Chapter 3 The basic theory of fluid motion

§3.1 Description method of fluid motion

3.1.1 Two description methods of fluid motion

There are two ways to describe fluid motion.

1．Lagrangian approach

The Lagrangian description is based on the motion of fluid particles.It is the direct extension of single particle kinematics to a whole field of fluid particles that are labeled by their location at a reference time.

Since the traj ectory of fluid particles is very complex, the Lagrange approach rarely used in fluid mechanics.This book uses Eulerian approach.

2．Eulerian approach

In the Eulerian description, a flow field's characteristics are monitored at fixed locations or in stationary regions of space.

The Eulerian description focuses on flow field properties at locations or in regions of interest, and involves four independent variables:the three spatial coordinates represented by the position vector x, y, z, and time t.Such as u=u(x, y, z, t), or

3.1.2 Euler acceleration

1．Composition of Euler acceleration

In fluid motion, the acceleration can be divided into two parts.

(1)local acceleration.

(2)Convection acceleration.

2．Mathematical description

The flow rate is a complex function of time.Euler acceleration can be obtained from velocity with respect to time.

so

∇ is differential operator of Hamilton.

The component form: