Mechanics of Fluid Flow -- Contents -- Preface -- PART I Fundamentals of the Mechanics of Continua -- I Basic Concepts of the Mechanics of Continua -- Introduction -- 1. Continuity hypothesis -- 2. Movement of continuous medium: description techniques -- 3. Local and substantive derivative -- 4. Scalar and vector fields -- 5. Forces and stresses in the continuous medium. Stress tensor -- II Conservation Laws. Integral and Differential Equations of Continuous Medium -- 1. Integral parameters of a continuous medium and the conservation laws -- 2. Time differentiation of the integral taken over a movable volume -- 3. Continuity equation (law of mass conservation) -- 4. Motion equation under stress -- 5. Law of variation of kinetic momentum. Law of pairing of tangential stresses -- 6. The law of conservation of energy -- 7. Theorem of variation of kinetic energy -- 8. Heat flow equation -- 9. Continuous medium motion equations -- III Continuous Medium Deformation Rate -- 1. Small particle deformation rate. Helmholtz theorem -- 2. Tensor of the deformation velocity -- 3. Physical meaning of the deformation velocity tensor components -- 4. Tensor surface of a symmetric second-rank tensor -- 5. Velocity circulation. Potential motion of the liquid -- IV Liquids -- 1. Mathematical model of ideal fluid -- 2. Mathematical model of ideal incompressible fluid -- 3. Viscous fluid. Stress tensor in viscous fluid -- 4. Motion equations of viscous fluids -- 5. Mathematical model of a viscous incompressible fluid -- 6. The work of internal forces. Equation of the heat inflow -- V Basics of the Dimensionality and Conformity Theory -- 1. Systems of units. Dimensionality -- 2. Dimensionality formula -- 3. Values with independent dimensionalities -- 4. (Pie)-theorem -- 5. Conformity of physical phenomena, modeling -- 6. Parameters determining the class of phenomena.

7. Examples of application of the (Pie)-theorem -- 8. Contraction of equations to dimensionless format -- PART II Hydromechanics -- VI Hydrostatics -- 1. Liquids and gas equilibrium equations -- 2. Equilibrium of a liquid in the gravitational field -- 3. Relative quiescence of fluid -- 4. Static pressure of liquid on firm surfaces -- 5. Elements of buoyancy theory -- VII Flow of Ideal Fluid -- 1. Euler's equations in the Gromeko-Lamb format -- 2. Bernoulli's integral -- 3. Particular forms of Bernoulli's integral -- 4. Simple applications of Bernoulli's integral -- 5. Cauchy-Lagrange's integral -- 6. Thomson's theorem -- 7. Helmholtz equation -- 8. Potential flow of an incompressible fluid -- 9. Flow around the sphere -- 10. Applications of the momentum law -- VIII Parallel-Plane Flows of Ideal Incompressible Fluid -- 1. Complex-valued potential of flow -- 2. Examples of parallel-plane potential flows -- 3. Conformous reflection of flows -- 4. Zhukovsky's transform -- 5. Flow-around an arbitrary profile -- 6. Forces acting on a profile under the stationary flow -- IX Flow of Viscous Incompressible Fluid in Prismatic Tubes -- 1. Equations descring straight-line motion of a viscous incompressible fluid in prismatic tubes -- 2. Straight-line flow between two parallel walls -- 3. Straight-line flow within axisymmetric tubes -- 4. Equation of transient-free circular motion of a viscous fluid -- 5. Flow between two revolving cylinders -- X Turbulent Flow of Fluids in Pipes -- 1. Reynolds'experiments -- 2. Averaging the parameters of turbulent flow -- 3. Reynolds'equations -- 4. Semi-empiric turbulency theory by L. Prandtl -- 5. Application of the dimensionality theory to the construction of semi-empirical turbulence theories -- 6. Logarithmic law of velocity distribution -- 7. Experimental studies of hydraulic resistance.

