Principles of Momentum transfer
1. Introduction
The flow and behavior of fluid is important in many of the unit operations in process engineering. A fluid may be defined as a substance that does not permanently resist distortion and, hence, will change its shape. In this text gases, liquids, and vapors are considered to have the characteristics of fluids and to obey many of the same laws.
2. Fluid Flow
The principles of the statics of fluids are almost an exact science. On the other hand, the principles of the motions of fluids are quite complex. The basic relations describing the motions of a fluid are the equations for the overall balances of mass, energy, and momentum, which will be covered in the following sections.
The study of momentum transfer, or fluids mechanics as it is often called, can be divided into tow branches: fluid statics, or fluid at rest, and fluid dynamics, or fluids in motion. In other sections we treat fluid statics; in the remaining sections, fluid dynamics. Since in fluid dynamics momentum is being transferred, the term “momentum transfer” or “transfer” is usually used.
In momentum transfer we treat the fluid as a continuous distribution of matter or as a “continuum”. This treatment as a continuum is valid when the smallest volume of fluid contains a large enough number of molecules so that a statistical average is meaningful and the macroscopic properties of the fluid such as density, pressure, and so on, vary smoothly or continuously from point to point.
Like all physical matter, a fluid is composed of an extremely large number of molecules per unit volume. A theory such as the kinetic theory of gases or statistical mechanics treats the motions of molecules in terms of statistical groups and not in terms of individual molecules. In engineering we are mainly concerned with the bulk or macroscopic behavior of a fluid rather than with the individual molecular or microscopic behavior. In the process industries, many of the materials are in fluid form and must be stored, handled, pumped, and processed, so it is necessary that we become familiar with the principles that govern the flow of fluids and also with the equipment used. Typical fluids encountered include water, air, CO2, oil, slurries, and thick syrups.If a fluid is inappreciably affected by change in pressure, it is said to be incompressible. Most liquids are incompressible. Gases are considered to be compressible fluids. However, if gases are subjected to small percentage changes in pressure and temperature, their density changes will be small and they can be considered to be incompressible. 3. Laminar and Turbulent Flow
The type of flow occurring in a fluid in a channel is important in fluid dynamics problems. When fluids move through a closed channel of any cross section, either of tow distinct types of flow can be observed according to the conditions present.
These two types of flow can be commonly seen in a flowing open stream or river. When the velocity of flow is slow, the flow patterns are smooth. However, when the velocity is quite high, an unstable pattern is observed in which eddies or small packets of fluid particles are present moving in all directions and at all angles to the normal line of flow.
The first type of flow at low velocities where the layers of fluid seem to slide by one another without eddies or swirls being present is called laminar flow and Newton’s law of viscosity holds. The second type of flow at higher velocities where eddies are present giving the fluid a fluctuating nature is called turbulent flow. The existence of laminar and turbulent flow is most easily visualized by the experiments of Reynolds. Water was allowed to flow at steady state through a transparent pipe with the flow rate controlled by a valve at the end of the pipe. A fine steady stream of dye-colored water was introduced from a fine jet as shown and its flow pattern observed. At low rates of water flow, the dye pattern was regular and formed a single line or stream similar to a thread. There was no lateral of the fluid, and it flowed in streamlines down the tube. By putting in additional jets at other points in the pipe cross section, it was shown that there was no mixing in any parts of the tube and the fluid flowed in straight parallel lines. This type of flow is called laminar or viscous flow.
As the velocity was increased, it was found that at a define velocity the thread of dye become dispersed and the pattern was very erratic. This type of flow is known as turbulent flow. The velocity at which the flow changes is known as the critical velocity.
4. Reynolds Number
Studies have shown that the transition from laminar to turbulent flow in tubes is not only a function of velocity but also of density and viscosity of the fluid and the tube diameter. These variables are combined into the Reynolds number, which is dimensionless. Re=
Dvρμ
Where Re is the Reynolds number, D the diameter in m, ρ the fluid density in kg/m3,u the fluid viscosity in Pa*s, and ν the average velocity of the fluid in m/s .(where average velocity is defined as the volumetric rate of flow divided by the cross sectional area of the pipe.)
The instability of the flow that leads to disturbed or turbulent flow is determined by the ratio of the kinetic or inertial forces to the viscous forces in the fluid stream.The inertial forces are proportional to ρνto μνD,and the ratio pv22 and the viscous forces
(yvD) is the Reynolds number Dvpy
For a straight circular pipe when the value of the Reynolds number is less than 2100, the flow is always laminar. When the value is over 4000, the flow will be turbulent, except in very special cases. In between, which is called the transition region, the flow can be viscous or turbulent, depending upon the apparatus details, which
cannot be predicted. 5. Simple Mass Balances In fluid dynamics fluids are in motion. Generally, they are moved from place to place by means of mechanical devices such as pumps or blowers, by gravity head, or by pressure, and flow through systems of piping and/or process equipment .The first step in the solution of flow problem is generally to apply the conservation of mass to the whole system or to any part of the system. We will consider an elementary balance on a simple geometry. Simple mass or material balances were followed. Input=output + accumulation since, in fluid flow, we are usually working with rates of flow and usually at steady state, the rate of accumulation is zero and we obtain rate of input = rate of output
When making overall balances on mass, energy, and momentum we are not interested in the details of what occurs inside the enclosure. For example, in an overall balance average inlet and outlet velocities are considered. However ,in a differential balance the velocity distribution inside an enclosure can be obtained with the use of Newton’s law of viscosity.
