Book contents
- Frontmatter
- Contents
- PREFACE
- 1 INTRODUCTION
- 2 STRESS IN A FLUID
- 3 FLUID STATICS
- 4 FLUIDS IN MOTION – INTEGRAL ANALYSIS
- 5 FLUIDS IN MOTION – DIFFERENTIAL ANALYSIS
- 6 EXACT SOLUTIONS OF THE NAVIER–STOKES EQUATIONS
- 7 ENERGY EQUATIONS
- 8 SIMILITUDE AND ORDER OF MAGNITUDE
- 9 FLOWS WITH NEGLIGIBLE ACCELERATION
- 10 HIGH REYNOLDS NUMBER FLOWS – REGIONS FAR FROM SOLID BOUNDARIES
- 11 HIGH REYNOLDS NUMBER FLOWS – THE BOUNDARY LAYER
- 12 TURBULENT FLOW
- 13 COMPRESSIBLE FLOW
- 14 NON-NEWTONIAN FLUIDS
- APPENDIXES
- INDEX
2 - STRESS IN A FLUID
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- PREFACE
- 1 INTRODUCTION
- 2 STRESS IN A FLUID
- 3 FLUID STATICS
- 4 FLUIDS IN MOTION – INTEGRAL ANALYSIS
- 5 FLUIDS IN MOTION – DIFFERENTIAL ANALYSIS
- 6 EXACT SOLUTIONS OF THE NAVIER–STOKES EQUATIONS
- 7 ENERGY EQUATIONS
- 8 SIMILITUDE AND ORDER OF MAGNITUDE
- 9 FLOWS WITH NEGLIGIBLE ACCELERATION
- 10 HIGH REYNOLDS NUMBER FLOWS – REGIONS FAR FROM SOLID BOUNDARIES
- 11 HIGH REYNOLDS NUMBER FLOWS – THE BOUNDARY LAYER
- 12 TURBULENT FLOW
- 13 COMPRESSIBLE FLOW
- 14 NON-NEWTONIAN FLUIDS
- APPENDIXES
- INDEX
Summary
In this chapter we consider stresses in a fluid. We start by setting the forces resulting from these stresses in their proper perspective, i.e., in relation to body forces, together with which they raise accelerations. This results in a set of momentum equations, which are needed later.
We then consider the relations between the various stress components and proceed to inspect stress in fluids at rest and in moving fluids.
The Momentum Equations
In this section we establish relations between body forces, stresses and their corresponding surface forces and accelerations. Newton's second law of motion is used, and the results are the general momentum equations for fluid flow.
Consider a system consisting of a small cube of fluid, as shown in Fig. 2.1. A system is defined in classical thermodynamics as a given amount of matter with well-defined boundaries. The system always contains the same matter and none may flow through its boundaries.
As a rule a fluid system does not retain its shape, unless, of course, the fluid is at rest. This does not prevent the choice of a system with a certain particular shape, e.g., a cube. The choice means that imaginary surfaces are defined inside the fluid such that at the considered moment they enclose a system of fluid with a given shape. A moment later the system may have a different shape, because the shape is not a property of the fluid or of the location.
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- Information
- Fluid Mechanics , pp. 19 - 52Publisher: Cambridge University PressPrint publication year: 1992