Fluid Mechanics and Turbomachinery

Problems and Solutions

Bijay K Sultanian

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367514747
• eBook ISBN: 9781000413823
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

Reflecting the author's years of industry and teaching experience, Fluid Mechanics and Turbomachinery features many innovative problems and their systematically worked solutions. To understand fundamental concepts and various conservation laws of fluid mechanics is one thing, but applying them to solve practical problems is another challenge. The book covers various topics in fluid mechanics, turbomachinery flowpath design, and internal cooling and sealing flows around rotors and stators of gas turbines.

As an ideal source of numerous practice problems with detailed solutions, the book will be helpful to senior-undergraduate and graduate students, teaching faculty, and researchers engaged in many branches of fluid mechanics. It will also help practicing thermal and fluid design engineers maintain and reinforce their problem-solving skills, including primary validation of their physics-based design tools.

1 Fluid Flow Kinematics and Key Concepts

Review of Key Concepts

We concisely present here some key concepts of fluid flow kinematics. More details on each topic are given, for example, in Sultanian (2015).

Velocity Field

All vector fields do not represent a velocity field; they must also satisfy the local mass conservation equation (continuity equation)—the first law of fluid mechanics

$\frac{\partial \rho }{\partial t}+\frac{\partial (\rho {\text{V}}_x)}{\partial x}+\frac{\partial (\rho {\text{V}}_y)}{\partial y}+\frac{\partial (\rho {\text{V}}_z)}{\partial z}=0(1.1)$

which is valid for any unsteady laminar or turbulent flow. For a steady compressible flow, this equation reduces to

$\frac{\partial (\rho {\text{V}}_x)}{\partial \mathit{\text{x}}}+\frac{\partial (\rho {\text{V}}_y)}{\partial \mathit{\text{y}}}+\frac{\partial (\rho {\text{V}}_z)}{\partial \text{z}}=0(1.2)$

For an incompressible flow with constant density, be it steady or unsteady, Equation 1.1 reduces to

$\frac{\partial {\text{V}}_x}{\partial \mathit{\text{x}}}+\frac{\partial {\text{V}}_y}{\partial \mathit{\text{y}}}+\frac{\partial {\text{V}}_z}{\partial \mathit{\text{z}}}=0(1.3)$

Streamline and Stream Tube

In a fluid flow, a streamline is an instantaneous line to which the local velocity vectors are tangent everywhere—no flow crosses a streamline. While velocity magnitude may vary along a streamline, its direction always coincides with the local tangent to the streamline. A bundle of streamlines forms a stream tube—no flow crosses the surface of a stream tube. We w...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Dedication
• Table of Contents
• Preface
• Acknowledgments
• Author
• Chapter 1 Fluid Flow Kinematics and Key Concepts
• Chapter 2 Control Volume Analysis
• Chapter 3 Bernoulli Equation: Mechanical Energy Equation
• Chapter 4 Compressible Flow
• Chapter 5 Potential Flow
• Chapter 6 Navier-Stokes Equations: Exact Solutions
• Chapter 7 Boundary Layer Flow
• Chapter 8 Centrifugal Pumps and Fans
• Chapter 9 Centrifugal Compressors
• Chapter 10 Axial-Flow Pumps, Fans, and Compressors
• Chapter 11 Radial-Flow Gas Turbines
• Chapter 12 Axial-Flow Gas Turbines
• Chapter 13 Diffusers
• Chapter 14 Internal Flow around Rotors and Stators
• Appendix A: Euler’s Turbomachinery Equation and Rothalpy
• Appendix B: Dimensionless Velocity Diagrams for Axial-Flow Compressors and Turbines
• Index