Basics of Fluid Mechanics

1 Basics of Fluid MechanicsGenick Bar Meir, Ph. S. , MN 2008, 2007, and 2006 by Genick Bar-MeirSee the file or for copying ( 11, 2008) We are like dwarfs sitting on the shoulders of giants from The Metalogicon by John in 1159 CONTENTSN omenclaturexiGNU Free Documentation License..xv1. APPLICABILITY AND DEFINITIONS..xvi2. VERBATIM COPYING..xvii3. COPYING IN QUANTITY..xviii4. MODIFICATIONS..xviii5. COMBINING DOCUMENTS..xx6. COLLECTIONS OF DOCUMENTS..xxi7. AGGREGATION WITH INDEPENDENT WORKS..xxi8. TRANSLATION..xxi9. TERMINATION..xxi10. FUTURE REVISIONS OF THIS LICENSE..xxiiADDENDUM: How to use this License for your documents..xxiiHow to contribute to this book..xxiiiCredits..xxiiiSteven from ..xxiiiDan Olsen..xxivRichard Hackbarth..xxivTousher Yang..xxivYour name here..xxivTypo corrections and other minor contributions..xxivVersion August 6, 2008..xxxiiipages 189 size ..xxxiiiVersion April 22, 2008..xxxiiipages 151 size ..xxxiiiProperties..xxxixiiiCONTENTSOpen Channel Flow.

2 Xxxix1 What is Fluid Mechanics ?.. Brief History.. Kinds of Fluids.. Shear Stress.. Viscosity.. General.. Non Newtonian Fluids.. Kinematic Viscosity.. Estimation of The Viscosity.. Bulk Modulus.. Surface Tension.. Wetting of Surfaces..242 Review of Basic Definitions..333 Review of Center of Mass.. Center of the Mass.. Center of Area.. Moment of Inertia.. Moment of Inertia for Mass.. Moment of Inertia for Area.. Examples of Moment of Inertia.. Product of Inertia.. Principal Axes of Inertia.. Newton s Laws of Motion.. Angular Momentum and Torque.. Tables of geometries..524 Fluids Introduction.. The Hydrostatic Equation.. Pressure and Density in a Gravitational Field.. Constant Density in Gravitational Field.. Pressure Measurement.. Varying Density in a Gravity Field.. The Pressure Effects Because Temperature Variations.. Gravity Variations Effects on Pressure and Density.

3 Liquid Phase.. Fluid in a Accelerated System.. Fluid in a Linearly Accelerated System.. Angular Acceleration Systems: Constant Density.. Fluid Forces on Surfaces.. Fluid Forces on Straight Surfaces.. Force on Curved Surfaces.. Buoyancy and Stability.. Stability.. Surface Tension.. Rayleigh Taylor Instability..1085 Multi Phase Introduction.. History.. What to Expect From This Chapter.. Kind of Multi-Phase Flow.. Classification of Liquid-Liquid Flow Regimes.. Co Current Flow.. Multi Phase Flow Variables Definitions.. Multi Phase Averaged Variables Definitions.. Homogeneous Models.. Pressure Loss Components.. Lockhart Martinelli Model.. Solid Liquid Flow.. Solid Particles with Heavier Density S> L.. Solid With Lighter Density S< and With Gravity.. Counter Current Flow.. Horizontal Counter Current Flow.. Flooding and Reversal Flow.. Multi Phase Conclusion..143 Index145 Subjects Index.

4 145 Authors Index..147ivCONTENTSLIST OF Diagram to explain part of relationships of Fluid Mechanics Density as a function of the size of .. Schematics to describe the shear stress in Fluid .. The deformation of Fluid due to shear stress as progression of the difference of power fluids.. Nitrogen (left) and Argon (right) viscosity as a function of the tem-perature and pressure after Lemmon and .. The shear stress as a function of the shear rate.. Air viscosity as a function of the .. Water viscosity as a function .. Liquid metals viscosity as a function of the .. Reduced viscosity as function of the reduced .. Reduced viscosity as function of the reduced .. Surface Tension control volume .. Forces in Contact .. Description of wetting and non wetting .. Description of liquid .. The raising height as a function of the .. The raising height as a function of the .. Description of how the center of mass is.

5 Thin body center of mass/area .. The schematic that explains the summation of moment of . The schematic to explain the summation of moment of .. Cylinder with the element for calculation moment of .. Description of rectangular in x y plane for calculation of moment ..46vviLIST OF A square element for the calculations of inertia of two-dimensionalto three dimensional .. The ratio of the moment of inertia of two-dimensional to three Description of parabola for calculation of moment of inertia and cen-ter of .. Product of inertia for .. Description of a Fluid element in accelerated system under body Pressure lines a static Fluid with a constant .. A schematic to explain the measure of the atmospheric . Schematic of gas measurement utilizing the U .. Schematic of sensitive measurement .. Hydrostatic pressure when there is compressibility in the liquid Two adjoin layers for stability .. The varying gravity effects on density and.

