Fluid Mechanics Chanter 3 Basis of Fluid Dynamics
1 Fluid Mechanics
流体力学
2
Chapter 3 Basis of Fluid Dynamics □§3-1 Preface 3-2 Methods to Describe Fluid Motion D83-3 Basic Concepts of Fluid Motion >83-4 Continuity Equation 83-5 Motion Differential Equation of Ideal Fluid 83-6 Bernoulli Equation and Its application D 83-7 System and Control Volume D$3-8 Momentum equation 83-9 Moment of Momentum Equation D Exercises of Chapter 3
3 Chapter 3 Basis of Fluid Dynamics §3–4 Continuity Equation §3–1 Preface §3–2 Methods to Describe Fluid Motion §3–3 Basic Concepts of Fluid Motion §3–5 Motion Differential Equation of Ideal Fluid §3–6 Bernoulli Equation and Its Application §3–7 System and Control Volume §3–8 Momentum Equation §3–9 Moment of Momentum Equation Exercises of Chapter 3
第三章流体动力学基础 §3-1引言 §3-2描述流体运动的方法 §3-3流体运动的基本概念 §3-4连续方程式 §3-5理想流体的运动微分方程 §3-6伯努利方程及其应用 §3-7系统与控制体 §3-8动量方程 §3-9动量矩方程 第三章习题
4 第三章 流体动力学基础 §3–4 连续方程式 §3–1 引言 §3–2 描述流体运动的方法 §3–3 流体运动的基本概念 §3–5 理想流体的运动微分方程 §3–6 伯努利方程及其应用 §3–7 系统与控制体 §3–8 动量方程 §3–9 动量矩方程 第三章 习 题
BasisofFhid Dynamic Chapter 3 Basis of Fluid Dynamics §3-1 Preface The backgrounds, fundamentals and fundamental equations of fluid dynamics all have certain relations with each part of engineering fluid mechanics, so this chapter is the emphases in the whole lessons
5 Chapter 3 Basis of Fluid Dynamics §3-1 Preface The backgrounds, fundamentals and fundamental equations of fluid dynamics all have certain relations with each part of engineering fluid mechanics, so this chapter is the emphases in the whole lessons
滤动之学基础 第三章流体动力学基础 §3-1引 流体动力学的基础知识,基本原理和基本方程与工程流 体力学的各部分均有一定的关联,因而本章是整个课程的重 点
6 第三章 流体动力学基础 §3-1 引言 流体动力学的基础知识，基本原理和基本方程与工程流 体力学的各部分均有一定的关联，因而本章是整个课程的重 点
BasisofFhid Dynamic s3-2 Methods to Describe the Fluid Motion Methods to describe the fluid motion 1. Lagrange's method Definition Lagrange's method is to consider the fluid particles as research objects and to research the motion course of each particle, and then gain the kinetic regulation of the whole fluid through synthesizing motion instances of all being researched objects. The essential of lagrangian method is a method of particle coordinates 7
7 §3-2 Methods to Describe the Fluid Motion Methods to describe the fluid motion ： 1. Lagrange’s method Definition： Lagrange’s method is to consider the fluid particles as research objects and to research the motion course of each particle , and then gain the kinetic regulation of the whole fluid through synthesizing motion instances of all being researched objects . The essential of lagrangian method is a method of particle coordinates
滤动之学基础 §3-2描述流体运动的方法 描述流体运动的方法: 、拉格朗日法 定义: 把流体质点作为研究对象,研究各质点的运动历程,然 后通过综合所有被研究流体质点的运动情况来获得整个流体 运动的规律,这种方法叫做拉格朗日法。实质是一种质点系 法
8 §3-2 描述流体运动的方法 描述流体运动的方法： 一、拉格朗日法 定义： 把流体质点作为研究对象，研究各质点的运动历程，然 后通过综合所有被研究流体质点的运动情况来获得整个流体 运动的规律，这种方法叫做拉格朗日法。实质是一种质点系 法
BasisofFhid Dynamic when we use lagrange's method to describe the fluid motion the position coordinates of motion particles are not independent variables but functions of original coordinate a, b, c and time variable t. that is x=xla, b,c y=ya, b, c, t) (31) z=2(a In this formula a b a, b, c and t are all called lagrangian variables Different particles have different original coordinates Difficulties will be met when using lagranges method to analyze fluid motion on math except for fewer instances(such as researching wave motion ). Eulers method is used mostly in fluid motion
9 when we use lagrange’s method to describe the fluid motion the position coordinates of motion particles are not independent variables but functions of original coordinate a, b, c and time variable t, that is ( ) ( ) z z(a b c t) y y a b c t x x a b c t , , , , , , , , , = = = （3—1） In this formula , a ,b ,c and t are all called lagrangian variables. Different particles have different original coordinates. Difficulties will be met when using lagrange’s method to analyze fluid motion on math except for fewer instances (such as researching wave motion). Euler’s method is used mostly in fluid motion
滤动之学基础 用拉格朗日法描述流体的运动时,运动质点的位置坐标 不是独立变量,而是起始坐标a、b、c和时间变量t的函数, x=x(a, b, c, i y=y(a, b, c, t) (3—1) 2三2a、b,C 式中a,b,c,t统称为拉格朗日变量,不同的运动质点, 起始坐标不同。 用拉格朗日法分析流体运动,在数学上将会遇到困难。 除少数情况外(如研究波浪运动),在流体运动中多采用欧拉 法 10
10 用拉格朗日法描述流体的运动时，运动质点的位置坐标 不是独立变量，而是起始坐标a、b、c和时间变量 t 的函数， 即 ( ) ( ) z z(a b c t) y y a b c t x x a b c t , , , , , , , , , = = = （3—1） 式中a，b，c，t 统称为拉格朗日变量，不同的运动质点， 起始坐标不同。 用拉格朗日法分析流体运动，在数学上将会遇到困难。 除少数情况外（如研究波浪运动），在流体运动中多采用欧拉 法