Viscous Fluid Flow

Tasos Papanastasiou, Georgios Georgiou, Andreas N. Alexandrou

• Publisher: CRC Press
• Year: 2021
• ISBN:
  9781000432619
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Energy

"With the appearance and fast evolution of high performance materials, mechanical, chemical and process engineers cannot perform effectively without fluid processing knowledge. The purpose of this book is to explore the systematic application of basic engineering principles to fluid flows that may occur in fluid processing and related activities.In Viscous Fluid Flow, the authors develop and rationalize the mathematics behind the study of fluid mechanics and examine the flows of Newtonian fluids. Although the material deals with Newtonian fluids, the concepts can be easily generalized to non-Newtonian fluid mechanics. The book contains many examples. Each chapter is accompanied by problems where the chapter theory can be applied to produce characteristic results.Fluid mechanics is a fundamental and essential element of advanced research, even for those working in different areas, because the principles, the equations, the analytical, computational and experimental means, and the purpose are common.

Chapter 1

VECTOR AND TENSOR CALCULUS

The physical quantities encountered in fluid mechanics can be sectionided into three classes: (a) scalars, such as pressure, density, viscosity, temperature, length, mass, volume, and time; (b) vectors, such as velocity, acceleration, displacement, linear momentum, and force; and (c) tensors, such as stress, rate of strain, and vorticity tensors.

Scalars are completely described by their magnitude or absolute value, and they do not require direction in space for their specification. In most cases, we shall denote scalars by lower case, lightface italic type, such as p for pressure and ρ for density. Operations with scalars, i.e., addition and multiplication, follow the rules of elementary algebra. A scalar field is a real-valued function that associates a scalar (i.e., a real number) with each point of a given region in space. Let us consider, for example, the right-handed Cartesian coordinate system of Fig. 1.1 and a closed three-dimensional region V occupied by a certain amount of a moving fluid at a given time instance ...