Commit 7fd230ac authored by Olivier's avatar Olivier
Browse files

Compilation 2019-04-03

parent 36ce996b
......@@ -58,6 +58,8 @@
<file>numeric.cbx</file>
<file>biblatex.cfg</file>
<file>english.lbx</file>
<file>french.lbx</file>
<file>greek.lbx</file>
</requires>
</internal>
<external package="biblatex" priority="5" active="0">
......
\contentsline {chapter}{Syllabus}{5}{section*.2}
\select@language {english}
\babel@toc {english}{}
\boolfalse {citerequest}\boolfalse {citetracker}\boolfalse {pagetracker}\boolfalse {backtracker}\relax
\defcounter {refsection}{0}\relax
\select@language {english}
\contentsline {chapter}{\numberline {0}Important concepts}{9}{chapter.0}
\contentsline {section}{\numberline {0.1}Concept of a fluid}{9}{section.0.1}
\contentsline {section}{\numberline {0.2}Fluid mechanics}{9}{section.0.2}
\contentsline {subsection}{\numberline {0.2.1}Solution of a flow}{9}{subsection.0.2.1}
\contentsline {subsection}{\numberline {0.2.2}Modeling of fluids}{10}{subsection.0.2.2}
\contentsline {subsection}{\numberline {0.2.3}Theory, numerics, and experiment}{11}{subsection.0.2.3}
\contentsline {section}{\numberline {0.3}Important concepts in mechanics}{11}{section.0.3}
\contentsline {subsection}{\numberline {0.3.1}Position, velocity, acceleration}{11}{subsection.0.3.1}
\contentsline {subsection}{\numberline {0.3.2}Forces and moments}{12}{subsection.0.3.2}
\contentsline {subsection}{Forces and moments}{13}{subsection.0.3.2}
\contentsline {subsection}{\numberline {0.3.3}Energy}{13}{subsection.0.3.3}
\contentsline {section}{\numberline {0.4}Properties of fluids}{14}{section.0.4}
\contentsline {subsection}{\numberline {0.4.1}Density}{14}{subsection.0.4.1}
\contentsline {subsection}{\numberline {0.4.2}Phase}{14}{subsection.0.4.2}
\contentsline {subsection}{\numberline {0.4.3}Temperature}{14}{subsection.0.4.3}
\contentsline {subsection}{\numberline {0.4.4}Perfect gas model}{15}{subsection.0.4.4}
\contentsline {subsection}{\numberline {0.4.5}Speed of sound}{15}{subsection.0.4.5}
\contentsline {subsection}{\numberline {0.4.6}Viscosity}{16}{subsection.0.4.6}
\contentsline {section}{\numberline {0.5}Forces on fluids}{17}{section.0.5}
\contentsline {subsection}{\numberline {0.5.1}Gravity}{17}{subsection.0.5.1}
\contentsline {subsection}{\numberline {0.5.2}Pressure}{17}{subsection.0.5.2}
\contentsline {subsection}{\numberline {0.5.3}Shear}{17}{subsection.0.5.3}
\contentsline {section}{\numberline {0.6}Basic flow quantities}{18}{section.0.6}
\contentsline {section}{\numberline {0.7}Five equations}{19}{section.0.7}
\contentsline {section}{\numberline {0.8}Classification of fluid flows}{20}{section.0.8}
\contentsline {section}{\numberline {0.9}Limits of fluid mechanics}{21}{section.0.9}
\contentsline {section}{\numberline {0.10}Exercises}{23}{section.0.10}
\contentsline {subsubsection}{\numberline {0.1}Compressibility effects}{23}{subsubsection.0.10.0.1}
\contentsline {subsubsection}{\numberline {0.2}Pressure-induced force}{23}{subsubsection.0.10.0.2}
\contentsline {subsubsection}{\numberline {0.3}Shear-induced force}{24}{subsubsection.0.10.0.3}
\contentsline {subsubsection}{\numberline {0.4}Speed of sound}{24}{subsubsection.0.10.0.4}
\contentsline {subsubsection}{\numberline {0.5}Power lost to drag}{24}{subsubsection.0.10.0.5}
\contentsline {subsubsection}{\numberline {0.6}Go-faster exhaust pipe}{25}{subsubsection.0.10.0.6}
\contentsline {subsubsection}{Go-faster exhaust pipe}{25}{subsubsection.0.10.0.6}
\contentsline {subsubsection}{\numberline {0.7}Acceleration of a particle}{25}{subsubsection.0.10.0.7}
\contentsline {subsubsection}{\numberline {0.8}Flow classifications}{26}{subsubsection.0.10.0.8}
\contentsline {chapter}{\numberline {1}Effects of pressure}{29}{chapter.1}
\contentsline {section}{\numberline {1.1}Motivation}{29}{section.1.1}
\contentsline {section}{\numberline {1.2}Concept of pressure}{29}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}The direction of pressure}{29}{subsection.1.2.1}
\contentsline {subsection}{\numberline {1.2.2}Pressure on an infinitesimal volume}{30}{subsection.1.2.2}
\contentsline {section}{\numberline {1.3}Pressure in static fluids}{31}{section.1.3}
\contentsline {subsection}{\numberline {1.3.1}Fluid statics}{31}{subsection.1.3.1}
\contentsline {subsection}{\numberline {1.3.2}Shear in static fluids}{31}{subsection.1.3.2}
\contentsline {subsection}{\numberline {1.3.3}Pressure and depth}{31}{subsection.1.3.3}
\contentsline {subsection}{\numberline {1.3.4}Pressure distribution}{33}{subsection.1.3.4}
\contentsline {subsection}{\numberline {1.3.5}Hydrostatic pressure}{33}{subsection.1.3.5}
\contentsline {subsection}{\numberline {1.3.6}Atmospheric pressure}{34}{subsection.1.3.6}
\contentsline {section}{\numberline {1.4}Wall pressure forces and buoyancy}{35}{section.1.4}
\contentsline {subsection}{\numberline {1.4.1}Pressure forces on plane surfaces}{35}{subsection.1.4.1}
\contentsline {subsection}{\numberline {1.4.2}Buoyancy and Archimedes\IeC {\textquoteright } principle}{37}{subsection.1.4.2}
\contentsline {subsection}{Buoyancy and Archimedes\IeC {\textquoteright } principle}{37}{subsection.1.4.2}
\contentsline {section}{\numberline {1.5}Exercises}{39}{section.1.5}
\contentsline {subsubsection}{\numberline {1.1}Pressure in a fluid}{39}{subsubsection.1.5.0.1}
\contentsline {subsubsection}{\numberline {1.2}Pressure measurement}{39}{subsubsection.1.5.0.2}
\contentsline {subsubsection}{\numberline {1.3}Straight water tank door}{40}{subsubsection.1.5.0.3}
\contentsline {subsubsection}{\numberline {1.4}Water canal access door}{40}{subsubsection.1.5.0.4}
\contentsline {subsubsection}{\numberline {1.5}Water lock}{41}{subsubsection.1.5.0.5}
\contentsline {subsubsection}{\numberline {1.6}Buoyancy force on a tin can}{42}{subsubsection.1.5.0.6}
\contentsline {subsubsection}{\numberline {1.7}Buoyancy of a barge}{42}{subsubsection.1.5.0.7}
