Page 12 - Aerodynamics for Engineering Students

Contents ix

6.4.9 Total pressure change across the normal shock 303
6.4.10 Pitdt tube equation 306
6.5 Mach waves and shock waves in two-dimensional flow 307
6.6 Mach waves 307
6.6.1 Mach wave reflection 315
6.6.2 Mach wave interference 317
6.7 Shock waves 318
6.7.1 Plane oblique shock relations 319
6.7.2 The shock polar 323
6.7.3 Two-dimensional supersonic flow past a wedge 329
6.8 Wings in compressible flow 331
6.8.1 Transonic flow, the critical Mach number 331
6.8.2 Subcritical flow, small perturbation theory
(Prandtl-Glauert rule) 334
6.8.3 Supersonic linearized theory (Ackeret’s rule) 347
6.8.4 Other aspects of supersonic wings 367
Exercises 372

7 Viscous flow and boundary layers 373
Preamble 373
7.1 Introduction 373
7.2 The development of the boundary layer 375
7.2.1 Velocity profile 375
7.2.2 Boundary-layer thickness 377
7.2.3 Non-dimensional profile 377
7.2.4 Laminar and turbulent flows 377
7.2.5 Growth along a flat surface 378
7.2.6 Effects of an external pressure gradient 379
7.3 The boundary-layer equations 380
7.3.1 Derivation of the laminar boundary-layer equations 381
7.3.2 Various definitions of boundary-layer thickness 385
7.3.3 Skin friction drag 387
7.3.4 Solution of the boundary-layer equations for a flat plate 390
7.3.5 Solution for the general case 395
7.4 Boundary-layer separation 396
7.4.1 Separation bubbles 398
7.5 Flow past cylinders and spheres 399
7.5.1 Turbulence spheres 405
7.5.2 Golf balls 406
7.5.3 Cricket balls 407
7.6 The momentum integral equation 408
7.6.1 An approximate velocity profile for the laminar
boundary layer 41 1
7.7 Approximate methods for a boundary layer on a flat plate
with zero pressure gradient 414
7.7.1 Simplified form of the momentum integral equation 415
7.7.2 Rate of growth of a laminar boundary layer on a flat plate 415
7.7.3 Drag coefficient for a flat plate of streamwise
length L with wholly laminar boundary layer 416
7.7.4 Turbulent velocity profile 416
7.7.5 Rate of growth of a turbulent boundary layer on a flat plate 418