Preface |
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v | |
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Introduction to Kinematics |
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1 | (53) |
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1 | (1) |
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Fluid parcels and flow kinematics |
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2 | (1) |
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Coordinates, velocity, and acceleration |
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3 | (13) |
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Cylindrical polar coordinates |
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6 | (3) |
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Spherical polar coordinates |
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9 | (4) |
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13 | (3) |
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16 | (3) |
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Velocity vector field, streamlines and stagnation points |
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18 | (1) |
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Point particles and their trajectories |
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19 | (9) |
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20 | (1) |
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Ordinary differential equations (ODEs) |
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20 | (1) |
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21 | (2) |
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23 | (3) |
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Description in polar coordinates |
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26 | (1) |
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27 | (1) |
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Material surfaces and elementary motions |
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28 | (10) |
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28 | (1) |
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29 | (1) |
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30 | (1) |
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Superposition of rotation, deformation, and expansion |
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31 | (1) |
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32 | (2) |
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34 | (4) |
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38 | (16) |
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Interpolation in one dimension |
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38 | (4) |
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Interpolation in two dimensions |
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42 | (3) |
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Interpolation of the velocity in a two-dimensional flow |
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45 | (4) |
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Streamlines by interpolation |
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49 | (5) |
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54 | (61) |
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Fundamental modes of fluid parcel motion |
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54 | (11) |
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55 | (2) |
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57 | (2) |
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Relative motion of point particles |
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59 | (1) |
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Fundamental motions in two-dimensional flow |
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60 | (2) |
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Fundamental motions in three-dimensional flow |
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62 | (1) |
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Gradient in polar coordinates |
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62 | (3) |
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65 | (1) |
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Fluid parcel rotation and vorticity |
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66 | (5) |
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68 | (2) |
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70 | (1) |
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70 | (1) |
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71 | (3) |
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Numerical differentiation |
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74 | (11) |
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Numerical differentiation in one dimension |
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74 | (2) |
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Numerical differentiation in two dimensions |
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76 | (2) |
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Velocity gradient and related functions |
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78 | (7) |
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85 | (9) |
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87 | (1) |
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Areal flow rate across a line |
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88 | (1) |
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89 | (1) |
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The Gauss divergence theorem in two dimensions |
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90 | (1) |
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Flow rate in a three-dimensional flow |
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91 | (1) |
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Gauss divergence theorem in three dimensions |
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92 | (1) |
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92 | (2) |
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94 | (5) |
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Mass flux and mass flow rate |
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94 | (1) |
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Mass flow rate across a closed line |
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94 | (1) |
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95 | (1) |
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96 | (1) |
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96 | (1) |
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Evolution equation for the density |
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97 | (2) |
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Properties of point particles |
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99 | (7) |
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100 | (1) |
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101 | (1) |
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Point particle acceleration |
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102 | (4) |
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Incompressible fluids and stream functions |
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106 | (5) |
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Mathematical consequences of incompressibility |
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107 | (1) |
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Stream function for two-dimensional flow |
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107 | (2) |
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Stream function for axisymmetric flow |
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109 | (2) |
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Kinematic conditions at boundaries |
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111 | (4) |
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The no-penetration boundary condition |
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111 | (4) |
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Flow Computation based on Kinematics |
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115 | (48) |
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Flow classification based on kinematics |
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115 | (2) |
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Irrotational flow and the velocity potential |
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117 | (7) |
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117 | (2) |
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Incompressible fluids and the harmonic potential |
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119 | (1) |