\contentsline {subsubsection}{\numberline {1.8}Atmospheric pressure distribution}{43}{subsubsection.1.5.0.8}
\contentsline {subsubsection}{\numberline {1.9}Reservoir door}{43}{subsubsection.1.5.0.9}
\contentsline {subsubsection}{\numberline {1.10}Atmospheric buoyancy force}{44}{subsubsection.1.5.0.10}
\contentsline {subsubsection}{\numberline {1.11}Lock with diagonally-mounted doors}{44}{subsubsection.1.5.0.11}
\contentsline {chapter}{\numberline {2}Effects of shear}{47}{chapter.2}
\contentsline {section}{\numberline {2.1}Motivation}{47}{section.2.1}
\contentsline {section}{\numberline {2.2}Concept of shear}{47}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}The direction of shear}{47}{subsection.2.2.1}
\contentsline {subsection}{\numberline {2.2.2}Shear on an infinitesimal volume}{48}{subsection.2.2.2}
\contentsline {section}{\numberline {2.3}Slip and viscosity}{50}{section.2.3}
\contentsline {subsection}{\numberline {2.3.1}The no-slip condition}{50}{subsection.2.3.1}
\contentsline {subsection}{\numberline {2.3.2}Viscosity}{51}{subsection.2.3.2}
\contentsline {subsection}{\numberline {2.3.3}Newtonian Fluid}{52}{subsection.2.3.3}
\contentsline {section}{\numberline {2.4}Wall shear forces}{53}{section.2.4}
\contentsline {section}{\numberline {2.5}Exercises}{55}{section.2.5}
\contentsline {subsubsection}{\numberline {2.1}Flow in between two plates}{55}{subsubsection.2.5.0.1}
\contentsline {subsubsection}{\numberline {2.2}Friction on a plate}{56}{subsubsection.2.5.0.2}
\contentsline {subsubsection}{\numberline {2.3}Viscometer}{56}{subsubsection.2.5.0.3}
\contentsline {subsubsection}{\numberline {2.4}Boundary layer}{56}{subsubsection.2.5.0.4}
\contentsline {subsubsection}{Boundary layer}{57}{subsubsection.2.5.0.4}
\contentsline {subsubsection}{\numberline {2.5}Clutch}{58}{subsubsection.2.5.0.5}
\contentsline {chapter}{\numberline {3}Analysis of existing flows}{61}{chapter.3}
\contentsline {section}{\numberline {3.1}Motivation}{61}{section.3.1}
\contentsline {section}{\numberline {3.2}The Reynolds transport theorem}{61}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Control volume}{61}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}Rate of change of an additive property}{61}{subsection.3.2.2}
\contentsline {subsection}{Rate of change of an additive property}{62}{subsection.3.2.2}
\contentsline {section}{\numberline {3.3}Mass conservation}{64}{section.3.3}
\contentsline {section}{\numberline {3.4}Change of linear momentum}{65}{section.3.4}
\contentsline {section}{\numberline {3.5}Change of angular momentum}{67}{section.3.5}
\contentsline {section}{\numberline {3.6}Energy conservation}{68}{section.3.6}
\contentsline {section}{\numberline {3.7}The Bernoulli equation}{69}{section.3.7}
\contentsline {section}{\numberline {3.8}Limits of integral analysis}{71}{section.3.8}
\contentsline {section}{\numberline {3.9}Exercises}{73}{section.3.9}
\contentsline {subsubsection}{\numberline {3.1}Pipe bend}{73}{subsubsection.3.9.0.1}
\contentsline {subsubsection}{\numberline {3.2}Water jet}{74}{subsubsection.3.9.0.2}
\contentsline {subsubsection}{\numberline {3.3}Exhaust gas deflector}{74}{subsubsection.3.9.0.3}
\contentsline {subsubsection}{Exhaust gas deflector}{75}{subsubsection.3.9.0.3}
\contentsline {subsubsection}{\numberline {3.4}Pelton water turbine}{75}{subsubsection.3.9.0.4}
\contentsline {subsubsection}{\numberline {3.5}Snow plow}{76}{subsubsection.3.9.0.5}
\contentsline {subsubsection}{\numberline {3.6}Drag on a cylindrical profile}{76}{subsubsection.3.9.0.6}
\contentsline {subsubsection}{Drag on a cylindrical profile}{77}{subsubsection.3.9.0.6}
\contentsline {subsubsection}{\numberline {3.7}Drag on a flat plate}{78}{subsubsection.3.9.0.7}
\contentsline {subsubsection}{\numberline {3.8}Drag measurements in a wind tunnel}{79}{subsubsection.3.9.0.8}
\contentsline {subsubsection}{\numberline {3.9}Moment on gas deflector}{80}{subsubsection.3.9.0.9}
\contentsline {subsubsection}{\numberline {3.10}Helicopter tail moment}{80}{subsubsection.3.9.0.10}
\contentsline {subsubsection}{\numberline {3.11}Pressure losses in a pipe flow}{81}{subsubsection.3.9.0.11}
\contentsline {subsubsection}{\numberline {3.12}Thrust reverser}{82}{subsubsection.3.9.0.12}
\contentsline {chapter}{\numberline {4}Predicting fluid flow}{85}{chapter.4}
\contentsline {section}{\numberline {4.1}Motivation}{85}{section.4.1}
\contentsline {section}{\numberline {4.2}Eulerian description of fluid flow}{85}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}Problem description}{85}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}Total time derivative}{86}{subsection.4.2.2}
\contentsline {section}{\numberline {4.3}Mass conservation}{89}{section.4.3}
\contentsline {section}{\numberline {4.4}Change of linear momentum}{92}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}The Cauchy equation}{92}{subsection.4.4.1}
\contentsline {subsection}{\numberline {4.4.2}The Navier-Stokes equation for incompressible flow}{94}{subsection.4.4.2}
\contentsline {subsection}{\numberline {4.4.3}The Bernoulli equation}{96}{subsection.4.4.3}
\contentsline {section}{\numberline {4.5}Change of angular momentum}{98}{section.4.5}
\contentsline {section}{\numberline {4.6}Energy conservation and increase in entropy}{98}{section.4.6}
\contentsline {section}{\numberline {4.7}CFD: the Navier-Stokes equations in practice}{100}{section.4.7}
\contentsline {subsection}{\numberline {4.7.1}Principle}{100}{subsection.4.7.1}
\contentsline {subsection}{\numberline {4.7.2}Two problems with CFD}{101}{subsection.4.7.2}
\contentsline {section}{\numberline {4.8}Exercises}{103}{section.4.8}
\contentsline {subsubsection}{\numberline {4.1}Revision questions}{103}{subsubsection.4.8.0.1}
\contentsline {subsubsection}{\numberline {4.2}Acceleration field}{103}{subsubsection.4.8.0.2}
