Fluid Mechanics for Mechanical Engineers

The aim of this textbook is to provide a structured introduction to fluid dynamics to process and mechanical engineers, presenting a unified method of analysis that involves three steps. First, the fundamental principles of fluid dynamics are discussed. Second, the governing equations and the physical models stemming from first principles are presented. Third, equations are solved considering a wide range of relevant engineering examples. It is worthwhile to note that many of the problems that will be analyzed in this book only admit an approximate solution and that the precise identification of the flow field in complex geometries is, in many cases, still an unsolved physical problem. This is why, in the broad area of applied sciences, fluid mechanics is and will continue to be a field of intense research activity. In recent years, research has received a considerable boost from the development of numerical techniques and the availability of increasingly powerful computing infrastructures, which have led to a growing interest in the solution of complex fluid dynamic problems relevant to both science and engineering. Examples include industrial applications such as multiphase flows, combustion, propulsion, fluid machinery and aerodynamics, as well as environmental applications, such as oceanic or atmospheric flows, rain formation and ice crystals growth in clouds..

The complexity of the equations of fluid dynamics has directed the research activity, since the origins of this scientific field, to combine theoretical analysis with careful experiments, which have often been the main source of new methods and models that can be used for the design and for the analysis of complex flow fields.

The detailed structure of a flow field and its evolution over time are described by a system of partial differential equations that stem from the conservation of scalar quantities such as mass and energy, or vector quantities such as momentum. Let \(\Gamma \) be some field variable, generally defined as a function of space and time, that can be associated to the fluid and V be a control volume that encloses some finite region in space occupied by the fluid at a given instant of time.

An exact solution of the Navier–Stokes equations can be obtained only in a limited number of cases. These include steady unidirectional flows in which the fluid moves in one direction only and, therefore, the velocity vector has just one non-zero component. The steady-state assumption limits the analysis to laminar flows.

Approximate solutions of the N-S equations can be obtained in many cases of practical interest, provided that suitable simplifications can be made. Simplifications stem from the evaluation of the order of magnitude of the different terms appearing in the N-S equations. To assess the order of magnitude of each term, it is useful to write the equations in dimensionless form so that the terms of similar magnitude can be identified and the dimensionless groups that determine the structure of the flow field can be determined.

In the previous chapters, the governing equations for Newtonian and incompressible fluids have been applied to internal flows, namely flows in which the fluid moves between solid walls (for example, Couette or Poiseuille motion in a channel or pipe).

The analysis of the potential flow around immersed bodies at high Reynolds number has led to the identification of two distinct flow regions:

The turbulent flow of a fluid is characterized by temporal and spatial fluctuations of its macroscopic properties, that is velocity, pressure and possibly temperature (in the case of non-isothermal flows), while preserving constant mean values over time in the case of steady flow in a broad sense.

The objective of this chapter is to derive the conservation equations in macroscopic form. Examples of applications for these equations will be presented in Chapters

Fluid flow measurements are necessary in a very wide range of applications that require the determination of the flow velocity, the mass flowrate or the volumetric flowrate.

Many hydraulic systems consist of pipeline networks in which pipes are connected together to enable the transport of a fluid.