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Understanding Fluid Flow takes a fresh approach to introducing fluid dynamics, with physical reasoning and mathematical developments inextricably intertwined. The 'dry' fluid dynamics described by potential theory is set within the context of real viscous flows to give fundamental insight into how fluids behave. The book gives a flavour of theoretical, experimental and numerical approaches to analysing fluid flow, and implicitly develops skills in applied mathematical modelling of physical systems. It is supplemented by movies that are freely downloadable.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems and refined illustrations, plus new coverage of digital photography, frequency analysis of signals and force measurement. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. Instructor resources include lecture slides, additional problems, laboratory support materials and online solutions. Ideal for senior undergraduate and graduate students studying experimental fluid mechanics, this textbook is also suitable for an introductory measurements laboratory, and is a valuable resource for practising engineers and scientists in experimental fluid mechanics.
Singularly perturbed ordinary differential equations often exhibit Stokes’ phenomenon, which describes the appearance and disappearance of oscillating exponentially small terms across curves in the complex plane known as Stokes lines. These curves originate at singular points in the leading-order solution to the differential equation. In many important problems, it is impossible to obtain a closed-form expression for these leading-order solutions, and it is therefore challenging to locate these singular points. We present evidence that the analytic leading-order solution of a linear differential equation can be replaced with a numerical rational approximation using the adaptive Antoulas–Anderson (AAA) method. Despite such an approximation having completely different singularity types and locations, we show that the subsequent exponential asymptotic analysis accurately predicts the exponentially small behaviour present in the solution. For sufficiently small values of the asymptotic parameter, this approach breaks down; however, the range of validity may be extended by increasing the number of poles in the rational approximation. We present a related nonlinear problem and discuss the challenges that arise due to nonlinear effects. Overall, our approach allows for the study of exponentially small asymptotic effects without requiring an exact analytic form for the leading-order solution; this permits exponential asymptotic methods to be used in a much wider range of applications.
We consider planar flow involving two viscous fluids in a porous medium. One fluid is injected through a line source at the origin and moves radially outwards, pushing the second, ambient fluid outwards. There is an interface between the two fluids and if the inner injected fluid is of lower viscosity, the interface is unstable to small disturbances and radially directed unstable Saffman–Taylor fingers are produced. A linearized theory is presented and is compared with nonlinear results obtained using a numerical spectral method. An additional theory is also discussed, in which the sharp interface is replaced with a narrow diffuse interfacial region. We show that the nonlinear results are in close agreement with the linearized theory for small-amplitude disturbances at early times, but that large-amplitude fingers develop at later times and can even detach completely from the initial injection region.
Mathematical modelling of microwaves travelling through bauxite ore provides a way to compute moisture content in the free space transmission method given data on signal attenuation, phase shift and variable bauxite depth. We extend a recently developed four-layer model that uses coupled ordinary differential wave equations for the electric field together with continuity boundary conditions at interfaces between ore, air and antenna to find a solution that incorporates multiple internal reflections in ore and air. The model provides good fits to data, depending on ore permittivity and conductivity.
Our extensions are to use effective medium models to obtain electromagnetic properties of the ore mixture from moisture content and to incorporate the damping effects of scattering from the ore surface. Our model leads to a formula for the received signal showing how signal strengths SS and phase shifts depend on the moisture content of the bauxite ore, through the effects of moisture on permittivity and conductivity. We show that SS may be noninvertible, indicating that attenuation data alone cannot be used to infer moisture content. Combining with phase data typically corrects the noninvertibility. Reducing the operating frequency dramatically improves the usefulness of signal strength data for inferring moisture content.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.
Thoroughly revised and expanded, the new edition of this established textbook equips readers with a robust and practical understanding of experimental fluid mechanics. Enhanced features include improved support for students with emphasis on pedagogical instruction and self-learning, end-of-chapter summaries, 127 examples, 165 problems, refined illustrations, as well as new coverage of techniques in digital photography, frequency analysis of signals and the measurement of forces. It describes comprehensively classical and modern methods for flow visualisation and measuring flow rate, pressure, velocity, temperature, concentration, forces and wall shear stress, alongside supporting material on system response, measurement uncertainty, signal analysis, data analysis, optics, laboratory apparatus and laboratory practice. With enhanced instructor resources, including lecture slides, additional problems, laboratory support materials and online solutions, this is the ideal textbook for senior undergraduate and graduate students studying experimental fluid mechanics and is also suitable for an introductory measurements laboratory. Moreover, it is a valuable resource for practising engineers and scientists in this area.