\contentsline {subsubsection}{\numberline {4.3}Volumetric dilatation rate}{104}{subsubsection.4.8.0.3}
\contentsline {subsubsection}{\numberline {4.4}Incompressibility}{104}{subsubsection.4.8.0.4}
\contentsline {subsubsection}{\numberline {4.5}Missing components}{104}{subsubsection.4.8.0.5}
\contentsline {subsubsection}{\numberline {4.6}Another acceleration field}{104}{subsubsection.4.8.0.6}
\contentsline {subsubsection}{\numberline {4.7}Vortex}{104}{subsubsection.4.8.0.7}
\contentsline {subsubsection}{\numberline {4.8}Pressure fields}{105}{subsubsection.4.8.0.8}
\contentsline {chapter}{\numberline {5}Pipe flow}{107}{chapter.5}
\contentsline {section}{\numberline {5.1}Motivation}{107}{section.5.1}
\contentsline {section}{\numberline {5.2}Perfect flow in ducts}{107}{section.5.2}
\contentsline {section}{\numberline {5.3}Viscous laminar flow in ducts}{109}{section.5.3}
\contentsline {subsection}{\numberline {5.3.1}The entry zone}{109}{subsection.5.3.1}
\contentsline {subsection}{\numberline {5.3.2}Laminar viscous flow in a one-dimensional duct}{109}{subsection.5.3.2}
\contentsline {section}{\numberline {5.4}Viscous laminar flow in cylindrical pipes}{111}{section.5.4}
\contentsline {subsection}{\numberline {5.4.1}Principle}{111}{subsection.5.4.1}
\contentsline {subsection}{\numberline {5.4.2}Velocity profile}{111}{subsection.5.4.2}
\contentsline {subsection}{Velocity profile}{112}{subsection.5.4.2}
\contentsline {subsection}{\numberline {5.4.3}Quantification of losses}{113}{subsection.5.4.3}
\contentsline {section}{\numberline {5.5}Viscous turbulent flow in cylindrical pipes}{114}{section.5.5}
\contentsline {subsection}{\numberline {5.5.1}Predicting the occurrence of turbulence}{114}{subsection.5.5.1}
\contentsline {subsection}{\numberline {5.5.2}Characteristics of turbulent flow}{116}{subsection.5.5.2}
\contentsline {subsection}{\numberline {5.5.3}Velocity profile in turbulent pipe flow}{116}{subsection.5.5.3}
\contentsline {subsection}{\numberline {5.5.4}Pressure losses in turbulent pipe flow}{117}{subsection.5.5.4}
\contentsline {section}{\numberline {5.6}Exercises}{119}{section.5.6}
\contentsline {subsubsection}{\numberline {5.1}Revision questions}{119}{subsubsection.5.6.0.1}
\contentsline {subsubsection}{Revision questions}{121}{subsubsection.5.6.0.1}
\contentsline {subsubsection}{\numberline {5.2}Air flow in a small pipe}{121}{subsubsection.5.6.0.2}
\contentsline {subsubsection}{\numberline {5.3}Couette flow}{121}{subsubsection.5.6.0.3}
\contentsline {subsubsection}{\numberline {5.4}Kugel fountain}{122}{subsubsection.5.6.0.4}
\contentsline {subsubsection}{\numberline {5.5}Water piping}{123}{subsubsection.5.6.0.5}
\contentsline {subsubsection}{\numberline {5.6}Pipeline}{124}{subsubsection.5.6.0.6}
\contentsline {subsubsection}{\numberline {5.7}Pump with pipe expansion}{124}{subsubsection.5.6.0.7}
\contentsline {subsubsection}{\numberline {5.8}A more complex ducted flow}{125}{subsubsection.5.6.0.8}
\contentsline {subsubsection}{\numberline {5.9}Wind tunnel}{125}{subsubsection.5.6.0.9}
\contentsline {subsubsection}{\numberline {5.10}Politically incorrect fluid mechanics}{125}{subsubsection.5.6.0.10}
\contentsline {subsubsection}{Politically incorrect fluid mechanics}{126}{subsubsection.5.6.0.10}
\contentsline {chapter}{\numberline {6}Scale effects}{129}{chapter.6}
\contentsline {section}{\numberline {6.1}Motivation}{129}{section.6.1}
\contentsline {section}{\numberline {6.2}Scaling forces}{129}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}Force coefficients}{129}{subsection.6.2.1}
\contentsline {subsection}{\numberline {6.2.2}Power coefficient, and other coefficients}{130}{subsection.6.2.2}
\contentsline {subsection}{\numberline {6.2.3}Physical similarity}{131}{subsection.6.2.3}
\contentsline {section}{\numberline {6.3}Scaling flows}{132}{section.6.3}
\contentsline {subsection}{\numberline {6.3.1}The non-dimensional Navier-Stokes equation}{132}{subsection.6.3.1}
\contentsline {subsection}{\numberline {6.3.2}The flow parameters of Navier-Stokes}{134}{subsection.6.3.2}
\contentsline {subsection}{\numberline {6.3.3}Scaling flows}{136}{subsection.6.3.3}
\contentsline {section}{\numberline {6.4}Flow parameters as force ratios}{137}{section.6.4}
\contentsline {subsection}{\numberline {6.4.1}Acceleration vs. viscous forces: the Reynolds number}{137}{subsection.6.4.1}
\contentsline {subsection}{\numberline {6.4.2}Acceleration vs. gravity force: the Froude number}{138}{subsection.6.4.2}
\contentsline {subsection}{\numberline {6.4.3}Acceleration vs. elastic forces: the Mach number}{138}{subsection.6.4.3}
\contentsline {subsection}{\numberline {6.4.4}Other force ratios}{139}{subsection.6.4.4}
\contentsline {section}{\numberline {6.5}The Reynolds number in practice}{139}{section.6.5}
\contentsline {section}{\numberline {6.6}Exercises}{141}{section.6.6}
\contentsline {subsubsection}{\numberline {6.1}Scaling with the Reynolds number}{141}{subsubsection.6.6.0.1}
\contentsline {subsubsection}{Scaling with the Reynolds number}{142}{subsubsection.6.6.0.1}
\contentsline {subsubsection}{\numberline {6.2}Fluid mechanics of a giant airliner}{142}{subsubsection.6.6.0.2}
\contentsline {subsubsection}{\numberline {6.3}Scale effects on a dragonfly}{143}{subsubsection.6.6.0.3}
\contentsline {subsubsection}{\numberline {6.4}Formula One testing}{143}{subsubsection.6.6.0.4}
\contentsline {chapter}{\numberline {7}Flow near walls}{147}{chapter.7}
\contentsline {section}{\numberline {7.1}Motivation}{147}{section.7.1}
\contentsline {section}{\numberline {7.2}Describing the boundary layer}{147}{section.7.2}
\contentsline {subsection}{\numberline {7.2.1}Concept}{147}{subsection.7.2.1}
\contentsline {subsection}{\numberline {7.2.2}Why do we study the boundary layer?}{149}{subsection.7.2.2}