These overall or macroscopic balances will be applied to a finite enclosure or control volume fixed in space. We use the term “overall” because we wish to describe these balances from outside the enclosure. The changes inside the enclosure are determined in terms of the properties of the streams entering and leaving and the exchanges of energy between the enclosure and its surroundings.
阅读材料 12
动量交换定理
1. 介绍
在许多工程的单元操作中流体的流量和状态是很重要的。流体可能定义为一种永久不会抵抗变形的物质 ,并会改变它的形状。在本文中 ,气体、液体和水蒸气被认为具有流体的特征并且遵守很多相同的规律。
在这个工业过程中，很多材料是液体形式并且被储存、搬运、抽取和加工，因此熟悉液体流动原理和设备运用对我们非常有必要。接触到的典型的流体包括水、空气、二氧化碳、油、泥浆和浓糖浆。如果一种流体不受压强改变的影响，这就说明它是不可压缩的。大部分的流体是不可压缩的，气体被认为是可压缩的。但是如果气体在压强和温度的小变化情况下，密度也只有很小的变化，则这些气体就被认为是不可压缩的。 和所有物理物质一样，单位体积的流体是由极其大量的分子构成。一种如气体运动学理论或统计力学把分子运动当做群组统计学而不是单个分子。在工程上，我们主要关注大量的或是宏观行为的流体，而不是单个分子或微观行为。
在动量交换中，我们把流体看做是一个连续分布的物质或者是一个“统一体”。这种看待是正当的当最小体积的流体包含足够大数目的分子，这时，平均统计学就会是有意义的，流体的宏观性质如密度、压强等从一点到一点的变化会是平滑和连续的。
研究动量交换或者是流体力学，正如所说的，它被分为两个分支：静态流体和动态流体或运动流体。在其他章节我们探讨静态流体；在剩下的章节探讨动态流体。因为在动态流体动量是改变的，“动量交换”或“转移”通常被运用。
2. 流体流动
流体静力学原理几乎是一门精确学科。另一方面，流体动力学原理是相当复杂的。流体运动的基本关系的描述是质量、能量和动力的整体平衡方程，这些会将在接下来的章节讲到。 这些整体或宏观平衡将适用于有限的封闭体或控制体积在一定的空间里。我们使用术语“整体”是因为我们希望描述这些封闭体以外的平衡。封闭体内的改变是由流进和流出体的性质与其封闭体和周围环境能量的改变决定的。
当整体质量守恒、能量守恒和动量守恒时，我们对封闭体内的详细情况不感兴趣。例如，在总体机箱平衡的平均进口和出口速度是要考虑的。然而，在微分平衡中，围封部分速度的分布可以通过牛顿的粘性定理来获得。 3. 层流和湍流
流体在管道中的流动类型在流体力学中很重要。当流体流过一个封闭通道的任何截面时，根据现给的条件，流动的任何一种类型都可以被观察得到。这两种流动通常可以在小溪或河里看得到。当流速低时，流动时很平稳的。但是，当流速很高时，流动的不平稳将被观察到，这些是漩涡或小块的流动微粒正往各方向和角度运动到正常的流道。 第一种类型是流动速度低时，流体的底层呈现的没有漩涡或盘旋的滑动就叫做层流，牛顿的粘性定理坚持这种观点。第二种类型是在流动速度很高时，漩涡的出现给流体一个波动的性质，这种就叫湍流。
平稳流动的带有颜色的水是从一个好的喷头引进的，它的流动模式可以被观察得到。 通过雷诺实验，层流和湍流的存在是最容易被直观化的，水在一个透明的管道中以很低的速度平稳地流动，水的速度是由管端点的阀门控制如图所示。在低速流动时，颜色的模式是整齐的并形成一条线或者是流动像一线状物。没有横向的流体，以流线型流过管道。通过在其他点增加额外的射流流过截面，管道中的任一部分都没有混合，流体仍然直线平行流动。这类流动就被称为层流或滞流。 随着速度的增加，我们发现在一个规定的速度里，染料的现状流动将变成分散的与其流动模式是非常不稳定的。这类型就是湍流。引起流动变化的那个速度称为临界速度。 4. 雷诺数
研究表明，在管道中从层流到湍流的过渡，不仅仅是速度的作用，而且是密度、流体粘度和管径的关系。这些变数合并成无量纲的雷诺数。
Re：雷诺准数 D：直径 m ρ：密度
kgm3 μ：流体黏度 Pas
Υ为流体的平均流动速度，单位：ms (其中平均速度由管横截面积分配的体积流量决定)。 流体的不稳定导致混乱或者说在液流中湍流由活跃度的比例或惯性力与粘性力的比决定的。 惯性力是和 ρν雷诺数Dvpy。
对于一个圆形管道，当雷诺值小于2100，则流动是层状的。当雷诺数大于4000，那就是湍流除了在特殊的情况。在两者之间，就叫做过渡区，流动将是层流或是湍流，这要根据仪器细节，没有办法预知的。 5. 简单的质量平衡
在流体动力学中流体是运动的。一般来说，它们是通过机械设备从一个地方移动到另一个地
2成比例的， 粘性力与 μνD成比例 ,与其pv2(yvD)就是
方，如水泵或风机，重力头，或通过压力，从而流过系统的管道和/或加工设备。第一步解决的流动问题是对整个系统或系统的任一部分应用质量守恒。我们用一个简单的几何学考虑一个基本的平衡问题。简单的质量或物料平衡如下：
输入=输出+积累
所以，在流体流动中，我们通常计算稳定状态下的流动比率，积累率是零，于是我们得到
输入率=输出率
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