## Worlds of Flow: A History of Hydrodynamics from the Bernoullis to PrandtlThe first of its kind, this book is an in-depth history of hydrodynamics from its eighteenth-century foundations to its first major successes in twentieth-century hydraulics and aeronautics. It documents the foundational role of fluid mechanics in developing a new mathematical physics. It gives full and clear accounts of the conceptual breakthroughs of physicists and engineers who tried to meet challenges in the practical worlds of hydraulics, navigation, blood circulation, meteorology, and aeronautics, and it shows how hydrodynamics at last began to fulfill its early promise to unify the different worlds of flow. Richly illustrated, technically thorough, and sensitive to cross-cultural effects, this history should attract a broad range of historians, scientists, engineers, and philosophers and be a standard reference for anyone interested in fluid mechanics. |

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### Contents

1 The dynamical equations | 1 |

2 Water waves | 31 |

3 Viscosity | 101 |

4 Vortices | 145 |

5 Instability | 183 |

6 Turbulence | 219 |

7 Drag and lift | 264 |

8 Conclusion | 323 |

Modern discussion of dAlemberts paradox | 326 |

329 | |

350 | |

### Common terms and phrases

acceleration applied Bernoulli body boundary conditions boundary layer Boussinesq Cauchy Cauchy’s constant continuity equation d’Alembert Daniel Bernoulli derived discontinuity surfaces dynamics eddies elasticity energy engineering equations of motion equilibrium Euler’s equation filaments finite flow fluid mechanics fluid motion fluid particles fluid resistance formula friction Froude Girard group velocity Helmholtz hydraulic hydrodynamics implies incompressible instability integral irrotational Johann Bernoulli Lagrange Lagrange’s laminar Lanchester Laplace’s live force Ludwig Prandtl mathematical mechanics memoir method molecular molecules momentum Navier Navier–Stokes equation Newton’s observed obtained oscillations pendulum perfect liquid perturbation pipe plane plate Poiseuille flow Poisson Prandtl pressure principle problem propagation Rayleigh Reynolds Reynolds’s rotation Russell Russell’s Saint-Venant Saint-Venant’s ship solid solitary wave solution stability Stokes Stokes’s stress surface of discontinuity theorem theory Thomson tube turbulent vanish velocity potential velocity profile viscosity vortex motion vortex rings vortex sheet vorticity wall water surface wind