Fluid Mechanics: Problems and Solutions

ISBN-13: 9783540616528 / Angielski / Twarda / 1997 / 605 str.

Springer; Joseph H. Spurk

Opis

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."

Spis treści

1 The Concept of Continuum and Kinematics.- 1.2 Kinematics.- Problem 1.2-1 Calculation of material coordinates for given pathlines.- Problem 1.2-2 Velocity and acceleration in material and spatial coordinates with given pathlines.- Problem 1.2-3 Material description of a potential vortex flow.- Problem 1.2-4 Material description of an axisymmetric stagnation point flow.- Problem 1.2-5 Pathlines, streamlines, and streaklines of an unsteady flow field.- Problem 1.2-6 Kinematics of an irrotational and divergence free flow field.- Problem 1.2-7 Kinematics of an unsteady, plane stagnation point flow.- Problem 1.2-8 Streakline of a water jet.- Problem 1.2-9 Streamlines and Streaklines in cylindrical coordinates.- Problem 1.2-10 Streamlines and pathlines of standing gravity waves.- Problem 1.2-11 Change of material line elements in a Couette- flow.- Problem 1.2-12 Change of material line elements in a three-dimensional flow.- Problem 1.2-13 Angular velocity vector and the change of material line elements in a two-dimensional flow field.- Problem 1.2-14 Rate of deformation and spin tensors of an unsteady two-dimensional flow.- Problem 1.2-15 Time change of the kinetic energy of a fluid body.- 2 Fundamental Laws of Continuum Mechanics.- 2.1 Conservation of Mass, Equation of Continuity.- Problem 2.1-1 One-dimensional unsteady flow with given density field.- Problem 2.1-2 Plane, steady flow with a given density field.- Problem 2.1-3 Velocity at the exit of a container.- Problem 2.1-4 Steady flow through a circular channel.- Problem 2.1-5 Squeeze film flow.- Problem 2.1-6 Moving Piston.- Problem 2.1-7 Flow between two inclined flat plates.- Problem 2.1-8 Oscillating journal bearing.- Problem 2.1-9 Effect of boundary layer displacement thickness.- Problem 2.1-10 Flow through a diffuser with a linear velocity change in flow direction.- Problem 2.1-11 Temperature boundary layer along a cold wall.- Problem 2.1-12 Flow in a lubrication gap.- 2.2 Balance of Momentum.- Problem 2.2-1 Principal axes of a stress tensor.- Problem 2.2-2 Fluid forces on a manifold.- Problem 2.2-3 Calculation of drag force.- Problem 2.2-4 Force on a slender nozzle.- 2.3 Balance of Angular Momentum.- Problem 2.3-1 Torque on pipe with slot.- Problem 2.3-2 Moment exerted on the inlet guide vanes of a water turbine.- Problem 2.3-3 Curvature radius of circular arc profiles of a circular cascade.- 2.4 Momentum and Angular Momentum in an Accelerating Frame.- Problem 2.4-1 Fluid sprayed on a rotating disk.- Problem 2.4-2 Velocity of a moving container with a.- Problem 2.4-3 Acceleration and velocity of a rocket.- Problem 2.4-4 Thrust reversal.- Problem 2.4-5 Torque on a rotating bent pipe.- Problem 2.4-6 Thrust of a jet engine.- 2.5 Applications to Turbomachines.- Problem 2.5-1 Circulation around a blade profile in a circular cascade.- Problem 2.5-2 Axial turbine stage.- Problem 2.5-3 Kaplan turbine.- Problem 2.5-4 Torque converter.- Problem 2.5-5 Balancing of axial thrust.- 2.6 Conservation of Energy.- Problem 2.6-1 Cylinder with heat flux.- Problem 2.6-2 Energy balance in an axial turbine stage.- 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.- Problem 4.1-1 Poiseuille flow.- Problem 4.1-2 Temperature distribution in a Poiseuille flow.- Problem 4.1-3 Pressure driven flow in a channel with porous walls.- Problem 4.1-4 Boundary layer suction.- Problem 4.1-5 Mixing of streams of fluids.- Problem 4.1-6 Drag on a flat plate.- Problem 4.1-7 Two-dimensional water jet impinging on a wedge.- Problem 4.1-8 Rigid body rotation and potential vortex.- Problem 4.1-9 Energy balance in a potential vortex flow.- 4.2 Inviscid flow.- Problem 4.2-1 Pressure and energy increase of fluid in a centrifugal pump.- Problem 4.2-2 Pressure distribution within a spiral casing.- Problem 4.2-3 Free surface in a potential vortex.- Problem 4.2-4 Circulation in a Couette flow.- Problem 4.2-5 Velocity induced by a vortex ring.- Problem 4.2-6 Two infinitely long vortex filaments near a wall.- Problem 4.2-7 Wing with an elliptic spanwise distribution of circulation.- Problem 4.2-8 Airfoil in parallel flow.- Problem 4.2-9 Jet angle in a Betz diffuser.- Problem 4.2-10 Contraction coefficient of a Borda mouthpiece.- Problem 4.2-11 Pressure distribution in an inviscid and ax- isymmetric flow.- Problem 4.2-12 Increase of static pressure in a Betz diffuser.- Problem 4.2-13 Fluid flowing out of a tank.- Problem 4.2-14 Air bubble moving in a channel.- Problem 4.2-15 Aircraft above the ground.- Problem 4.2-16 Flow between two rotating cylinders, circulation and vorticity.- Problem 4.2-17 Power of a Pelton turbine.- 4.3 Initial and Boundary Conditions.- Problem 4.3-1 Oscillation of an elliptic cylinder in fluid.- Problem 4.3-2 Flat plate with a pitching and oscillating motion.