\contentsline {subsection}{\numberline {7.2.3}Characterization of the boundary layer}{149}{subsection.7.2.3}
\contentsline {section}{\numberline {7.3}The laminar boundary layer}{151}{section.7.3}
\contentsline {subsection}{\numberline {7.3.1}Governing equations}{151}{subsection.7.3.1}
\contentsline {subsection}{\numberline {7.3.2}Blasius\IeC {\textquoteright } solution}{152}{subsection.7.3.2}
\contentsline {subsection}{\numberline {7.3.3}Pohlhausen\IeC {\textquoteright }s model}{153}{subsection.7.3.3}
\contentsline {section}{\numberline {7.4}Transition}{155}{section.7.4}
\contentsline {section}{\numberline {7.5}The turbulent boundary layer}{155}{section.7.5}
\contentsline {section}{\numberline {7.6}Separation}{157}{section.7.6}
\contentsline {subsection}{\numberline {7.6.1}Principle}{157}{subsection.7.6.1}
\contentsline {subsection}{\numberline {7.6.2}Separation according to Pohlhausen}{159}{subsection.7.6.2}
\contentsline {section}{\numberline {7.7}Exercises}{161}{section.7.7}
\contentsline {subsubsection}{\numberline {7.1}Water and air flow}{161}{subsubsection.7.7.0.1}
\contentsline {subsubsection}{Water and air flow}{162}{subsubsection.7.7.0.1}
\contentsline {subsubsection}{\numberline {7.2}Boundary layer sketches}{162}{subsubsection.7.7.0.2}
\contentsline {subsubsection}{\numberline {7.3}Shear force due to boundary layer}{163}{subsubsection.7.7.0.3}
\contentsline {subsubsection}{\numberline {7.4}Wright Flyer I}{163}{subsubsection.7.7.0.4}
\contentsline {subsubsection}{\numberline {7.5}Power lost to shear on an airliner fuselage}{164}{subsubsection.7.7.0.5}
\contentsline {subsubsection}{\numberline {7.6}Separation according to Pohlhausen}{164}{subsubsection.7.7.0.6}
\contentsline {subsubsection}{\numberline {7.7}Laminar wing profile}{164}{subsubsection.7.7.0.7}
\contentsline {subsubsection}{\numberline {7.8}Separation mechanism}{164}{subsubsection.7.7.0.8}
\contentsline {subsubsection}{Separation mechanism}{166}{subsubsection.7.7.0.8}
\contentsline {subsubsection}{\numberline {7.9}Thwaites\IeC {\textquoteright } separation model}{166}{subsubsection.7.7.0.9}
\contentsline {chapter}{\numberline {8}Modeling large- and small-scale flows}{169}{chapter.8}
\contentsline {section}{\numberline {8.1}Motivation}{169}{section.8.1}
\contentsline {section}{\numberline {8.2}Flow at large scales}{169}{section.8.2}
\contentsline {subsection}{\numberline {8.2.1}Problem statement}{169}{subsection.8.2.1}
\contentsline {subsection}{\numberline {8.2.2}Investigation of inviscid flows}{170}{subsection.8.2.2}
\contentsline {section}{\numberline {8.3}Plotting velocity with functions}{171}{section.8.3}
\contentsline {subsection}{\numberline {8.3.1}Kinematics that fit conservation laws}{171}{subsection.8.3.1}
\contentsline {subsection}{\numberline {8.3.2}Strengths and weaknesses of potential flow}{172}{subsection.8.3.2}
\contentsline {subsection}{\numberline {8.3.3}Superposition: the lifting cylinder}{173}{subsection.8.3.3}
\contentsline {subsection}{\numberline {8.3.4}Circulating cylinder}{175}{subsection.8.3.4}
\contentsline {subsection}{Circulating cylinder}{176}{subsection.8.3.4}
\contentsline {subsection}{\numberline {8.3.5}Modeling lift with circulation}{177}{subsection.8.3.5}
\contentsline {section}{\numberline {8.4}Flow at very small scales}{180}{section.8.4}
\contentsline {section}{\numberline {8.5}Exercises}{183}{section.8.5}
\contentsline {subsubsection}{\numberline {8.1}Volcanic ash from the Eyjafjallaj\IeC {\"o}kull}{183}{subsubsection.8.5.0.1}
\contentsline {subsubsection}{\numberline {8.2}Water drop}{183}{subsubsection.8.5.0.2}
\contentsline {subsubsection}{\numberline {8.3}Hangar roof}{183}{subsubsection.8.5.0.3}
\contentsline {subsubsection}{Hangar roof}{184}{subsubsection.8.5.0.3}
\contentsline {subsubsection}{\numberline {8.4}Cabling of the Wright Flyer}{185}{subsubsection.8.5.0.4}
\contentsline {subsubsection}{\numberline {8.5}Ping pong ball}{185}{subsubsection.8.5.0.5}
\contentsline {subsubsection}{Ping pong ball}{187}{subsubsection.8.5.0.5}
\contentsline {subsubsection}{\numberline {8.6}Lift on a symmetrical object}{187}{subsubsection.8.5.0.6}
\contentsline {subsubsection}{Lift on a symmetrical object}{188}{subsubsection.8.5.0.6}
\contentsline {subsubsection}{\numberline {8.7}Air flow over a wing profile}{188}{subsubsection.8.5.0.7}
\contentsline {subsubsection}{\numberline {8.8}Flow field of a tornado}{189}{subsubsection.8.5.0.8}
\contentsline {chapter}{\numberline {9}Introduction to compressible flow}{193}{chapter.9}
\contentsline {section}{\numberline {9.1}Motivation}{193}{section.9.1}
\contentsline {section}{\numberline {9.2}Compressibility and its consequences}{193}{section.9.2}
\contentsline {subsection}{\numberline {9.2.1}Problem description}{193}{subsection.9.2.1}
\contentsline {subsection}{\numberline {9.2.2}The speed of pressure}{194}{subsection.9.2.2}
\contentsline {subsection}{\numberline {9.2.3}The measure of compressibility}{196}{subsection.9.2.3}
\contentsline {section}{\numberline {9.3}Thermodynamics of isentropic flow for a perfect gas}{196}{section.9.3}
\contentsline {subsection}{\numberline {9.3.1}Principle}{196}{subsection.9.3.1}
\contentsline {subsection}{\numberline {9.3.2}Pressure, temperature, density and the speed of sound}{198}{subsection.9.3.2}
\contentsline {section}{\numberline {9.4}Speed and cross-sectional area}{200}{section.9.4}
\contentsline {section}{\numberline {9.5}Isentropic flow in converging and diverging nozzles}{202}{section.9.5}
\contentsline {section}{\numberline {9.6}The perpendicular shock wave}{204}{section.9.6}
\contentsline {section}{\numberline {9.7}Compressible flow beyond frictionless pipe flow}{206}{section.9.7}
\contentsline {section}{\numberline {9.8}Exercises}{207}{section.9.8}
\contentsline {subsubsection}{\numberline {9.1}Flow in a converging nozzle}{207}{subsubsection.9.8.0.1}
