Thermodynamics

Chapter 17 | 845(b) Since the flow is isentropic, the properties at the exit plane can also becalculated by using data from Table A–32. For Ma 2 we readP eP 0 0.1278Thus,andThe nozzle exit velocity could also be determined from V e Ma e c e , where c eis the speed of sound at the exit conditions: 845.2 m>sT eT 0 0.5556r er 0 0.2300 Ma t * 1.6330P e 0.1278P 0 10.12782110 MPa2 0.1278 MPaT e 0.5556T 0 10.55562 1800 K2 444.5 Kr e 0.2300r 0 10.23002 14.355 kg>m 3 2 1.002 kg/m 3A e 1.6875A* 11.68752 120 cm 2 2 33.75 cm 2V e Ma e *c* 11.633021517.5 m>s2 845.1 m/sA eA* 1.6875V e Ma e c e Ma e 2kRT e 2 B11.42 10.287 kJ>kg # K21444.5 K2 a1000 m 2 >s 21 kJ>kg b(c) Since the flow is steady, the mass flow rate of the fluid is the same at allsections of the nozzle. Thus it may be calculated by using properties at anycross section of the nozzle. Using the properties at the throat, we find thatthe mass flow rate ism # r*A*V* 12.761 kg>m 3 2120 10 4 m 2 21517.5 m>s2 2.86 kg/sDiscussion Note that this is the highest possible mass flow rate that canflow through this nozzle for the specified inlet conditions.17–5 ■ SHOCK WAVES AND EXPANSION WAVESWe have seen that sound waves are caused by infinitesimally small pressuredisturbances, and they travel through a medium at the speed of sound. Wehave also seen that for some back pressure values, abrupt changes in fluidproperties occur in a very thin section of a converging–diverging nozzleunder supersonic flow conditions, creating a shock wave. It is of interest tostudy the conditions under which shock waves develop and how they affectthe flow.Normal ShocksFirst we consider shock waves that occur in a plane normal to the directionof flow, called normal shock waves. The flow process through the shockwave is highly irreversible and cannot be approximated as being isentropic.Next we follow the footsteps of Pierre Lapace (1749–1827), G. F. BernhardRiemann (1826–1866), William Rankine (1820–1872), Pierre HenryHugoniot (1851–1887), Lord Rayleigh (1842–1919), and G. I. Taylor