Physical Fluid Dynamics by D. J. Tritton What is Fluid Dynamics? Fluid dynamics is the study of the aforementioned phenomenon. The purpose of this study is to predict what will happen in a given arrangement and to understand why. The tools used for theoretical analyses consist of physics and mathematics. The basic physical laws governing the behavior of fluids in motion are the usual well-known laws of mechanics – conservation of mass and Newton’s laws of motion and the laws of thermodynamics. These laws are used to build and connect theoretical and conceptual structure and experimental or field observations.

The Scientific Method Hypothesis Model Prediction Verification of prediction Forecast Get better data or change method Predictions satisfactory Predictions unsatisfactory Ex.1Ex.2 (1)Natural phenomena are controlled by simple relationships. (2)These relationships can be discovered by careful observations or measurements. Observations are analyzed and then organized into statements. revolution

Our class is primarily concerned with ‘pure’ fluid dynamics rather than with applications. This is a basic difference between “Engineering Fluid Dynamics” and “Physical Fluid Dynamics”. Scope of this class: 1.The laws of classical mechanics apply throughout. Quantum mechanics is excluded. 2.The length scale of the flow is always taken to be large compared with the molecular mean-free-path, so that the fluid can be treated as a continuum. 3.Only incompressible flow is considered. That is flow in which the pressure variations do not produce any significant density variations. In isothermal flows this means that the density is a constant; in other flows that it is a function of the temperature alone. Two approximations for that the fluids can be treated as incompressible flow: (1) The fluid has a small compressibility that, even if large pressure variations are present, they produce only slight density variations (liquid flows); (2) the pressure variations are sufficiently small that, even if the compressibility is not so small, the density variations are small (gas flows – the flow speed is everywhere low compared with the speed of sound).

4.Only Newtonian fluids are considered. This is a statement about the physical properties that affect the stresses developed within a fluid as a result of its motion and thus enter the dynamics of a flow. Behaviors of all gases and liquids with small molecules interacting in a simple way are close to Newtonian. Non-Newtonian fluids? 5. Free surfaces are not considered. This means that surface waves are outside the scope of our class. 6. Electromagnetic effects are not considered. x y A B u Velocity profile force/unit area  =  du/dy  is a constant coefficient of viscosity

Notation and definitions x y z u v w Velocity in Cartesian coordinate u=ui+vj+wk Pressure: p (force/unitt area) Temperature: T Fluid density:  (mass/unit volume) Viscosity:  Kinematic viscosity: (  /  ) We typically use MKS system for the unit. That is length: meter mass: kilogram time: second

Definition of two terms: (1) Steady flow t = 0 (2) Two-dimensional flow z = 0 w = 0,

1. Introduction 2. Pipe and channel flow 3. Flow past a circular cylinder 4. Free convection between parallel walls 5. Equation of motion 6. Further basic ideas 7. Dynamical similarity 8. Inviscid flow 9. Boundary layers, wakes, and jets 10. Stratified flow 11. Flow in rotating fluids 12. Experimental methods 13. Numerical modeling Content