Flow through a Constricted Channel 227

Cylindrical Obstacle across a Straight Channel 231

Obstacle Close to a Wall 234

Drag and Lift on an Inclined Plate 235

19 Circulation around an Obstacle 240

Circulation Integral 242

Combined Velocity Fields 244

Forces on an Inclined Plate 247

20 Viscous Flow in Channels 252

Boundary Conditions 255

Steady Flow at Small Speeds (Re<<1) 256

Flow Due to a Moving Wall 257

Pressure-Driven Flow through a Channel 259

Viscous Flow through a Constricted Channel 262

Comparison with Irrotational Flow 266

Tangential Input Velocity 267

Channel with a Lateral Cavity 269

Uniform Velocity of Injection 271

Dynamic Similarity 273

21 Viscous Flow past an Obstacle 277

Viscous Flow past a Circular Cylinder 277

Viscous Force on a Solid Surface 280

Forces on a Circular Cylinder 282

Force Equilibrium 283

Viscous Dissipation 285

Constricted Tube 291

Constricted Tube with a Spherical Obstacle 294

Boundary Conditions 298

Steady Flow at Small Speeds 299

Tube with Uniform Driving Pressure 300

Tube with Uniform Input Velocity 302

Viscous Flow by Gravity through a Funnel 305

Forces on the Funnel 307

Dissipation in the Funnel 308

Viscous Flow past a Sphere 310

Comparison with an Analytic Solution 312

24 Seeping through Porous Materials 316

Percolation in (x,y) Space 316

Percolation in (x,y) by Navier-Stokes PDE 318

Percolation in (r ,z) Space 322

Percolation in (r ,z) by Navier-Stokes 324

25 Viscous Flow at Re>>1 in (x,y) 328

Viscous Flow in a Channel 330

Viscous Flow past a Circular Cylinder 332

Viscous Boundary Layer 335

Viscous Flow past a Rotating Cylinder 337

Viscous Flow past an Inclined Plate 340

Viscous Flow past an Airfoil 343

26 Viscous Flow at Re>>1 in (r ,z) 346

Parabolic Velocity Injection into a Tube 348

Jet into a Liquid 350

Viscous Flow Past a Sphere 352

27 Transient Viscous Flow at Re<<1 355

Transient Flow due to a Moving Wall 356

Transient Flow due to a Localized Force 357

Heat Transport by Conduction and Convection 361

Natural Convection in (x,y) 363

Natural Convection in (r ,z) 366

28 Viscous Flow in Three Dimensions 369

Extension of the Formalism to 3D 369

Flow through a Rectangular Duct 370

Flow through a Box with Two Orifices 374

Viscous Flow around a Cubical Obstacle 376

Viscous Flow by Gravity through a Funnel 380

Rotating Flow through a Funnel 383

Seeping through a Concrete Plate with a Pillar 385

29 Simplified PDEs for Viscous Flow 389

Steady Flow in a Constricted Channel at Re<<1 390

Flow past a Circular Cylinder at Re<<1 392

Flow through a Box with Two Orifices 394

Steady Viscous Flow at Re>>1 397

Flow past a Circular Cylinder at Re>>1 397

Flow in (r ,z) past a Sphere at Re>>1 399

References 402