Thermodynamics

858 | ThermodynamicsFIGURE 17–47The complex interactions betweenshock waves and expansion waves inan “overexpanded” supersonic jet.The flow is visualized by a schlierenlikedifferential interferogram.Photo by H. Oertel sen. Reproduced by courtesy ofthe French-German Research Institute of Saint-Louis, ISL. Used with permission.EXAMPLE 17–10Estimation of the Mach Numberfrom Mach LinesEstimate the Mach number of the free-stream flow upstream of the spaceshuttle in Fig. 17–36 from the figure alone. Compare with the known valueof Mach number provided in the figure caption.Ma 1WeakshockSolution We are to estimate the Mach number from a figure and compareit to the known value.Analysis Using a protractor, we measure the angle of the Mach lines in thefree-stream flow: m 19°. The Mach number is obtained from Eq. 17–47,b weakd 10°m sin 1 a 1Ma 1b S Ma 1 1sin 19°S Ma 1 3.07Our estimated Mach number agrees with the experimental value of 3.0 0.1.Discussion The result is independent of the fluid properties.(a)Ma 1StrongshockEXAMPLE 17–11Oblique Shock Calculationsb strongd 10°Supersonic air at Ma 1 2.0 and 75.0 kPa impinges on a two-dimensionalwedge of half-angle d 10° (Fig. 17–48). Calculate the two possibleoblique shock angles, b weak and b strong , that could be formed by this wedge.For each case, calculate the pressure and Mach number downstream of theoblique shock, compare, and discuss.(b)FIGURE 17–48Two possible oblique shock angles,(a) b weak and (b) b strong , formed by atwo-dimensional wedge of half-angled 10.Solution We are to calculate the shock angle, Mach number, and pressuredownstream of the weak and strong oblique shocks formed by a twodimensionalwedge.Assumptions 1 The flow is steady. 2 The boundary layer on the wedge isvery thin.Properties The fluid is air with k 1.4.