Fundamentals of Fluid Dynamics - Computational Fluid and Particle Dynamics in the Human Respiratory System - page 99

Chapter 5
Fundamentals of Fluid Dynamics

5.1 Introduction

Ultimately, the goal of Computational Fluid Dynamics (CFD) is to provide a nu-
merical description of fluid flow behaviour. This is achieved through solving the
governing equations that are mathematical statements of the physical conservation
laws :

• conservation of mass;

• balance of momentum (Newton's second law, the rate of change of momentum

equals the sum of forces acting on the fluid) and;

• conservation of energy (first law of thermodynamics, the rate of change of energy

equals the sum of rate of heat addition to, and the rate of work done on, the
fluid).

The governing equations represent not only the transport of mass, momentum, and
energy but also the interaction of phenomena such as diffusion, convection, boundary
layers, and turbulence. This chapter presents the derivation of the governing equations
for a single fluid phase, and provides an understanding of the basic processes of fluid
flow and the significance of different terms in the governing equations. Furthermore,
a CFD user must understand the physical behaviour of fluid motion, as it is these
phenomena that CFD analyses and predicts.

5.2 Fluid Dynamics and Governing Equations

5.2.1 Mass Conservation

The conservation of mass is the basic principle which states that matter may neither
be created nor destroyed. This means that a fluid in motion moves through a region
of space in a way that the mass is conserved. In steady flow, the rate of mass enter-
ing the control volume equals the net rate at which mass exits the control volume