XI Hydraulic Calculation for Pipelines -- 1. Bernoulli's equation for a viscous fluid flow -- 2. Types of head loss -- 3. Designing simple pipelines -- 4. Designing complex pipelines -- 5. Pipelines performing under vacuum -- XII Fluid's Outflow from Orifices and Nozzles -- 1. Outflow from a small orifice -- 2. Outflow through nozzles -- 3. Outflow of fluid at variable head -- XIII Non-Stationary Flow of Viscous Fluid in Tubes -- 1. Equations of the non-stationary fluid flow in tubes -- 2. Equation of non-stationary flow for slightly-compressible fluid in tubes -- 3. Equations of non-stationary gas flow in tubes at low subsonic velocities -- 4. Integrating equations of non-stationary fluid and gas flow using the characteristics technique -- 5. Integrating linearized equations of non-stationary flow using Laplace transformation -- 6. Examples of computing non-stationary flow in tubes -- 7. Hydraulic shock -- 8. Effect of flow instability on force of friction -- XIV Laminar Boundary Layer -- 1. Equations of the boundary layer -- 2. Blasius problem -- 3. Detachment of the boundary layer -- XV Unidimensional Gas Flows -- 1. Sound velocity -- 2. Energy conservation law -- 3. Mach number. Velocity factor -- 4. Linkage between the flow tube's cross-section area and flow velocity -- 5. Gas outflow through a convergent nozzle -- 6. De Laval's nozzle -- 7. Gas-dynamic functions -- 8. Shock waves -- 9. Computation of gas ejector -- 10. Transient-free gas flow in tubes -- 11. Shukhov's equation -- XVI Laminar Flow of Non-Newtonian Fluids -- 1. Simple shear -- 2. Classification of non-Newtonian fluids -- 3. Viscosimetry -- 4. Fluid flow in an infinitely-long round tube -- 5. Rotational fluid flow within a ring gap -- 6. Integral technique in viscosimetry -- 7. Hydraulic resistance factor.

8. Additional remarks to the calculation of non-Newtonian fluids flow in tubes -- XVII Two-Phase Flow in Pipes -- 1. Equations of the conservation laws -- 2. Equations of two-phase mixture flow in tubes -- 3. Transformation of equations of two-phase flow in pipes -- 5. Absolute open flow of a gas-condensate well -- PART III Oil and Gas Subsurface Hydromechanics -- XVIII Main Definitions and Concepts of Fluid and Gas Flow. Darcy's Law and Experiment -- 1. Specifics of fluid flow in natural reservoirs -- 3. Reservoir properties of porous bodies. Porosity, specific surface area -- 4. Darcy's experiment and Darcy's law. Permeability. The concept of "true" average flow velocity and flow velocity -- 5. Applicability limits of Darcy's law. Analysis and interpretation of experimental data -- 6. Nonlinear laws of filtration -- 7. Structural model of porous media -- 8. Darcy's law for anisotropic media -- XIX Mathematical Models of Uniphase Filtration -- 1. Introductory notes. The concept of the mathematical model of a physical process -- 2. Mass conservation laws in a porous medium -- 3. Differential equation of fluid flow -- 4. Closing equations. Mathematical models of isothermal filtration -- 5. Filtration model of incompressible viscous fluid under Darcy's law in a non-deformable reservoir -- 6. Gas filtration model under Darcy's law. Leibensohn's function -- 7. Uniphase filtration models in non-deformable reservoir under non-linear filtration laws -- 8. Correlation between fluid parameters and porous medium parameters with pressure -- XX Unidimensional Transient-Free Filtration of Incompressible Fluid and Gas in an Uniform Porous Medium -- 1. Schematics of unidimensional filtration flows -- 2. Rectiliner-parallel filtration of incompressible fluid -- 3. Radial-plane filtration of incompressible fluid.

4. Radial-spherical filtration of incompressible fluid -- 5. Filtration similarity between incompressible liquid and gas -- 6. Unidimensional filtration flow of ideal gas -- 7. Parallel-plane filtration flow of real gas under Darcy's law -- 8. Radial-plane filtration flow of incompressible liquid and gas under binomial filtration law -- 9. Radial-plane filtration flow on incompressible liquid and gas under the exponential filtration law -- XXI Unidimensional Filtration of Incompressible Liquid and Gas in a Nonuniform Reservoirs Under Darcy's Law -- 1. Major types of reservoir nonuniformities -- 2. Rectilinear-parallel flow within nonuniformly-laminated reservoir -- 3. Rectilinear-parallel flow in zonally-nonuniform bed -- 4. On the calculation of continuously-nonuniform reservoirs -- 5. Radial-plane flow in a nonuniformly stratified reservoir -- 6. Rectilineal-parallel flow in a nonuniformly stratified reservoir -- XXII Flat Transient-Free Filtration Flows -- 1. Major definitions and concepts -- 2. Potential of a point source and sink on an isotropic plane. Superposition method -- 3. Liquid flow to a group of wells with the remote charge contour -- 4. Liquid inflow to a well in the reservoir with a rectilinear charge contour -- 5. Liquid inflow to a well in the reservoir near the impermeable boundary -- 6. Liquid inflow to a well positioned eccentrically in a round reservoir -- 7. On the use of superposition technique at the gas filtration -- 8. Fluids inflow to infinite well lines and ring well rows -- XXIII Non-Stationary Flow of an Elastic Fluid in an Elastic Reservoir -- 1. Elastic reservoir drive -- 2. Calculation of elastic fluid reserves of a reservoir -- 3. Mathematical model of the elastic fluid non-stationary filtration in an elastic porous medium.

4. Derivation of the differential equation of the elastic fluid filtration in an elastic porous medium under Darcy's law.