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.

The multiscale nature of dispersed multiphase flows makes their characterization challenging. A single-phase flow may be reasonably characterized in terms of nondimensional parameters, such as the Reynolds number, Mach number, or Rayleigh number. But characterization of a multiphase flow requires additional parameters that describe the dispersed phase and its relation to the continuous phase. In this chapter we will introduce mathematical definitions of some basic quantities and explain how they characterize the dispersed multiphase flow.

The Euler–Euler (EE) approach derives its name from the fact that both the continuous and the dispersed phases are solved in the Eulerian frame of reference. For the fluid phase, the Eulerian frame is the natural choice and was pursued both in the particle-resolved (PR) and the Euler–Lagrange (EL) approaches. Particles are, however, inherently Lagrangian, and an Eulerian representation is possible only when the individual nature of the particles is erased. This requires that the particle-related Lagrangian quantities be suitably averaged, so that Eulerian fields of these quantities can be defined. The averaging process will allow particle volume fraction, particle velocity, and particle temperature fields to be defined as functions of space and time.

In this chapter, we investigate the problem of heat transfer from an isolated rigid sphere subjected to a cross flow of different temperature. This thermal problem is analogous to the flow problem considered earlier, and the interest here is to establish an expression for heat transfer in terms of the undisturbed ambient flow, which must now be characterized both in terms of relative velocity and temperature difference. We will start our investigation with rigorous analytical results in the Stokes and the small Péclet number regime.

The Eulerian representation of the continuous phase is natural, where quantities such as fluid velocity u(x,t) represent the average velocity of all the fluid molecules within a suitably chosen volume for continuum description. In the previous section, we considered filtering of these flow quantities over a suitably chosen length scale that is much larger than the size of the individual particles.

In this chapter we will consider in detail the interaction of an isolated rigid particle with the surrounding continuous-phase flow. In the low Reynolds number limit, the problem can be solved analytically. At finite Reynolds number, one must resort to numerical simulations. Nevertheless, in both cases, by simultaneously solving the Navier–Stokes equations for the fluid, equations of rigid-body motion for the particle, and coupling them with no-slip and no-penetration boundary conditions, we can obtain complete details of the flow around the particle.

From the range of topics and the depth of physics that were discussed in the previous chapters, it is quite clear that multiphase flow is a challenging subject even at the level of an individual particle. But clearly we need to move forward and begin to consider more complex multiphase-flow physics. Toward this goal, we will progress beyond an isolated particle in an unbounded medium in two different ways. First, in this chapter we will consider the problem of an isolated particle in an ambient flow, but in the presence of a nearby wall.