- Problem 4.3-3 Rotating cylinder moving through fluid.- Problem 4.3-4 Vortical flow inside an elliptic cylinder.- 5 Hydrostatics.- 5.1 Hydrostatic Pressure Distribution.- Problem 5.1-1 U-tube manometer.- Problem 5.1-2 Hydraulic safety clutch.- Problem 5.1-3 Rotating container filled with fluid.- Problem 5.1-4 Centrifugal casting process.- Problem 5.1-5 Depth gauge.- 5.2 Hydrostatic Lift, Force on Walls.- Problem 5.2-1 Force and moment on a throttle valve.- Problem 5.2-2 Half sphere closing an orifice.- Problem 5.2-3 Force on a dam.- Problem 5.2-4 Half sphere cup sealing by its own weight.- Problem 5.2-5 Cylindrical submarine.- Problem 5.2-6 Car under water.- 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.- Problem 9.1-1 Rotating tube acting as pump.- Problem 9.1-2 Volume flux through an orifice.- Problem 9.1-3 Injector pump.- Problem 9.1-4 Radial pump.- Problem 9.1-5 Bulb turbine.- Problem 9.1-6 Coanda effect.- Problem 9.1-7 Principle of a shaped charge.- Problem 9.1-8 Penstock and nozzle of a Pelton turbine.- Problem 9.1-9 Operating characteristic of a fan.- Problem 9.1-10 Water power plant.- Problem 9.1-11 Flow through an exhaust gas analyser.- Problem 9.1-12 Flow deflection through a screen.- Problem 9.1-13 Hovercraft.- Problem 9.1-14 Wind turbine.- Problem 9.1-15 Discharge pipe of a reservoir: Comparison between different pipe geometries.- Problem 9.1-16 Vibrating system consisting of a fluid column and a spring suspended piston.- Problem 9.1-17 Unsteady flow in a tube with flexible walls.- Problem 9.1-18 Plunger pump.- Problem 9.1-19 Flow within an urethra prothesis.- 9.2 Steady Compressible Flow.- Problem 9.2-1 Force on a plate in subsonic flow.- Problem 9.2-2 Channel flow with heat addition.- Problem 9.2-3 Normal shocks in an inlet guide vane.- Problem 9.2-4 Blunt body in supersonic flow.- Problem 9.2-5 Shock waves in the divergent part of a Laval nozzle.- Problem 9.2-6 Supersonic nozzle in a spinneret.- Problem 9.2-7 Ram jet in subsonic flow.- Problem 9.2-8 High speed train in a tunnel.- Problem 9.2-9 Labyrinth seal of a turbomachine.- Problem 9.2-10 Gas flow through an orifice.- 9.3 Unsteady Compressible Flow.- Problem 9.3-1 Traveling normal shock in a pipe.- Problem 9.3-2 Shock tube.- Problem 9.3-3 Motion of a piston in a tube.- Problem 9.3-4 Reflection of a normal shock wave at the open end of a tube.- Problem 9.3-5 Principle of an expansion tube.- Problem 9.3-6 Propagation of acoustic waves in a closed tube.- 10 Potential Flow.- 10.3 Incompressible Potential Flow.- Problem 10.3-1 Expanding sphere.- Problem 10.3-2 Sphere in a translational flow.- Problem 10.3-3 Flow near the stagnation point of a body in parallel flow.- Problem 10.3-4 Point source in a rotationally symmetric stagnation point flow.- Problem 10.3-5 Point source above an impermeable wall.- Problem 10.3-6 Source distribution in parallel flow.- Problem 10.3-7 Expanding sphere in an inviscid and in a viscous flow.- Problem 10.3-8 Growth of a vapor filled cavity.- Problem 10.3-9 Contraction coefficient for a circular orifice.- Problem 10.3-10 Sphere rising in water.- Problem 10.3-11 Unsteady motion of a cylinder perpendicular to its axis.- Problem 10.3-12 Rotor oscillating in an inviscid fluid.- 10.4 Plane Potential Flow.- Problem 10.4-1 Flow in the squeeze gap between a moving piston and a wall.- Problem 10.4-2 Sink distribution in a stagnation point flow.- Problem 10.4-3 Circle theorem.- Problem 10.4-4 Half cylinder in stagnation point flow.- Problem 10.4-5 Dipol flow around a circular cylinder.- Problem 10.4-6 Flow around a thin plate.- Problem 10.4-7 Airfoil over a fixed wall.- Problem 10.4-8 Semi infinite body in a channel.- Problem 10.4-9 Kármán’s vortex street.- Problem 10.4-10 Joukowski mapping of a circular cylinder in a uniform flow.- Problem 10.4-11 Plane circular cascade.- Problem 10.4-12 Schwarz-Christoffel transformation of a wall of infinite extent.- Problem 10.4-13 Schwarz-Christoffel transformation of a convergent channel.- Problem 10.4-14 Cavitation in a channel.- Problem 10.4-15 Representation of a slender body by a source distribution.- Problem 10.4-16 Distribution of vortex intensity and mean camber line of a slender airfoil.- Problem 10.4-17 Straight cascade.- Problem 10.4-18 Vortex distribution of a flat-plate cascade.- Problem 10.4-19 Compressible flow over a wavy wall.- 11 Supersonic Flow.- 11.1 Oblique Shock Waves.- Problem 11.1-1 Wedge with a thin plate in front of it.- Problem 11.1-2 Inlet of a plane channel.- 11.3 Reflection of Oblique Shock Waves.- Problem 11.3-1 Flow over a wedge in a supersonic wind tunnel.- Problem 11.3-2 Supersonic flow in a convergent channel.- 11.5 Prandtl-Meyer Flow.- Problem 11.5-1 Centered expansion wave in a divergent channel.- 11.6 Shock Expansion Theory.- Problem 11.6-1 Airfoil in supersonic flow.- Problem 11.6-2 Inlet of a supersonic jet engine.- 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.