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120 | (1) |
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121 | (1) |
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Cylindrical polar coordinates |
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122 | (1) |
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Spherical polar coordinates |
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122 | (1) |
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123 | (1) |
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Finite-difference methods |
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124 | (14) |
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124 | (2) |
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126 | (1) |
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Finite-difference discretization |
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127 | (1) |
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Compilation of a linear system |
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128 | (10) |
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138 | (3) |
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139 | (1) |
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A menagerie of other methods |
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140 | (1) |
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Two-dimensional point sources and point-source dipoles |
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141 | (10) |
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Function superposition and fundamental solutions |
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141 | (1) |
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Two-dimensional point source |
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141 | (3) |
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Two-dimensional point-source dipole |
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144 | (4) |
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Flow past a circular cylinder |
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148 | (1) |
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Sources and dipoles in the presence of boundaries |
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149 | (2) |
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Three-dimensional point sources and point-source dipoles |
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151 | (4) |
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Three-dimensional point source |
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151 | (1) |
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Three-dimensional point-source dipole |
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152 | (1) |
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Streaming flow past a sphere |
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153 | (1) |
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Sources and dipoles in the presence of boundaries |
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154 | (1) |
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Point vortices and line vortices |
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155 | (8) |
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The potential of irrotational circulatory flow |
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156 | (1) |
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Flow past a circular cylinder |
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157 | (1) |
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158 | (3) |
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Line vortices in three-dimensional flow |
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161 | (2) |
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163 | (55) |
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Body forces and surface forces |
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163 | (2) |
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163 | (1) |
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164 | (1) |
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Traction and the stress tensor |
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165 | (6) |
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Traction on either side of a fluid surface |
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168 | (1) |
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169 | (1) |
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Symmetry of the stress tensor |
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170 | (1) |
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Traction jump across a fluid interface |
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171 | (12) |
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Force balance at a two-dimensional interface |
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172 | (4) |
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Force balance at a three-dimensional interface |
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176 | (3) |
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179 | (4) |
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Stresses in a fluid at rest |
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183 | (3) |
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Pressure from molecular motions |
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184 | (1) |
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Jump in the pressure across an interface |
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185 | (1) |
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186 | (10) |
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188 | (1) |
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Incompressible Newtonian fluids |
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188 | (2) |
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190 | (2) |
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192 | (1) |
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Significance of the pressure in incompressible fluids |
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193 | (1) |
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Pressure in compressible fluids |
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193 | (3) |
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Simple non-Newtonian fluids |
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196 | (3) |
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Unidirectional shear flow |
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197 | (2) |
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Stresses in polar coordinates |
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199 | (7) |
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Cylindrical polar coordinates |
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200 | (2) |
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Spherical polar coordinates |
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202 | (2) |
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204 | (2) |
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Boundary conditions for the tangential velocity |
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206 | (2) |
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No-slip boundary condition |
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206 | (1) |
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207 | (1) |
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Wall stresses in Newtonian fluids |
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208 | (2) |
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208 | (1) |
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209 | (1) |
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Interfacial surfactant transport |
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210 | (8) |
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Two-dimensional interfaces |
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210 | (4) |
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214 | (2) |
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Three-dimensional interfaces |
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216 | (2) |
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218 | (90) |
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Equilibrium of pressure and body forces |
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218 | (7) |
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Equilibrium of an infinitesimal parcel |
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220 | (2) |
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222 | (1) |
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223 | (2) |
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Force exerted on immersed surfaces |
