Fluid Mechanics

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.