FLUID MECHANICS

FLUID MECHANICS

流体力学

Jin Xiaohong

金晓宏 Rong Zhijun 容芷君 Fu Liandong 付连东

FLUID POWER TRANSMISSION & CONTROL INSTITUTE

流体传动及控制研究所

MECHATRONIC CONTROL ENGINEERING DEPARTMENT

机械电子工程系

WUHAN UNIVERSITY OF SCIENCE AND TECHNOLOGY

武汉科技大学 2003.09

CONTENTS目录

1. Fluid Properties 流体性质

1.1 Definition of a fluid 流体定义

1.2 Force, Mass, Length, and Time Units 力、质量、长度和时间单位

1.3 Viscosity（流体的）粘性

1.4 Continuum（流体的）连续介质（假设）

1.5 Density, Specific Volume, Specific Weight, Specific Gravity, Pressure

密度、比容、重度、比重、压强 1.6 *Perfect Gas 理想气体

1.7 Bulk modulus of elasticity 体积弹性模量 1.8 Vapor pressure 蒸气压 2. Fluid Statics 流体静力学 2.1 Pressure at a point 点压力

2.2 Basic equation of fluid statics 静压基本方程

2.3 Units and scales of pressure measurement 压力单位和度量 2.4 Manometers 测压计

2.5 Forces on plane areas 平面上的作用力 2.6 *Relative Equilibrium 相对平衡

3. Fluid-Flow Concepts, Basic Equations 流动概念和基本方程 3.1 Flow characteristics 流动特征

3.2 The Concepts of System and Control Volume（流体的）系统与控制体概念

3.3 Application of the Control Volume To Continuity, Energy, and Momentum

控制体（概念）应用于（流体的）连续性（假设）、能量、

动量

3.4 Continuity Equation（流体运动的）连续性方程

3.5 *Euler’s Equation of Motion along a Streamline 沿流线运动的

欧拉方程

3.6 The Bernoulli Equation 伯努力方程

3.7 Reversibility, Irreversibility, and Losses 可逆性、不可逆性与（流动）损失

3.8 *The Steady-State Energy Equation 稳态流动能量方程

3.9 *Interrelations Between Euler’s Equation and the Thermodynamic Relations

欧拉方程与热力学之间的相互联系

3.10 Application of the Energy Equation to Steady Fluid- Flow Situations

能量方程在稳态流动情况下的应用

3.11 Applications of the Linear-Momentum Equation 动量方程的应用

4. Fluid Resistance 流体阻力

4.1 The Reynolds Number 雷诺数

4.2 Laminar（层流）, Incompressible（不可压缩）, Steady Flow between Parallel Plates

两平行板间定常流动

4.3 Laminar Flow through Circular Tubes and Circular Annuli 圆管和环形管中的层流

4.4 *Prandtl Mixing Length; Velocity Distribution in Turbulent Flow

普郎多混合长度模型；湍流的速度分布 4.5 *Boundary-Layer Concepts 边界层的概念

4.6 Resistance to Turbulent Flow in Open and Closed Conduits 开管和闭管中的湍流阻力

4.7 Steady Incompressible Flow through Simple Pipe Systems 单管不可压缩定常流动

5. Applications of Fluid Mechanics 流体力学应用 5.1 Orifices 孔口流动 5.2 Cavitation 气穴现象

5.3 Waterhammer 水击（水锤）

1. FLUID PROPERTIES

流体的性质

The engineering science of fluid mechanics has been developed through an understanding

of fluid properties, the application of the basic laws of mechanics and thermodynamics, and orderly experiment.随着对流体性质的了解，力学与热学基本定律的应用以及一系列逐步深入的实验研究，流体力学这门工程科学得到了长足的发展。

In this chapter a fluid is defined and consistent systems of force, mass, length, and time

units are discussed before the discussion of properties and definition of terms is taken up.本章在讨论流体的性质以及一些列定义前，将先对流体的定义，力、质量、长度和时间一致的单位制进行讨论。

1.1 DEFINITION OF A FLUID 流体的定义

A fluid is a substance that deforms continuously when subjected to a shear stress, no matter how small that shear stress may be. 在任何微小剪切力的持续作用下能够不断变形的物质称为流体。A shear force is the force component tangent to a surface, and this force divided by the area of the surface is the average shear stress over the area. 剪切力是相切于（受力）

Figure 1.1 Deformation resulting from application of constant shear force.

图1.1 恒定剪切力作用时的角变形

表面方向上的分力，并且这个力被（受力）表面面积相除后就是这个表

面的平均切应力。Shear stress at a point is the limiting value of shear force to area as the area is reduced to the point.一点处的切应力就是当平均切应力在这一点上取得极限值，就是当剪切力和面积值同时减小至一点时（的情况）。

In Fig.1.1 a substance is plated between two closely spaced parallel plates so large that conditions at their edges may be neglected.在图1.1中，一种物质被置于两巨大平行平面上，（此两平面）面积足够大以至于它们的边界条件可以忽略。The lower plate is fixed, and a force F is applied to the upper plate, which exerts a shear stress F/A on any substance between the plates. 下平板固定，并有一力F作用于上平板，这一力的施加，发挥出切应力F/A 作用于任何在两平板之间的任何物质。A is the area of the upper plate. A是上平板的面积。When the force F causes the upper plate to move with a steady(nonzero) velocity, no matter how small the magnitude of

F, one may conclude that the substance between the two plates is a fluid.无论这个力F多小，当力F的作用导致上平板以一恒定速度（非零）运动时，我们就可以断定在这两板之间的物质是流体。

The fluid in immediate contact with a solid boundary has the same velocity as the boundary; i.e., there is no slip at the boundary.直接接触固体边界的流体与边界有着相同的速度，也就是流体和边界间没有滑动。This is an experimental fact which has been verified in countless tests with various kinds of fluids and boundary materials.这一实验事实已被用多种不同的流体与边界物质的无数实验所验证。The fluid in the area abcd flows to the new position ab'c'd, each fluid particle moving parallel to the plate and the velocity u varying uniformly from zero at the stationary plate to U at the upper plate.在abcd区域的流体流动到新的位置ab'c'd，每一流体质点平行与平板移动，并且其速度u一律由零（在固定板）到U（上板）的变化着。Experiments show that, other quantities being held constant, F is directly proportional to A and to U and is inversely proportional to thickness t. 实验表明，其它物理量保持不变时，力F正比于A和U，反比于厚度t。In equation form 在方程中

In which u is the proportionality factor and includes the effect of the particular fluid. u 这一比例因子的值由具体的流体所决定。If the shear stress,

The ratio U/t is the angular velocity of line ab, or it is the rate of angular deformation of the fluid, i.e., the rate of decrease of angle bad.

for

是切应力，U/t 这一比值是线ab的角速度，或者说是流体的

角变形速率，就是角bad的减小率。The angular velocity may also be

written du/dy, as both U/t and du/dy express the velocity change divided by the distance over which the change occurs.这一角速度也可以写成du/dy，由于U/t和du/dy都表示在这一现象发生时的速度该变量除以距离。However, du/dy is more general, as it holds for situations in which the angular velocity and shear stress change with y. 然而，du/dy的表示更为普遍，它表示角速度和切应力随y的改变情况。The velocity

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