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225 | (6) |
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A sphere floating on a flat interface |
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226 | (5) |
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231 | (4) |
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Net force on a submerged body |
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233 | (1) |
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234 | (1) |
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235 | (4) |
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236 | (1) |
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The Laplace-Young equation |
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237 | (1) |
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Three-dimensional interfaces |
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238 | (1) |
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A semi-infinite interface attached to an inclined plate |
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239 | (6) |
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241 | (4) |
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A meniscus between two parallel plates |
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245 | (8) |
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249 | (4) |
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A two-dimensional drop on a horizontal or inclined plane |
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253 | (20) |
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Drop on a horizontal plane |
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253 | (8) |
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A drop on an inclined plane |
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261 | (12) |
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Axisymmetric meniscus inside a tube |
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273 | (3) |
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Axisymmetric drop on a horizontal plane |
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276 | (10) |
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278 | (8) |
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A sphere straddling an interface |
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286 | (12) |
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296 | (2) |
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A three-dimensional meniscus |
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298 | (10) |
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299 | (1) |
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300 | (6) |
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Capillary force and torque |
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306 | (2) |
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Equation of Motion and Vorticity Transport |
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308 | (52) |
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Newton's second law of motion for a fluid parcel |
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308 | (5) |
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Rate of change of linear momentum |
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309 | (1) |
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Equation of parcel motion |
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309 | (1) |
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310 | (3) |
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Integral momentum balance |
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313 | (6) |
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Flow through a sudden enlargement |
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316 | (2) |
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Iseritropic flow through a conduit |
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318 | (1) |
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Cauchy's equation of motion |
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319 | (8) |
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Hydrodynamic volume force |
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320 | (1) |
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Force on an infinitesimal parcel |
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320 | (2) |
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322 | (1) |
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323 | (1) |
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Cylindrical polar coordinates |
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323 | (2) |
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Spherical polar coordinates |
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325 | (1) |
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325 | (1) |
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326 | (1) |
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Summary of governing equation |
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326 | (1) |
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Accelerating frame of reference |
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326 | (1) |
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Euler's and Bernoulli's equations |
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327 | (10) |
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328 | (1) |
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329 | (2) |
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331 | (3) |
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334 | (1) |
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Flow with uniform vorticity |
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335 | (2) |
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The Navier-Stokes equation |
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337 | (6) |
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Pressure and viscous forces |
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338 | (1) |
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A radially expanding or contracting bubble |
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339 | (1) |
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340 | (1) |
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341 | (2) |
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343 | (7) |
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343 | (3) |
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346 | (1) |
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347 | (3) |
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Dynamic similitude and the Reynolds number |
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350 | (5) |
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352 | (3) |
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Structure of a flow as a function of the Reynolds number |
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355 | (2) |
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356 | (1) |
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Flow at high Reynolds numbers |
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356 | (1) |
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Laminar and turbulent flow |
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357 | (1) |
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Dimensionless numbers in fluid dynamics |
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357 | (3) |
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Channel, Tube, and Film Flow |
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360 | (64) |
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Steady flow in a two-dimensional channel |
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360 | (13) |
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363 | (2) |
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365 | (5) |
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370 | (3) |
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Steady film flow down an inclined plane |
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373 | (4) |
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374 | (1) |
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375 | (2) |
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Steady flow through a circular tube |
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377 | (6) |
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380 | (1) |
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Flow due to a translating sector |
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380 | (3) |
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Steady flow through an annular tube |
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383 | (4) |
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387 | (1) |
