Preface |
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xvii | |
Author's Notes |
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xxi | |
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1 | (1) |
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2 | (1) |
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Solids, Liquids, and Gases |
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3 | (1) |
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4 | (1) |
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5 | (3) |
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8 | (1) |
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9 | (3) |
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12 | (4) |
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16 | (2) |
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Static Equilibrium of a Compressible Medium |
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18 | (6) |
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22 | (1) |
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23 | (1) |
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23 | (1) |
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24 | (1) |
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Rotation of Axes: Formal Definition of a Vector |
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25 | (3) |
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Multiplication of Matrices |
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28 | (1) |
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29 | (2) |
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Contraction and Miltiplication |
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31 | (1) |
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32 | (3) |
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Kronecker Delta and Alternating Tensor |
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35 | (1) |
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36 | (1) |
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36 | (1) |
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Operator ∇: Gradient, Divergence, and Curl |
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37 | (2) |
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Symmetric and Antisymmetric Tensors |
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39 | (1) |
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Eigenvalues and Eigenvectors of a Symmetric Tensor |
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40 | (2) |
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42 | (1) |
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43 | (1) |
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44 | (1) |
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Boldface versus Indicial Notation |
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45 | (2) |
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45 | (1) |
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46 | (1) |
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46 | (1) |
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47 | (1) |
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Lagrangian and Eulerian Specifications |
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48 | (1) |
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49 | (2) |
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Streamline, Path Line, and Streak Line |
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51 | (2) |
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Reference Frame and Streamline Pattern |
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53 | (1) |
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54 | (1) |
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55 | (1) |
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Vorticity and Circulation |
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56 | (2) |
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Relative Motion near a Point: Principal Axes |
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58 | (3) |
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Kinematic Considerations of Parallel Shear Flows |
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61 | (1) |
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Kinematic Considerations of Vortex Flows |
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62 | (4) |
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One-, Two-, and Three-Dimensional Flows |
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66 | (1) |
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66 | (3) |
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69 | (5) |
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70 | (3) |
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73 | (1) |
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74 | (1) |
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Time Derivatives of Volume Integrals |
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75 | (2) |
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77 | (2) |
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Origin of Forces in Fluid |
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79 | (2) |
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81 | (2) |
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83 | (1) |
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Momentum Principle for a Mixed Volume |
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84 | (3) |
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Angular Momentum Principle for a Fixed Volume |
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87 | (2) |
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Constitutive Equation for Newtonian Fluid |
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89 | (4) |
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93 | (1) |
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94 | (5) |
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Mechanical Energy Equation |
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99 | (4) |
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First Law of Thermodynamics: Thermal Energy Equation |
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103 | (2) |
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Second Law of Thermodynamics: Entropy Production |
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105 | (1) |
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106 | (3) |
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Applications of Bernoulli's Equation |
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109 | (3) |
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112 | (7) |
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116 | (1) |
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117 | (1) |
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118 | (1) |
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119 | (1) |
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Vortex Lines and Vortex Tubes |
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120 | (1) |
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Role of Viscosity in Rotational and Irrotational Vortices |
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121 | (3) |
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Kelvin's Circulation Theorem |
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124 | (5) |
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Vorticity Equation in a Nonrotating Frame |
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129 | (1) |
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Vorticity Equation in a Rotating Frame |
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130 | (5) |
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135 | (3) |
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138 | (3) |
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139 | (1) |
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140 | (1) |
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140 | (1) |
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Relevance of Irrotational Flow Theory |
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141 | (2) |
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Velocity Potential: Laplace Equation |
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143 | (2) |
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Application of Complex Variables |
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145 | (2) |
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147 | (2) |
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149 | (1) |
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149 | (1) |
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150 | (2) |
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152 | (1) |
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Flow past a Circular Cylinder without Circulation |
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153 | (3) |
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Flow past a Circular Cylinder with Circulation |
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156 | (3) |
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Forces on a Two-Dimensional Body |
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159 | (3) |
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Source near a Wall: Method of Images |
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162 | (1) |
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163 | (2) |
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Flow around an Elliptic Cylinder with Circulation |
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165 | (1) |
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Uniqueness of Irrotational Flows |
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166 | (2) |