\contentsline {subsubsection}{Flow in a converging nozzle}{210}{subsubsection.9.8.0.1}
\contentsline {subsubsection}{Flow in a converging nozzle}{210}{subsubsection.9.8.0.1}
\contentsline {subsubsection}{\numberline {9.2}Flow in a converging-diverging nozzle}{210}{subsubsection.9.8.0.2}
\contentsline {subsubsection}{\numberline {9.3}Capsule re-entry}{211}{subsubsection.9.8.0.3}
\contentsline {subsubsection}{\numberline {9.4}Explosion shock wave}{211}{subsubsection.9.8.0.4}
\contentsline {subsubsection}{\numberline {9.5}Home-made supersonic tunnel}{211}{subsubsection.9.8.0.5}
\contentsline {chapter}{Appendix}{215}{section*.137}
\contentsline {section}{\numberline {A1}Notation}{216}{section.Alph0.1}
\contentsline {section}{\numberline {A2}Field operators}{217}{section.Alph0.2}
\contentsline {subsection}{\numberline {A2.1}Gradient}{217}{subsection.Alph0.2.1}
\contentsline {subsection}{\numberline {A2.2}Divergent}{217}{subsection.Alph0.2.2}
\contentsline {subsection}{\numberline {A2.3}Laplacian}{218}{subsection.Alph0.2.3}
\contentsline {subsection}{\numberline {A2.4}Curl}{218}{subsection.Alph0.2.4}
\contentsline {section}{\numberline {A3}List of references}{219}{section.Alph0.3}
\babel@toc {english}{}
\contentsline {chapter}{Contents}{2}{section*.1}
\contentsline {chapter}{Syllabus}{5}{section*.2}
\contentsline {chapter}{\numberline {1}Basic flow quantities}{9}{chapter.1}
\contentsline {section}{\numberline {1.1}Concept of a fluid}{9}{section.1.1}
\contentsline {section}{\numberline {1.2}Fluid mechanics}{9}{section.1.2}
\contentsline {subsection}{\numberline {1.2.1}Solution of a flow}{9}{subsection.1.2.1}
\contentsline {subsection}{\numberline {1.2.2}Modeling of fluids}{10}{subsection.1.2.2}
\contentsline {subsection}{\numberline {1.2.3}Theory, numerics, and experiment}{11}{subsection.1.2.3}
\contentsline {section}{\numberline {1.3}Important concepts in mechanics}{11}{section.1.3}
\contentsline {subsection}{\numberline {1.3.1}Position, velocity, acceleration}{11}{subsection.1.3.1}
\contentsline {subsection}{\numberline {1.3.2}Forces and moments}{12}{subsection.1.3.2}
\contentsline {subsection}{\numberline {1.3.3}Energy}{13}{subsection.1.3.3}
\contentsline {section}{\numberline {1.4}Properties of fluids}{14}{section.1.4}
\contentsline {subsection}{\numberline {1.4.1}Density}{14}{subsection.1.4.1}
\contentsline {subsection}{\numberline {1.4.2}Phase}{14}{subsection.1.4.2}
\contentsline {subsection}{\numberline {1.4.3}Temperature}{14}{subsection.1.4.3}
\contentsline {subsection}{\numberline {1.4.4}Perfect gas model}{15}{subsection.1.4.4}
\contentsline {subsection}{\numberline {1.4.5}Speed of sound}{15}{subsection.1.4.5}
\contentsline {subsection}{\numberline {1.4.6}Viscosity}{16}{subsection.1.4.6}
\contentsline {section}{\numberline {1.5}Forces on fluids}{17}{section.1.5}
\contentsline {subsection}{\numberline {1.5.1}Gravity}{17}{subsection.1.5.1}
\contentsline {subsection}{\numberline {1.5.2}Pressure}{17}{subsection.1.5.2}
\contentsline {subsection}{\numberline {1.5.3}Shear}{17}{subsection.1.5.3}
\contentsline {section}{\numberline {1.6}Basic flow quantities}{18}{section.1.6}
\contentsline {section}{\numberline {1.7}Four balance equations}{19}{section.1.7}
\contentsline {section}{\numberline {1.8}Classification of fluid flows}{20}{section.1.8}
\contentsline {section}{\numberline {1.9}Limits of fluid mechanics}{22}{section.1.9}
\contentsline {section}{\numberline {1.10}Problems}{23}{section.1.10}
\contentsline {subsubsection}{\numberline {1.1}Compressibility effects}{23}{subsubsection.1.10.0.1}
\contentsline {subsubsection}{\numberline {1.2}Pressure-induced force}{23}{subsubsection.1.10.0.2}
\contentsline {subsubsection}{\numberline {1.3}Shear-induced force}{24}{subsubsection.1.10.0.3}
\contentsline {subsubsection}{\numberline {1.4}Speed of sound}{24}{subsubsection.1.10.0.4}
\contentsline {subsubsection}{\numberline {1.5}Power lost to drag}{24}{subsubsection.1.10.0.5}
\contentsline {subsubsection}{\numberline {1.6}Go-faster exhaust pipe}{25}{subsubsection.1.10.0.6}
\contentsline {subsubsection}{\numberline {1.7}Acceleration of a particle}{26}{subsubsection.1.10.0.7}
\contentsline {subsubsection}{\numberline {1.8}Flow classifications}{26}{subsubsection.1.10.0.8}
\contentsline {chapter}{\numberline {2}Analysis of existing flows with\nobreakspace {}one\nobreakspace {}dimension}{29}{chapter.2}
\contentsline {section}{\numberline {2.1}Motivation}{29}{section.2.1}
\contentsline {section}{\numberline {2.2}One-dimensional flow problems}{29}{section.2.2}
\contentsline {section}{\numberline {2.3}Balance of mass}{31}{section.2.3}
\contentsline {section}{\numberline {2.4}Balance of momentum}{32}{section.2.4}
\contentsline {section}{\numberline {2.5}Balance of energy}{34}{section.2.5}
\contentsline {section}{\numberline {2.6}The Bernoulli equation}{36}{section.2.6}
\contentsline {subsection}{\numberline {2.6.1}Theory}{36}{subsection.2.6.1}
\contentsline {subsection}{\numberline {2.6.2}Reality}{37}{subsection.2.6.2}
\contentsline {section}{\numberline {2.7}Problems}{39}{section.2.7}
\contentsline {subsubsection}{\numberline {2.1}Pipe expansion without losses}{39}{subsubsection.2.7.0.1}
\contentsline {subsubsection}{\numberline {2.2}Pipe flow with losses}{40}{subsubsection.2.7.0.2}
\contentsline {subsubsection}{\numberline {2.3}Combustor from a jet engine}{40}{subsubsection.2.7.0.3}
\contentsline {subsubsection}{\numberline {2.4}Water jet on a wall}{41}{subsubsection.2.7.0.4}
\contentsline {subsubsection}{\numberline {2.5}High-speed gas flow}{41}{subsubsection.2.7.0.5}
\contentsline {chapter}{\numberline {3}Analysis of existing flows with\nobreakspace {}three\nobreakspace {}dimensions}{45}{chapter.3}
\contentsline {section}{\numberline {3.1}Motivation}{45}{section.3.1}
\contentsline {section}{\numberline {3.2}The Reynolds transport theorem}{45}{section.3.2}