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Steady flow in channels and tubes |
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387 | (8) |
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388 | (2) |
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390 | (3) |
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393 | (1) |
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Semi-infinite rectangular channel |
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393 | (2) |
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395 | (5) |
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396 | (3) |
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399 | (1) |
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400 | (9) |
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400 | (3) |
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Impulsive motion of a plate in a semi-infinite fluid |
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403 | (3) |
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Pressure- and gravity-driven flow |
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406 | (3) |
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409 | (6) |
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409 | (2) |
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Rayleigh's oscillating plate |
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411 | (2) |
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Pulsating pressure-driven flow |
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413 | (2) |
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Transient and oscillatory flow in a circular tube |
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415 | (9) |
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Transient Poiseuille flow |
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415 | (5) |
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Pulsating pressure-driven flow |
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420 | (2) |
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Transient circular Couette flow |
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422 | (1) |
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422 | (2) |
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Finite-Difference Methods |
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424 | (70) |
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Choice of governing equations |
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424 | (1) |
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Unidirectional flow; velocity/pressure formulation |
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425 | (18) |
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426 | (1) |
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Explicit finite-difference method |
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426 | (3) |
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Implicit finite-difference method |
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429 | (6) |
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435 | (1) |
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436 | (7) |
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Unidirectional flow; velocity/vorticity formulation |
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443 | (4) |
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Boundary conditions for the vorticity |
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444 | (1) |
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Alternative set of equations |
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445 | (1) |
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Comparison with the velocity/pressure formulation |
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446 | (1) |
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Unidirectional flow; stream function/vorticity formulation |
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447 | (4) |
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Boundary conditions for the vorticity |
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448 | (1) |
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449 | (2) |
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Two-dimensional flow; stream function/vorticity formulation |
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451 | (12) |
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451 | (1) |
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452 | (1) |
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453 | (1) |
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454 | (6) |
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460 | (3) |
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Velocity/pressure formulation |
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463 | (3) |
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Alternative system of governing equations |
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464 | (1) |
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Pressure boundary conditions |
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465 | (1) |
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Compatibility condition for the pressure |
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465 | (1) |
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Operator splitting and solenoidal projection |
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466 | (19) |
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Convection-diffusion step |
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467 | (2) |
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469 | (2) |
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Boundary conditions for the intermediate velocity |
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471 | (1) |
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471 | (13) |
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Computation of the pressure |
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484 | (1) |
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485 | (9) |
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494 | (68) |
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494 | (11) |
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495 | (1) |
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495 | (2) |
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Equations of lubrication flow |
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497 | (1) |
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Lubrication in a slider bearing |
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497 | (3) |
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500 | (3) |
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503 | (2) |
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Film flow on a horizontal or inclined wall |
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505 | (6) |
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506 | (3) |
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509 | (2) |
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Multi-film flow on a horizontal or inclined wall |
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511 | (12) |
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514 | (2) |
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516 | (7) |
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523 | (11) |
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Flow due to the motion of a sphere |
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534 | (7) |
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Formulation in terms of the stream function |
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535 | (4) |
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Traction, force, and the Archimedes-Stokes law |
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539 | (2) |
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Point forces and point sources in Stokes flow |
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541 | (8) |
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The Oseen tensor and the point force |
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542 | (2) |
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Flow representation in terms of singularities |
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544 | (1) |
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A sphere moving inside a circular tube |
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544 | (3) |
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Boundary integral representation |
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547 | (2) |
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Two-dimensional Stokes flow |
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549 | (5) |