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Numerical Solution of Plane Irrotational Flow |
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168 | (5) |
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Axisymmetric Irrotational Flow |
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173 | (2) |
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Stream Function and Velocity Potential for Axisymmetric Flow |
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175 | (1) |
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Simple Examples of Axisymmetric Flows |
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176 | (2) |
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Flow around a Streamlined Body of Revolution |
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178 | (1) |
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Flow around an Arbitrary Body of Revolution |
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179 | (1) |
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180 | (4) |
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181 | (2) |
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183 | (1) |
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183 | (1) |
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184 | (1) |
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185 | (2) |
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187 | (3) |
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190 | (4) |
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Some Features of Surface Gravity Waves |
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194 | (6) |
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Approximations for Deep and Shallow Water |
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200 | (5) |
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Influence of Surface Tension |
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205 | (3) |
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208 | (1) |
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Group Velocity and Energy Flux |
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209 | (3) |
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Group Velocity and Wave Dispersion |
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212 | (4) |
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Nonlinear Steepening in a Nondispersive Medium |
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216 | (2) |
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218 | (3) |
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Finite Amplitude Waves of Unchanging Form in a Dispersive Medium |
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221 | (2) |
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223 | (3) |
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Waves at a Density Interface between Infintely Deep Fluids |
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226 | (3) |
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Waves in a Finite Layer Overlying an Infinitely Deep Fluid |
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229 | (3) |
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Shallow Layer Overlying an Infinitely Deep Fluid |
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232 | (2) |
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Equations of Motion for a Continuously Stratified Fluid |
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234 | (2) |
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Internal Waves in a Continuously Stratified Fluid |
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236 | (4) |
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Dispersion of Internal Waves in a Stratified Fluid |
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240 | (2) |
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Energy Considerations of Internal Waves in a Stratified Fluid |
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242 | (6) |
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246 | (1) |
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247 | (1) |
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248 | (1) |
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Nondimensional Parameters Determined from Differential Equations |
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249 | (3) |
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252 | (1) |
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253 | (2) |
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Nondimensional Parameters and Dynamic Similarity |
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255 | (2) |
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Comments on Model Testing |
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257 | (2) |
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Significance of Common Nondimensional Parameters |
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259 | (4) |
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262 | (1) |
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263 | (2) |
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Analogy between Heat and Vorticity Diffusion |
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265 | (1) |
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Pressure Change Due to Dynamic Effects |
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265 | (1) |
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Steady Flow between Parallel Plates |
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266 | (4) |
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270 | (1) |
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Steady Flow between Concentric Cylinders |
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271 | (3) |
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Impulsively Started Plate: Similarity Solutions |
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274 | (6) |
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Diffusion of a Vortex Sheet |
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280 | (2) |
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282 | (2) |
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Flow Due to an Oscillating Plate |
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284 | (3) |
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High and Low Reynolds Number Flows |
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287 | (2) |
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Creeping Flow around a Sphere |
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289 | (3) |
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Nonuniformity of Stokes's Solution and Oseen's Improvement |
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292 | (4) |
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296 | (3) |
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296 | (2) |
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298 | (1) |
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298 | (1) |
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Boundary Layers and Related Topics |
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299 | (1) |
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Boundary Layer Approximation |
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300 | (5) |
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Different Measures of Boundary Layer Thickness |
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305 | (2) |
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Boundary Layer on a Flat Plate: Blasius Solution |
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307 | (8) |
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315 | (2) |
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Effects of Pressure Gradient |
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317 | (1) |
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318 | (3) |
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Description of Flow past a Circular Cylinder |
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321 | (6) |
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Description of Flow past a Sphere |
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327 | (1) |
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327 | (6) |
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333 | (3) |
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336 | (4) |
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An Example of a Regular Perturbation Problem |
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340 | (2) |
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An Example of a Singular Perturbation Problem |
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342 | (8) |
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347 | (1) |
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348 | (1) |
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348 | (2) |
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350 | (1) |
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351 | (1) |
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Thermal Instability: The Benard Problem |
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352 | (11) |
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Double-Diffusive Instability |
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363 | (5) |
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Centrifugal Instability: Taylor Problem |
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368 | (5) |
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Kelvin-Helmholtz Instability |
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373 | (8) |
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Instability of Continuously Stratified Parallel Flows |
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381 | (6) |
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Squire's Theorem and Orr-Sommerfeld Equation |