O autorze

Meinhard Taher Schobeiri, Ph.D., is Professor of Mechanical Engineering at Texas A&M University in College Station, where he studies fluid flow within turbomachinery components, behavior of turbomachinery systems, turbine performance, aerodynamics, heat transfer, and thermodynamics. Dr. Schobeiri is received his B.S., M.S., and Ph.D. degrees from the Technical University Darmstadt in Germany, later joining the Department of Mechanical Engineering to establish two gas turbine research areas at Texas A&M University. He also worked for the Brown Boveri Gas Turbine Division in Switzerland, where he headed R&D for high efficiency gas turbine engines. Dr. Schobeiri holds a number of external grants and contracts, has won the Alexander von Humboldt Research Award (2000), and is a TAMU Faculty Fellow (2001) and TEES Fellow (1998).

Blurb

his collection of over 200 detailed worked exercises adds to and complements the textbook Fluid Mechanics by the same author, and illustrates the teaching material through examples. In the exercises the fundamental concepts of Fluid Mechanics are applied to obtaining the solution of diverse concrete problems, and in doing this the student's skill in the mathematical modeling of practical problems is developed. In addition, 30 challenging questions without detailed solutions have been included, and while lecturers will find these questions suitable for examinations and tests, the student himself can use them to check his understanding of the subject.