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Flow due to the motion of a cylinder |
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549 | (3) |
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Rotation of a circular cylinder |
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552 | (1) |
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Simple shear flow past a circular cylinder |
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552 | (1) |
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The Oseen tensor and the point force |
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553 | (1) |
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554 | (8) |
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555 | (2) |
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557 | (5) |
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High Reynolds Number Flow |
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562 | (69) |
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Changes in the structure of a flow with increasing Reynolds number |
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562 | (4) |
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Prandtl boundary layer analysis |
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566 | (5) |
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568 | (1) |
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Surface curvilinear coordinates |
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569 | (1) |
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570 | (1) |
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570 | (1) |
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Blasius boundary layer on a semi-infinite plate |
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571 | (8) |
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Self-similarity and the Blasius equation |
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571 | (3) |
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574 | (2) |
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Wall shear stress and drag force |
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576 | (1) |
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577 | (2) |
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Displacement and momentum thickness |
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|
579 | (4) |
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Von Karman's approximate method |
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581 | (2) |
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Boundary layers in accelerating and decelerating flow |
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583 | (4) |
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585 | (1) |
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586 | (1) |
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587 | (12) |
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The von Karman-Pohlhausen method |
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589 | (1) |
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590 | (2) |
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592 | (3) |
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Boundary layer around a curved body |
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595 | (4) |
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Instability of shear flows |
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599 | (11) |
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Stability analysis of shear flow |
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600 | (1) |
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601 | (3) |
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Finite-difference solution |
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604 | (6) |
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610 | (13) |
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611 | (2) |
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613 | (1) |
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Features of turbulent motion |
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|
613 | (2) |
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Decomposition into mean and fluctuating components |
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615 | (2) |
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617 | (1) |
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618 | (1) |
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Relation between inviscid and viscous scales |
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618 | (1) |
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619 | (4) |
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Analysis and modeling of turbulent flow |
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623 | (8) |
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623 | (2) |
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Prandtl's mixing length model |
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625 | (2) |
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Logarithmic law for wall-bounded shear flow |
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627 | (1) |
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628 | (3) |
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631 | (49) |
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Vorticity and circulation in two-dimensional flow |
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631 | (2) |
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633 | (12) |
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Dirac's delta function in a plane |
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|
634 | (2) |
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Evolution of the point vortex strength |
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636 | (1) |
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Velocity of a point vortex |
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|
636 | (1) |
|
Motion of a collection of point vortices |
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|
636 | (1) |
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|
637 | (2) |
|
A periodic array of point vortices |
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|
639 | (2) |
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A point vortex between two parallel walls |
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|
641 | (1) |
|
A point vortex in a semi-infinite strip |
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|
641 | (4) |
|
Two-dimensional flow with distributed vorticity |
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|
645 | (12) |
|
Vortex patches with uniform vorticity |
|
|
646 | (3) |
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|
649 | (2) |
|
Gauss integration quadrature |
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|
651 | (1) |
|
Representation with circular arcs |
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|
652 | (5) |
|
Vorticity and circulation in three-dimensional flow |
|
|
657 | (4) |
|
Preservation of circulation |
|
|
658 | (2) |
|
Flow induced by vorticity |
|
|
660 | (1) |
|
Axisymmetric flow induced by vorticity |
|
|
661 | (14) |
|
Biot-Savart integral for axisymmetric flow |
|
|
663 | (3) |
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|
666 | (2) |
|
Vortex rings with a finite core |
|
|
668 | (4) |
|
Motion of a collection of vortex rings |
|
|
672 | (1) |
|
Vortex patch in axisymmetric flow |
|
|
673 | (2) |
|
Three-dimensional vortex motion |
|
|
675 | (5) |
|
|
676 | (1) |
|
Line vortices and the local induction approximation (LIA) |
|
|
676 | (4) |
|
|
680 | (48) |
|
General features of flow past an aircraft |
|
|
680 | (2) |
|
Airfoils and the Kutta-Joukowski condition |
|
|
682 | (5) |
|
The Kutta-Joukowski theorem |
|
|
686 | (1) |
|
The Kutta-Joukowski condition |
|
|
687 | (1) |
|
|
687 | (7) |
|
From point vortices to vortex panels |
|
|
688 | (1) |
|
Vortex panels with uniform strength |
|
|
689 | (2) |
|
Vortex panel with linear strength density |
|
|
691 | (3) |
|
|
694 | (15) |
|
Velocity in terms of the panel strength |
|
|
698 | (1) |
|
|
699 | (1) |
|
Circulation and pressure coefficient |
|
|
700 | (1) |
|
|
700 | (2) |
|
|
702 | (7) |
|
Vortex sheet representation |
|
|
709 | (8) |
|
|
709 | (8) |
|
Point-source-dipole panels |
|
|
717 | (6) |
|
Source-dipole panel method |
|
|
718 | (2) |
|
Source-dipole representation |
|
|
720 | (1) |
|
Solution of the interior problem |
|
|
721 | (2) |
|
Point-source panels and Green's third identity |
|
|
723 | (5) |
|
Source panels with constant density |
|
|
723 | (2) |
|
|
725 | (3) |
|
|
728 | (10) |
|
|
738 | (3) |
|
|
741 | (22) |
|
|
741 | (1) |
|
|
742 | (1) |
|
Matlab Grammar and syntax |
|
|
743 | (1) |
|
|
744 | (1) |
|
|
744 | (3) |
|
|
747 | (3) |
|
|
750 | (1) |
|
|
751 | (4) |
|
|
755 | (8) |
Index |
|
763 | |