\contentsline {subsection}{\numberline {3.2.1}Control volume}{45}{subsection.3.2.1}
\contentsline {subsection}{\numberline {3.2.2}Rate of change of an additive property}{46}{subsection.3.2.2}
\contentsline {section}{\numberline {3.3}Balance of mass}{48}{section.3.3}
\contentsline {section}{\numberline {3.4}Balance of momentum}{49}{section.3.4}
\contentsline {section}{\numberline {3.5}Balance of angular momentum}{51}{section.3.5}
\contentsline {section}{\numberline {3.6}Balance of energy}{52}{section.3.6}
\contentsline {section}{\numberline {3.7}Limits of integral analysis}{52}{section.3.7}
\contentsline {section}{\numberline {3.8}Problems}{55}{section.3.8}
\contentsline {subsubsection}{\numberline {3.1}Pipe bend}{56}{subsubsection.3.8.0.1}
\contentsline {subsubsection}{\numberline {3.2}Exhaust gas deflector}{56}{subsubsection.3.8.0.2}
\contentsline {subsubsection}{\numberline {3.3}Pelton water turbine}{57}{subsubsection.3.8.0.3}
\contentsline {subsubsection}{\numberline {3.4}Snow plow}{58}{subsubsection.3.8.0.4}
\contentsline {subsubsection}{\numberline {3.5}Drag on a cylindrical profile}{58}{subsubsection.3.8.0.5}
\contentsline {subsubsection}{\numberline {3.6}Drag on a flat plate}{59}{subsubsection.3.8.0.6}
\contentsline {subsubsection}{\numberline {3.7}Drag measurements in a wind tunnel}{60}{subsubsection.3.8.0.7}
\contentsline {subsubsection}{\numberline {3.8}Moment on gas deflector}{61}{subsubsection.3.8.0.8}
\contentsline {subsubsection}{\numberline {3.9}Helicopter tail moment}{62}{subsubsection.3.8.0.9}
\contentsline {subsubsection}{\numberline {3.10}Pressure losses in a pipe flow}{63}{subsubsection.3.8.0.10}
\contentsline {subsubsection}{\numberline {3.11}Thrust reverser}{63}{subsubsection.3.8.0.11}
\contentsline {chapter}{\numberline {4}Effects of pressure}{67}{chapter.4}
\contentsline {section}{\numberline {4.1}Motivation}{67}{section.4.1}
\contentsline {section}{\numberline {4.2}Pressure forces on walls}{67}{section.4.2}
\contentsline {subsection}{\numberline {4.2.1}Magnitude of the pressure force}{67}{subsection.4.2.1}
\contentsline {subsection}{\numberline {4.2.2}Position of the pressure force}{68}{subsection.4.2.2}
\contentsline {section}{\numberline {4.3}Pressure fields in fluids}{69}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}The direction of pressure}{69}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}Pressure on an infinitesimal volume}{70}{subsection.4.3.2}
\contentsline {section}{\numberline {4.4}Special case: pressure in static fluids}{71}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}Forces in static fluids}{71}{subsection.4.4.1}
\contentsline {subsection}{\numberline {4.4.2}Pressure and depth}{72}{subsection.4.4.2}
\contentsline {subsection}{\numberline {4.4.3}Buoyancy}{74}{subsection.4.4.3}
\contentsline {section}{\numberline {4.5}Problems}{77}{section.4.5}
\contentsline {subsubsection}{\numberline {4.1}Pressure in a static fluid}{77}{subsubsection.4.5.0.1}
\contentsline {subsubsection}{\numberline {4.2}Pressure measurement}{77}{subsubsection.4.5.0.2}
\contentsline {subsubsection}{\numberline {4.3}Straight water tank door}{78}{subsubsection.4.5.0.3}
\contentsline {subsubsection}{\numberline {4.4}Water canal access door}{78}{subsubsection.4.5.0.4}
\contentsline {subsubsection}{\numberline {4.5}Pressure force on a cylinder}{79}{subsubsection.4.5.0.5}
\contentsline {subsubsection}{\numberline {4.6}Buoyancy of a barge}{79}{subsubsection.4.5.0.6}
\contentsline {subsubsection}{\numberline {4.7}Atmospheric pressure distribution}{80}{subsubsection.4.5.0.7}
\contentsline {chapter}{\numberline {5}Effects of shear}{83}{chapter.5}
\contentsline {section}{\numberline {5.1}Motivation}{83}{section.5.1}
\contentsline {section}{\numberline {5.2}Shear forces on walls}{83}{section.5.2}
\contentsline {subsection}{\numberline {5.2.1}Magnitude of the shear force}{83}{subsection.5.2.1}
\contentsline {subsection}{\numberline {5.2.2}Direction and position of the shear force}{84}{subsection.5.2.2}
\contentsline {section}{\numberline {5.3}Shear fields in fluids}{84}{section.5.3}
\contentsline {subsection}{\numberline {5.3.1}The direction of shear}{84}{subsection.5.3.1}
\contentsline {subsection}{\numberline {5.3.2}Shear on an infinitesimal volume}{85}{subsection.5.3.2}
\contentsline {subsection}{\numberline {5.3.3}The no-slip condition}{87}{subsection.5.3.3}
\contentsline {subsection}{\numberline {5.3.4}Viscosity}{88}{subsection.5.3.4}
\contentsline {subsection}{\numberline {5.3.5}Newtonian Fluid}{89}{subsection.5.3.5}
\contentsline {section}{\numberline {5.4}Special case: shear in simple laminar flows}{90}{section.5.4}
\contentsline {section}{\numberline {5.5}Problems}{91}{section.5.5}
\contentsline {subsubsection}{\numberline {5.1}Flow in between two plates}{91}{subsubsection.5.5.0.1}
\contentsline {subsubsection}{\numberline {5.2}Friction on a plate}{92}{subsubsection.5.5.0.2}
\contentsline {subsubsection}{\numberline {5.3}Viscometer}{92}{subsubsection.5.5.0.3}
\contentsline {subsubsection}{\numberline {5.4}Boundary layer}{92}{subsubsection.5.5.0.4}
\contentsline {subsubsection}{\numberline {5.5}Clutch}{94}{subsubsection.5.5.0.5}
\contentsline {chapter}{\numberline {6}Prediction of fluid flows}{97}{chapter.6}
\contentsline {section}{\numberline {6.1}Motivation}{97}{section.6.1}
\contentsline {section}{\numberline {6.2}Organizing calculations}{97}{section.6.2}
\contentsline {subsection}{\numberline {6.2.1}Problem description}{97}{subsection.6.2.1}
\contentsline {subsection}{\numberline {6.2.2}The total time derivative}{98}{subsection.6.2.2}
\contentsline {section}{\numberline {6.3}Equations for all flows}{101}{section.6.3}
\contentsline {subsection}{\numberline {6.3.1}Balance of mass}{101}{subsection.6.3.1}
\contentsline {subsection}{\numberline {6.3.2}Balance of linear momentum}{103}{subsection.6.3.2}
