Elementary Fluid DynamicsThe study of the dynamics of fluids is a central theme of modern applied mathematics. It is used to model a vast range of physical phenomena and plays a vital role in science and engineering. This textbook provides a clear introduction to both the theory and application of fluid dynamics, and will be suitable for all undergraduates coming to the subject for the first time. Prerequisites are few: a basic knowledge of vector calculus, complex analysis, and simple methods for solving differential equations are all that is needed. Throughout, numerous exercises (with hints and answers) illustrate the main ideas and serve to consolidate the reader's understanding of the subject. The book's wide scope (including inviscid and viscous flows, waves in fluids, boundary layer flow, and instability in flow) and frequent references to experiments and the history of the subject, ensures that this book provides a comprehensive and absorbing introduction to the mathematical study of fluid behaviour. |
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aerofoil amplitude angular velocity axis axisymmetric blob boundary conditions boundary layer circular cylinder circulation round complex potential components Consider constant deduce denotes density disturbances divergence theorem Euler's equation Exercise finite flow speed fluid element Fluid Mech force free surface group velocity high Reynolds number incompressible instability integral irrotational flow past Kelvin's circulation theorem line vortex linear low Reynolds number momentum Navier-Stokes equations no-slip condition obtain P₁ P₂ particular plane polar coordinates pressure gradient problem region result rigid boundary rotating satisfy solution sphere stagnation point steady flow stream function streamline stress Suppose term theorem thin trailing edge u₁ v₁ vector velocity potential velocity profile viscous viscous flow viscous fluid vortex rings vortex tube waves z-plane zero θυ ди ди др эф Эх ду ᎥᎱ