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387 | (4) |
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Inviscid Stability of Parallel Flows |
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391 | (4) |
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Some Results of Parallel Viscous Flows |
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395 | (6) |
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Experimental Verification of Boundary Layer Instability |
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401 | (1) |
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Comments on Nonlinear Effects |
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402 | (1) |
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403 | (2) |
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405 | (11) |
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413 | (2) |
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415 | (1) |
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416 | (2) |
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418 | (2) |
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420 | (3) |
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423 | (3) |
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Averaged Equations of Motion |
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426 | (7) |
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Kinetic Energy Budget of Mean Flow |
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433 | (2) |
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Kinetic Energy Budget of Turbulent Flow |
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435 | (3) |
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Turbulence Production and Cascade |
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438 | (3) |
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Spectrum of Turbulence in Inertial Subrange |
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441 | (2) |
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443 | (5) |
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448 | (7) |
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Eddy Viscosity and Mixing Length |
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455 | (3) |
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Coherent Structures in a Wall Layer |
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458 | (2) |
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Turbulence in a Stratified Medium |
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460 | (6) |
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Taylor's Theory of Turbulent Dispersion |
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466 | (8) |
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471 | (2) |
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473 | (1) |
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Geophysical Fluid Dynamics |
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474 | (2) |
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Vertical Variation of Density in Atmosphere and Ocean |
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476 | (2) |
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478 | (3) |
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Approximate Equations for a Thin Layer on a Rotating Sphere |
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481 | (3) |
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484 | (5) |
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Ekman Layer at a Free Surface |
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489 | (3) |
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Ekman Layer on a Rigid Surface |
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492 | (4) |
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496 | (2) |
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Normal Modes in a Continuously Stratified Layer |
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498 | (6) |
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High and Low Frequency Regimes in Shallow Water Equations |
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504 | (2) |
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Gravity Waves with Rotation |
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506 | (3) |
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509 | (4) |
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Potential Vorticity Conservation in Shallow Water Theory |
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513 | (4) |
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517 | (9) |
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526 | (6) |
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532 | (1) |
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533 | (8) |
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541 | (6) |
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545 | (1) |
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546 | (1) |
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547 | (1) |
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The Aircraft and Its Controls |
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548 | (2) |
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550 | (1) |
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551 | (1) |
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552 | (2) |
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Generation of Circulation |
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554 | (2) |
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Conformal Transformation for Generating Airfoil Shape |
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556 | (4) |
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Lift of Zhukhovski Airfoil |
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560 | (2) |
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562 | (2) |
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Lifting Line Theory of Prandtl and Lanchester |
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564 | (4) |
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Results for Elliptic Circulation Distribution |
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568 | (3) |
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Lift and Drag Characteristics of Airfoils |
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571 | (2) |
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Propulsive Mechanisms of Fish and Birds |
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573 | (2) |
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575 | (4) |
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576 | (1) |
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577 | (1) |
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578 | (1) |
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579 | (4) |
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583 | (2) |
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Basic Equations for One-Dimensional Flow |
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585 | (3) |
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Stagnation and Sonic Properties |
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588 | (2) |
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Area-Velocity Relations in One-Dimensional Insentropic Flow |
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590 | (7) |
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597 | (4) |
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Operation of Nozzles at Different Back Pressures |
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601 | (5) |
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606 | (2) |
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608 | (5) |
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Expansion and Compression in Supersonic Flow |
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613 | (1) |
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Thin Airfoil Theory in Supersonic Flow |
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614 | (4) |
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616 | (1) |
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617 | (1) |
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617 | (1) |
Appendix A Some Properties of Common Fluids |
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A1. Useful Conversion Factors |
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618 | (1) |
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A2. Properties of Pure Water at Atmospheric Pressure |
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619 | (1) |
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A3. Properties of Dry Air at Atmospheric Pressure |
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619 | (1) |
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A4. Properties of Standard Atmosphere |
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620 | (1) |
Appendix B Curvilinear Coordinates |
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B1. Cylindrical Polar Coordinates |
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621 | (2) |
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B2. Plane Polar Coordinates |
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623 | (1) |
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B3. Spherical Polar Coordinates |
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624 | (2) |
Appendix C Founders of Modern Fluid Dynamics |
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Ludwig Prandtl (1875-1953) |
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626 | (1) |
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Geoffrey Ingram Taylor (1886-1975) |
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627 | (1) |
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628 | (1) |
Index |
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629 | |