Fluid Mechanics Problems and Solutions

This collection of exercises is meant as a companion volume to the textbook Fluid Mechanics. It is the translation of the second edition of Aufgaben zur Stromungslehre. The book contains about 200 problems worked out in detail. In selecting the exercises I have been guided by didactical consider­ ations and included problems that demonstrate the application of the gen­ eral principles of continuum mechanics to more or less classical problems in fluid mechanics. Most of these problems are found in other textbooks or collections. On the other hand, there is a good number of exercises designed to develop and further the ability to model and solve practical problems. Besides these worked examples, thirty examination problems with answers only are included. In addition there are also exercises for Cartesian tensor calculus. The book has been translated by Professor M. T. Schobeiri, Texas A & M University. I thank him and also Dorothee Sommer and Peter Pelz for their help with this book.

1 The Concept of Continuum and Kinematics.- 1.2 Kinematics.- 2 Fundamental Laws of Continuum Mechanics.- 2.1 Conservation of Mass, Equation of Continuity.- 2.2 Balance of Momentum.- 2.3 Balance of Angular Momentum.- 2.4 Momentum and Angular Momentum in an Accelerating Frame.- 2.5 Applications to Turbomachines.- 2.6 Conservation of Energy.- 3 Constitutive equations.- Problem 3-1 Velocity of a raft.- Problem 3-2 Energy balance in a journal bearing.- Problem 3-3 Pressure driven flow of paper pulp.- Problem 3-4 Flow of a non-Newtonian fluid.- Problem 3-5 Extensional flow.- 4 Equation of Motion for Particular Fluids.- 4.1 Newtonian Fluids.- 4.2 Inviscid flow.- 4.3 Initial and Boundary Conditions.- 5 Hydrostatics.- 5.1 Hydrostatic Pressure Distribution.- 5.2 Hydrostatic Lift, Force on Walls.- 6 Laminar Unidirectional Flow.- Problem 6-1 Flow in an annular gap.- Problem 6-2 Crude oil transport through pipeline.- Problem 6-3 Oscillating pipe flow.- Problem 6-4 Comparison of a Couette-Poiseuille flow of a Newtonian fluid, a Stokes fluid, and a Bingham material.- 7 Fundamentals of Turbulent Flows.- Problem 7-1 Turbulent Couette flow.- Problem 7-2 Velocity distribution in turbulent Couette flow with given Reynolds number.- Problem 7-3 Turbulent pipe flow.- Problem 7-4 Crystal growth on pipe walls.- Problem 7-5 Comparison of momentum and energy flux in laminar and turbulent flow in a pipe.- Problem 7-6 Velocity distribution in a turbulent pipe flow resulting from the Blasius friction law.- Problem 7-7 Location of a pipe leakage.- Problem 7-8 Cooling of superheated steam by water injection.- 8 Hydrodynamic Lubrication.- Problem 8-1 Bearing with step slider.- Problem 8-2 Friction torque transmitted by the shaft to the journal.- Problem 8-3 Slider load in squeeze flow: Comparison between different slider geometries.- 9 Stream filament theory.- 9.1 Incompressible Flow.- 9.2 Steady Compressible Flow.- 9.3 Unsteady Compressible Flow.- 10 Potential Flow.- 10.3 Incompressible Potential Flow.- 10.4 Plane Potential Flow.- 11 Supersonic Flow.- 11.1 Oblique Shock Waves.- 11.3 Reflection of Oblique Shock Waves.- 11.5 Prandtl-Meyer Flow.- 11.6 Shock Expansion Theory.- 12 Boundary Layer Theory.- Problem 12-1 Boundary layer momentum equation.- Problem 12-2 Flow over a wedge.- Problem 12-3 Diffuser with discontinuous change of the cross-section.- Problem 12-4 Drag coefficient of a diamond airfoil.