Mechanics of fluid Chanter Fundament oi viscosity liquid dynamics
1 Mechanics of Fluid
流体力学
2
Chapter 7 Fundament of viscosity liquid dynamics 」§7-1 Introduction > 87-2 Dynamic differential equation of viscosity liquid-Navier-Stokes equation D 87-3 Axial flowing between two concentric cylinder 」§7-4 Flow between two parallel plates 87-5 Flow around a sphere Flow with minor Reynolds number D87-6 Fundamental equation of turbulent flow--Reynolds equation Chapter 7 exercises
3 Chapter 7 Fundament of viscosity liquid dynamics §7–1 Introduction §7–2 Dynamic differential equation of viscosity liquid-Navier-Stokes equation §7–3 Axial flowing between two concentric cylinder §7–4 Flow between two parallel plates §7–5 Flow around a sphere Flow with minor Reynolds number §7–6 Fundamental equation of turbulent flow—Reynolds equation Chapter 7 exercises
第七章粘性流体动力学基础 □§7-1引言 §7-2粘性流体的运动微分方程 纳维一斯托克斯方程 §7-3两同心圆柱间的轴向流动 两平行平板间的流动 §75绕圆球的小雷诺数流动 §7-6紊流的基本方程雷诺方程 第七章习题
4 第七章 粘性流体动力学基础 §7–1 引言 §7–2 粘性流体的运动微分方程 ——纳维—斯托克斯方程 §7–3 两同心圆柱间的轴向流动 §7–4 两平行平板间的流动 §7–5 绕圆球的小雷诺数流动 §7–6 紊流的基本方程—雷诺方程 第七章 习题
Chapter 7 Fundament of viscosity liquid dynamics §7-1 Introduction Real liquid in nature takes on viscosity, so study dynamics of viscosity liquid is important to project
5 Chapter 7 Fundament of viscosity liquid dynamics §7-1 Introduction Real liquid in nature takes on viscosity,so study dynamics of viscosity liquid is important to project
粘滤动力学基础 第七章粘性流体动力学基础 §7-1引言 自然界中的真实流体都是具有粘性的,因此研究粘性流 体的动力学问题,对于工程实际有着重要的意义
6 第七章 粘性流体动力学基础 §7-1 引言 自然界中的真实流体都是具有粘性的，因此研究粘性流 体的动力学问题，对于工程实际有着重要的意义
87-2 Dynamic differential equation of viscosity liquid -Navier-Stokes equation 一、 stress in viscosity fluid In balanced or dynamic ideal fluid, surface force act on fluid micro-group only is compressive stress(pressure)that normal to surface, and compressive stress takes on a little isotropy. But in dynamic viscosity fluid, because of influence of viscosity, surface force act on fluid micelle is not only compressive stress p but also shear stress T And compressive stress at one point does not take on isotropy any longer. Shown as figure (7-1), because surface force have three component in each infinitesimal,so one point in real fluid, such as stress of point A in figure can be expressed with stress matrix composed of nine elements 7
7 §7-2 Dynamic differential equation of viscosity liquid ——Navier—Stokes equation In balanced or dynamic ideal fluid ,surface force act on fluid micro-group only is compressive stress(pressure) that normal to surface,and compressive stress takes on a little isotropy.But in dynamic viscosity fluid , because of influence of viscosity,surface force act on fluid micelle is not only compressive stress but also shear stress . And compressive stress at one point does not take on isotropy any longer.Shown as figure（7—1）,because surface force have three component in each infinitesimal,so one point in real fluid , such as stress of point A in figure can be expressed with stress matrix composed of nine elements. Pn 一、stress in viscosity fluid
粘滤动力学基础 §7-2粘性流体的运动微分方程 纳维一斯托克斯方程 一、粘性流体中的应力 在平衡流体或运动的理想流体中,作用在流体微团上的表面力 只有与表面相垂直的压应力(压强),而且压应力又具有一点上各 向同性的性质。但在运动的粘性流体中,由于粘性的影响,作用在 流体微团上的表面力不仅有压应力Pn还有切应力T。而且一点上 的压应力也不在具有各向同性的性质了。如图(7—1)所示,因为 每个微元表面上的表面力都有三个分量,故而实际流体中一点, 例 如图中A点上的应力可用九个元素组成的一个应力矩阵
8 §7-2 粘性流体的运动微分方程 ——纳维—斯托克斯方程 在平衡流体或运动的理想流体中，作用在流体微团上的表面力 只有与表面相垂直的压应力（压强），而且压应力又具有一点上各 向同性的性质。但在运动的粘性流体中，由于粘性的影响，作用在 流体微团上的表面力不仅有压应力 还有切应力 。而且一点上 的压应力 也不在具有各向同性的性质了。如图（7—1）所示，因为 每个微元表面上的表面力都有三个分量，故而实际流体中一点，例 如图中A点上的应力可用九个元素组成的一个应力矩阵 Pn 一、粘性流体中的应力
v r2 UPw T (7—1) 2. 2y P2 Called two rank symmetrical stress tensor Sum of normal stress of its diagonal is invariable of stress tensor definition: Slat. that third of stress tensor invariable is average isotropy pressure p
9 zx zy zz yx yy yz xx xy xz p p p （7—1） Called two rank symmetrical stress tensor.Sum of normal stress of its diagonal is invariable of stress tensor. definition： Slat. that third of stress tensor invariable is average isotropy pressure p
粘滤动力学基础 v r2 UPw T (7—1) 2. 2y 来代表。称之为二阶对称应力 张量。其对角线上法向应力之和为应力张量不变量。 定义 应力张量不变量的三分之一统计平均各向各向同性压强p。 10
10 zx zy zz yx yy yz xx xy xz p p p （7—1） 来代表。称之为二阶对称应力 张量。其对角线上法向应力之和为应力张量不变量。 定义： 应力张量不变量的三分之一统计平均各向各向同性压强p