6 The effective gravity is for accelerated .. A cart slide on inclined plane.. Forces diagram of cart sliding on inclined plane.. Schematic to explain the angular .. Rectangular area under .. Schematic of submerged area to explain the center forces and mo-ments.. The general forces acting on submerged .. The general forces acting on non symmetrical straight .. The general forces acting on non symmetrical straight .. The effects of multi layers density on static .. The forces on curved .. Schematic of Net Force on floating .. Dam is a part of a circular .. Area above the dam arc subtract .. Area above the dam arc calculation for the .. Moment on arc element around Point O.. Polynomial shape dam description for the moment around point O and force .. The difference between the slop and the direction .. Schematic of Immersed .. The floating forces on Immersed .. Schematic of a thin wall floating .. Schematic of floating.

7 Schematic of floating .. Stability analysis of floating .. Cubic body dimensions for stability .. Stability of cubic body infinity .. The maximum height reverse as a function of density ..102 LIST OF The effects of liquid movement on .. Measurement of GM of floating .. Calculations ofGMfor abrupt shape .. A heavy needle is floating on a .. Description of depression to explain the Rayleigh Taylor Description of depression to explain the .. The cross section of the interface. The purple color represents themaximum heavy liquid raising area. The yellow color represents themaximum lighter liquid that are going down.. lines a static Fluid with a constant .. Stratified flow in horizontal tubes when the liquids flow is very Kind of Stratified flow in horizontal .. Plug flow in horizontal tubes when the liquids flow is faster . Modified Mandhane map for flow regime in horizontal .. lines a static Fluid with a constant.

8 A dimensional vertical flow map under very low gravity against .. The terminal velocity that left the solid .. The flow patterns in solid-liquid .. Counter current flow in a can (the left figure) has only one hole thuspulse flow and a flow with two holes (right picture).. Counter flow in vertical tubes .. Pictures of Counter-current flow in liquid gas and solid gas config-urations. The container is made of two compartments. The uppercompartment is filled with the heavy phase (liquid, water solution,or small wood particles) by rotating the container. Even thoughthe solid gas ratio is smaller, it can be noticed that the solid gasis faster than the liquid gas .. Flood in vertical .. A flow map to explain the horizontal counter current .. A diagram to explain the flood in a two dimension .. General forces diagram to calculated the in a two dimension OF FIGURESLIST OF TABLES1 Books Under Potto Project..xxix1continue.. Sutherland s equation coefficients.

9 Viscosity of selected gases.. Viscosity of selected liquids.. Properties at the critical stage.. Bulk modulus for selected materials.. The contact angle for air/water with selected .. The surface tension for selected .. continue.. Properties of Various Ideal Gases [300K].. Moments of Inertia for various plane surfaces about their center ofgravity (full shapes).. Moment of inertia for various plane surfaces about their center ofgravity..54ixxLIST OF TABLESNOMENCLATURE RUniversal gas constant, see equation ( ), page 38`Units length., see equation ( ), page 33 viscosity at input temperature T, see equation ( ), page 12 0reference viscosity at reference temperature,Ti0, see equation ( ), page 12 Martinelli parameter, see equation ( ), page 129 AThe area of surface, see equation ( ), page 85aThe acceleration of object or system, see equation ( ), page 55 BfBody force, see equation ( ), page 35 CpSpecific pressure heat, see equation ( ), page 37 CvSpecific volume heat, see equation ( ), page 37 EUInternal energy, see equation ( ), page 34 EuInternal Energy per unit mass, see equation ( ), page 34 EiSystem energy at state i, see equation ( ), page 34 GThe gravitation constant, see equation ( ), page 70gGgeneral Body force, see equation ( ), page 55 HEnthalpy, see equation ( ), page 36hSpecific enthalpy, see equation ( ), page 36xixiiLIST OF TABLES kthe ratio of the specific heats, see equation ( ), page 37 LAngular momentum, see equation ( ), page 51 PatmosAtmospheric Pressure, see equation ( )

10 , page 77qEnergy per unit mass, see equation ( ), page 34Q12 The energy transfered to the system between state 1 and state 2, see equa-tion ( ), page 34 RSpecific gas constant, see equation ( ), page 38 SEntropy of the system, see equation ( ), page 36 SuthSuth is Sutherland s constant and it is presented in the , see equa-tion ( ), page 12T Torque, see equation ( ), page 51Ti0reference temperature in degrees Kelvin, see equation ( ), page 12 Tininput temperature in degrees Kelvin, see equation ( ), page 12 Uvelocity , see equation ( ), page 34wWork per unit mass, see equation ( ), page 34W12 The work done by the system between state 1 and state 2, see equa-tion ( ), page 34zthe coordinate inzdirection, see equation ( ), page 58 The Book Change LogVersion 6, 2008 ( M 189 pages) Add the chapter on introduction to muli phase flow Again additional improvement to the index (thanks to Irene). Add the Rayleigh Taylor instability. Improve the doChap scrip to break up the book to 30, 2008 ( M 151 pages) Fix the English in the introduction chapter, (thanks to Tousher).