Book contents
- Frontmatter
- Contents
- Preface
- A Word to the Instructor
- 1 Basic Concepts and Fluid Properties
- 2 The Fluid Dynamic Equation
- 3 Fluid Statics
- 4 Introduction to Fluid in Motion – One-Dimensional (Frictionless) Flow
- 5 Viscous Incompressible Flow: Exact Solutions
- 6 Dimensional Analysis and High-Reynolds-Number Flows
- 7 The (Laminar) Boundary Layer
- 8 High-Reynolds-Number Flow over Bodies (Incompressible)
- 9 Introduction to Computational Fluid Dynamics
- 10 Elements of Inviscid Compressible Flow
- 11 Fluid Machinery
- Appendix A Conversion Factors
- Appendix B Properties of Compressible Isentropic Flow
- Appendix C Properties of Normal Shock Flow
- Index
6 - Dimensional Analysis and High-Reynolds-Number Flows
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- A Word to the Instructor
- 1 Basic Concepts and Fluid Properties
- 2 The Fluid Dynamic Equation
- 3 Fluid Statics
- 4 Introduction to Fluid in Motion – One-Dimensional (Frictionless) Flow
- 5 Viscous Incompressible Flow: Exact Solutions
- 6 Dimensional Analysis and High-Reynolds-Number Flows
- 7 The (Laminar) Boundary Layer
- 8 High-Reynolds-Number Flow over Bodies (Incompressible)
- 9 Introduction to Computational Fluid Dynamics
- 10 Elements of Inviscid Compressible Flow
- 11 Fluid Machinery
- Appendix A Conversion Factors
- Appendix B Properties of Compressible Isentropic Flow
- Appendix C Properties of Normal Shock Flow
- Index
Summary
Introduction
We have seen in the previous chapter that for specific cases certain terms of the fluid dynamic equations can be neglected, yet these simplified solutions still contain the dominant physical elements. The flow in pipes was an excellent example for developing exact solutions for the low-Reynolds-number case and then the formulation was extended to the higher-Reynolds-number cases, based on experimental observations. Also, the examples presented in the previous chapter can be considered as internal flows. The discussion in this chapter extends the modeling capability to include external flows as well. One of the objectives of this chapter is to demonstrate that neglecting certain terms in the governing equations can be done systematically. The use of dimensional analysis allows a logical approach for simplifying the governing equations and provides relative scaling for the various terms. A secondary objective of this chapter is to introduce a flow regime called the high-Reynolds-number flow (discussed in Chapters 7 and 8) and to explain the success of incompressible flow models. In spite of the complex equations, a reasonable solution for the flow over bodies (and the resulting forces such as lift and drag) can be obtained and their physical origins explained. This approach of treating high-Reynolds-number flows provides the basis for modern aerodynamics and hydrodynamics.
The process of simplifying the fluid dynamic equations (and neglecting certain terms) is not arbitrary. In fact, it is based on rigorous assumptions.
- Type
- Chapter
- Information
- Introductory Fluid Mechanics , pp. 213 - 226Publisher: Cambridge University PressPrint publication year: 2010