regimes are often described in terms of the flow Mach number.The flow is called sonic when Ma 1, subsonic when Ma 1, supersonicwhen Ma 1, hypersonic when Ma 1, and transonic when Ma 1.EXAMPLE 17–2Mach Number of Air Entering a DiffuserAir enters a diffuser shown in Fig. 17–11 with a velocity of 200 m/s. Determine(a) the speed of sound and (b) the Mach number at the diffuser inletwhen the air temperature is 30°C.Solution Air enters a diffuser with a high velocity. The speed of sound andthe Mach number are to be determined at the diffuser inlet.Assumptions Air at specified conditions behaves as an ideal gas.Properties The gas constant of air is R 0.287 kJ/kg · K, and its specificheat ratio at 30°C is 1.4 (Table A–2a).Analysis We note that the speed of sound in a gas varies with temperature,which is given to be 30°C.(a) The speed of sound in air at 30°C is determined from Eq. 17–11 to bec 2kRT B11.4210.287 kJ>kg # K21303 K2a1000 m 2 >s 2(b) Then the Mach number becomesMa V c200 m>s349 m>s 0.5731 kJ>kg b 349 m /sDiscussion The flow at the diffuser inlet is subsonic since Ma 1.AIR200 KAIR300 KChapter 17 | 829V = 320 m/sMa = 1.13V = 320 m/sMa = 0.92FIGURE 17–10The Mach number can be different atdifferent temperatures even if thevelocity is the same.AIRV = 200 m/sT = 30°CDiffuserFIGURE 17–11Schematic for Example 17–2.17–3 ■ ONE-DIMENSIONAL ISENTROPIC FLOWDuring fluid flow through many devices such as nozzles, diffusers, and turbineblade passages, flow quantities vary primarily in the flow directiononly, and the flow can be approximated as one-dimensional isentropic flowwith good accuracy. Therefore, it merits special consideration. Before presentinga formal discussion of one-dimensional isentropic flow, we illustratesome important aspects of it with an example.EXAMPLE 17–3Gas Flow through a Converging–Diverging DuctCarbon dioxide flows steadily through a varying cross-sectional-area ductsuch as a nozzle shown in Fig. 17–12 at a mass flow rate of 3 kg/s. The carbondioxide enters the duct at a pressure of 1400 kPa and 200°C with a lowvelocity, and it expands in the nozzle to a pressure of 200 kPa. The duct isdesigned so that the flow can be approximated as isentropic. Determine thedensity, velocity, flow area, and Mach number at each location along theduct that corresponds to a pressure drop of 200 kPa.Solution Carbon dioxide enters a varying cross-sectional-area duct at specifiedconditions. The flow properties are to be determined along the duct.Stagnationregion: m ⋅1400 kPa200°CCO 21400 1000 767 200P, kPa3 kg/sFIGURE 17–12Schematic for Example 17–3.