\contentsline {subsection}{\numberline {6.3.3}Balance of energy}{105}{subsection.6.3.3}
\contentsline {subsection}{\numberline {6.3.4}Other terms and equations}{106}{subsection.6.3.4}
\contentsline {subsection}{\numberline {6.3.5}Interlude: where does this leave us?}{107}{subsection.6.3.5}
\contentsline {section}{\numberline {6.4}Equations for incompressible flow}{107}{section.6.4}
\contentsline {subsection}{\numberline {6.4.1}Balance of mass}{107}{subsection.6.4.1}
\contentsline {subsection}{\numberline {6.4.2}Balance of linear momentum}{108}{subsection.6.4.2}
\contentsline {subsection}{\numberline {6.4.3}The Bernoulli equation (again)}{110}{subsection.6.4.3}
\contentsline {section}{\numberline {6.5}CFD: the Navier-Stokes equations in practice}{110}{section.6.5}
\contentsline {section}{\numberline {6.6}Problems}{113}{section.6.6}
\contentsline {subsubsection}{\numberline {6.1}Revision questions}{113}{subsubsection.6.6.0.1}
\contentsline {subsubsection}{\numberline {6.2}Acceleration field}{113}{subsubsection.6.6.0.2}
\contentsline {subsubsection}{\numberline {6.3}Volumetric dilatation rate}{114}{subsubsection.6.6.0.3}
\contentsline {subsubsection}{\numberline {6.4}Incompressibility}{114}{subsubsection.6.6.0.4}
\contentsline {subsubsection}{\numberline {6.5}Missing components}{114}{subsubsection.6.6.0.5}
\contentsline {subsubsection}{\numberline {6.6}Another acceleration field}{114}{subsubsection.6.6.0.6}
\contentsline {subsubsection}{\numberline {6.7}Vortex}{114}{subsubsection.6.6.0.7}
\contentsline {subsubsection}{\numberline {6.8}Pressure fields}{115}{subsubsection.6.6.0.8}
\contentsline {chapter}{\numberline {7}Pipe flows}{117}{chapter.7}
\contentsline {section}{\numberline {7.1}Motivation}{117}{section.7.1}
\contentsline {section}{\numberline {7.2}Friction-less flow in pipes}{117}{section.7.2}
\contentsline {section}{\numberline {7.3}Quantifying losses in pipes}{118}{section.7.3}
\contentsline {section}{\numberline {7.4}Laminar flow in pipes}{119}{section.7.4}
\contentsline {subsection}{\numberline {7.4.1}Laminar flow between plates}{119}{subsection.7.4.1}
\contentsline {subsection}{\numberline {7.4.2}Laminar flow in pipes}{121}{subsection.7.4.2}
\contentsline {section}{\numberline {7.5}Turbulent flow in pipes}{124}{section.7.5}
\contentsline {subsection}{\numberline {7.5.1}When is a pipe flow turbulent?}{124}{subsection.7.5.1}
\contentsline {subsection}{\numberline {7.5.2}Characteristics of turbulent flow}{125}{subsection.7.5.2}
\contentsline {subsection}{\numberline {7.5.3}Velocity profile in turbulent pipe flow}{126}{subsection.7.5.3}
\contentsline {subsection}{\numberline {7.5.4}Pressure losses in turbulent pipe flow}{127}{subsection.7.5.4}
\contentsline {section}{\numberline {7.6}Summary}{128}{section.7.6}
\contentsline {section}{\numberline {7.7}Problems}{129}{section.7.7}
\contentsline {subsubsection}{\numberline {7.1}Revision questions}{129}{subsubsection.7.7.0.1}
\contentsline {subsubsection}{\numberline {7.2}Air flow in a small pipe}{131}{subsubsection.7.7.0.2}
\contentsline {subsubsection}{\numberline {7.3}Water piping}{131}{subsubsection.7.7.0.3}
\contentsline {subsubsection}{\numberline {7.4}Design of a water piping system}{132}{subsubsection.7.7.0.4}
\contentsline {subsubsection}{\numberline {7.5}Major oil pipeline}{133}{subsubsection.7.7.0.5}
\contentsline {subsubsection}{\numberline {7.6}Pump with pipe expansion}{134}{subsubsection.7.7.0.6}
\contentsline {subsubsection}{\numberline {7.7}Kugel fountain}{134}{subsubsection.7.7.0.7}
\contentsline {subsubsection}{\numberline {7.8}A more complex ducted flow}{136}{subsubsection.7.7.0.8}
\contentsline {subsubsection}{\numberline {7.9}Politically incorrect fluid mechanics}{136}{subsubsection.7.7.0.9}
\contentsline {chapter}{\numberline {8}Dealing with\nobreakspace {}turbulence}{139}{chapter.8}
\contentsline {chapter}{\numberline {9}Engineering models}{141}{chapter.9}
\contentsline {section}{\numberline {9.1}Motivation}{141}{section.9.1}
\contentsline {section}{\numberline {9.2}Comparing influences: the weighted momentum balance}{141}{section.9.2}
\contentsline {subsection}{\numberline {9.2.1}Principle}{141}{subsection.9.2.1}
\contentsline {subsection}{\numberline {9.2.2}The non-dimensional Navier-Stokes equation}{142}{subsection.9.2.2}
\contentsline {subsection}{\numberline {9.2.3}The flow parameters of Navier-Stokes}{144}{subsection.9.2.3}
\contentsline {subsection}{\numberline {9.2.4}Flow parameters obtained as force ratios}{145}{subsection.9.2.4}
\contentsline {subsection}{\numberline {9.2.5}The Reynolds number in practice}{145}{subsection.9.2.5}
\contentsline {section}{\numberline {9.3}Making models}{147}{section.9.3}
\contentsline {section}{\numberline {9.4}Comparing results: coefficients}{148}{section.9.4}
\contentsline {subsection}{\numberline {9.4.1}Principle}{148}{subsection.9.4.1}
\contentsline {subsection}{\numberline {9.4.2}Force coefficients}{148}{subsection.9.4.2}
\contentsline {subsection}{\numberline {9.4.3}Power coefficient, and other coefficients}{149}{subsection.9.4.3}
\contentsline {subsection}{\numberline {9.4.4}The systematic non-dimensionalization of problems}{150}{subsection.9.4.4}
\contentsline {section}{\numberline {9.5}Problems}{151}{section.9.5}
\contentsline {subsubsection}{\numberline {9.1}Scaling with the Reynolds number}{151}{subsubsection.9.5.0.1}
\contentsline {subsubsection}{\numberline {9.2}Fluid mechanics of a giant airliner}{152}{subsubsection.9.5.0.2}
\contentsline {subsubsection}{\numberline {9.3}Scale effects on a dragonfly}{153}{subsubsection.9.5.0.3}
\contentsline {subsubsection}{\numberline {9.4}Formula One testing}{153}{subsubsection.9.5.0.4}
\contentsline {chapter}{\numberline {10}Flow near walls}{157}{chapter.10}
\contentsline {section}{\numberline {10.1}Motivation}{157}{section.10.1}
\contentsline {section}{\numberline {10.2}The concept of boundary layer}{157}{section.10.2}
\contentsline {subsection}{\numberline {10.2.1}Rationale}{157}{subsection.10.2.1}
\contentsline {subsection}{\numberline {10.2.2}Why do we study the boundary layer?}{159}{subsection.10.2.2}
\contentsline {subsection}{\numberline {10.2.3}Characterization of the boundary layer}{159}{subsection.10.2.3}
\contentsline {section}{\numberline {10.3}Laminar boundary layers}{161}{section.10.3}
\contentsline {subsection}{\numberline {10.3.1}Governing equations}{161}{subsection.10.3.1}
\contentsline {subsection}{\numberline {10.3.2}Blasius\IeC {\textquoteright } solution}{162}{subsection.10.3.2}
\contentsline {section}{\numberline {10.4}Boundary layer transition}{163}{section.10.4}
\contentsline {section}{\numberline {10.5}Turbulent boundary layers}{164}{section.10.5}
\contentsline {section}{\numberline {10.6}Flow separation}{165}{section.10.6}
\contentsline {section}{\numberline {10.7}Problems}{169}{section.10.7}
\contentsline {subsubsection}{\numberline {10.1}Water and air flow}{169}{subsubsection.10.7.0.1}
\contentsline {subsubsection}{\numberline {10.2}Boundary layer sketches}{170}{subsubsection.10.7.0.2}
\contentsline {subsubsection}{\numberline {10.3}Shear force due to boundary layer}{171}{subsubsection.10.7.0.3}
\contentsline {subsubsection}{\numberline {10.4}Wright Flyer I}{171}{subsubsection.10.7.0.4}
\contentsline {subsubsection}{\numberline {10.5}Power lost to shear on an airliner fuselage}{172}{subsubsection.10.7.0.5}
\contentsline {subsubsection}{\numberline {10.6}Laminar wing profile}{172}{subsubsection.10.7.0.6}
\contentsline {subsubsection}{\numberline {10.7}Separation mechanism}{172}{subsubsection.10.7.0.7}
\contentsline {chapter}{\numberline {11}Large- and small-scale\nobreakspace {}flows}{177}{chapter.11}
\contentsline {section}{\numberline {11.1}Motivation}{177}{section.11.1}
\contentsline {section}{\numberline {11.2}Flow at large scales}{177}{section.11.2}
\contentsline {subsection}{\numberline {11.2.1}Problem statement}{177}{subsection.11.2.1}
\contentsline {subsection}{\numberline {11.2.2}Investigation of inviscid flows}{178}{subsection.11.2.2}
\contentsline {section}{\numberline {11.3}Plotting velocity with functions}{179}{section.11.3}
\contentsline {subsection}{\numberline {11.3.1}Kinematics that fit conservation laws}{179}{subsection.11.3.1}
\contentsline {subsection}{\numberline {11.3.2}Strengths and weaknesses of potential flow}{180}{subsection.11.3.2}
\contentsline {subsection}{\numberline {11.3.3}Superposition: the lifting cylinder}{181}{subsection.11.3.3}
\contentsline {subsection}{\numberline {11.3.4}Circulating cylinder}{183}{subsection.11.3.4}
\contentsline {subsection}{\numberline {11.3.5}Modeling lift with circulation}{185}{subsection.11.3.5}
\contentsline {section}{\numberline {11.4}Flow at very small scales}{188}{section.11.4}
\contentsline {section}{\numberline {11.5}Problems}{191}{section.11.5}
\contentsline {subsubsection}{\numberline {11.1}Volcanic ash from the Eyjafjallaj\IeC {\"o}kull}{191}{subsubsection.11.5.0.1}
\contentsline {subsubsection}{\numberline {11.2}Water drop}{191}{subsubsection.11.5.0.2}
\contentsline {subsubsection}{\numberline {11.3}Idealized flow over a hangar roof}{191}{subsubsection.11.5.0.3}
\contentsline {subsubsection}{\numberline {11.4}Cabling of the Wright Flyer}{193}{subsubsection.11.5.0.4}
\contentsline {subsubsection}{\numberline {11.5}Ping pong ball}{193}{subsubsection.11.5.0.5}
\contentsline {subsubsection}{\numberline {11.6}Flow field of a tornado}{196}{subsubsection.11.5.0.6}
\contentsline {subsubsection}{\numberline {11.7}Lift on a symmetrical object}{198}{subsubsection.11.5.0.7}
\contentsline {subsubsection}{\numberline {11.8}Air flow over a wing profile}{198}{subsubsection.11.5.0.8}
\contentsline {chapter}{Appendix}{201}{section*.121}
\contentsline {section}{\numberline {A1}Notation}{202}{section.Alph0.1}
\contentsline {section}{\numberline {A2}Field operators}{203}{section.Alph0.2}
\contentsline {subsection}{\numberline {A2.1}Gradient}{203}{subsection.Alph0.2.1}
\contentsline {subsection}{\numberline {A2.2}Divergent}{203}{subsection.Alph0.2.2}
\contentsline {subsection}{\numberline {A2.3}Laplacian}{204}{subsection.Alph0.2.3}
\contentsline {subsection}{\numberline {A2.4}Curl}{204}{subsection.Alph0.2.4}
\contentsline {section}{\numberline {A3}Derivations of the Bernoulli equation}{205}{section.Alph0.3}
\contentsline {subsection}{\numberline {A3.1}The Bernoulli equation from the energy equation}{205}{subsection.Alph0.3.1}
\contentsline {subsection}{\numberline {A3.2}The Bernoulli equation from the integral momentum equation}{205}{subsection.Alph0.3.2}
\contentsline {subsection}{\numberline {A3.3}The Bernoulli equation from the Navier-Stokes equation}{205}{subsection.Alph0.3.3}
\contentsline {section}{\numberline {A4}Flow parameters as force ratios}{208}{section.Alph0.4}
\contentsline {subsection}{\numberline {A4.1}Acceleration vs. viscous forces: the Reynolds number}{208}{subsection.Alph0.4.1}
\contentsline {subsection}{\numberline {A4.2}Acceleration vs. gravity force: the Froude number}{209}{subsection.Alph0.4.2}
\contentsline {subsection}{\numberline {A4.3}Acceleration vs. elastic forces: the Mach number}{209}{subsection.Alph0.4.3}
\contentsline {subsection}{\numberline {A4.4}Other force ratios}{210}{subsection.Alph0.4.4}
\contentsline {section}{\numberline {A5}List of references}{211}{section.Alph0.5}
This source diff could not be displayed because it is too large. You can view the blob instead.
This source diff could not be displayed because it is too large. You can view the blob instead.
Markdown is supported
0% or .
You are about to add 0 people to the discussion. Proceed with caution.
Finish editing this message first!
Please register or to comment