物理代写|流体力学代写Fluid Mechanics代考|Momentum and Angular Momentum

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流体力学是物理学的一个分支,涉及流体(液体、气体和等离子体)的力学和对它们的力。它的应用范围很广,包括机械、土木工程、化学和生物医学工程、地球物理学、海洋学、气象学、天体物理学和生物学。

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  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
物理代写|流体力学代写Fluid Mechanics代考|Momentum and Angular Momentum

物理代写|流体力学代写Fluid Mechanics代考|Accelerating Frame

The balance of momentum and angular momentum that we have discussed so far are only valid in inertial reference frames. An inertial reference frame in classical mechanics could be a Cartesian coordinate system whose axes are fixed in space (relative, for example, to the fixed stars), and which uses the average solar day as a unit of time, the basis of all our chronology. All reference frames which move uniformly, i.e.., not acceelerrating in this systêm, arre equivallênt añd thus aree inertiāl frames.

The above balances do not hold in frames which are accelerating relative to an inertial frame. But the forces of inertia which arise from nonuniform motion of the frame are often so small that reference frames can by regarded as being approximately inertial frames. On the other hand, we often have to use reference frames where such forces of inertia cannot be neglected.

To illustrate this we will look at a horizontal table which is rotating with angular velocity $\Omega$. On the table and rotating with it is an observer, who is holding a string at the end of which is a stone, lying a distance $R$ from the fulcrum of the table. The observer experiences a force (the centrifugal force) in the string. Since the stone is at rest in his frame, and therefore the acceleration in his reference frame is zero, the rate of change of momentum must also be zero, and thus, by the balance of momentum (2.9), the force in the string should vanish. The observer then correctly concludes that the balance of momentum does not hoold in his reference frame. The rotating table must be treated as an noninertial reference frame. The source of the force in the string is obvious to an observer who is standing beside the rotating table. He sees that the stone is moving on a circular path and so it experiences an acceleration toward the center of the circle, and that according to the balance of momentum, there must be an external force acting on the stone. The acceleration is the centripetal acceleration, which is given here by $\Omega^{2} \mathrm{R}$. The force acting inwards is the centripetal force which is exactly the same size as the centrifugal force experienced by the rotating observer.

In this example the reference frame of the observer at rest, that is the earth, can be taken as an inertial reference frame. Yet in other cases deviations from what is expected from the balance of momentum appear. This is because the earth is rotating and therefore the balance of momentum strictly does not hold in a reference frame moving with the earth. With respect to a frame fixed relative to the earth we observe, for example, the deflection of a free falling body to the east, or the way that the plane of oscillation of Foucault’s pendulum rotates. These examples, and many others, are not compatible with the validity of the balance of momentum in the reference frame chosen to be the earth. For most terrestrial events, however, a coordinate system whose origin is at the center of the earth, and whose axes are directed towards the fixed stars, is valid as an inertial reference frame. The easterly deflection mentioned above can then be explained by the fact that the body, in its initial position, has a somewhat higher circumferential speed because of the rotation of the earth than at the impact point nearer the center of the earth. To explain Foucault’s pendulum, we notice that, in agreement with (2.9), the pendulum maintains its plane of oscillation relative to the inertial frame. The reference frame attached to the earth rotates about this plane, and an observer in the laboratory experiences a rotation of the plane of oscillation relative to his system with a period of twenty-four hours.

物理代写|流体力学代写Fluid Mechanics代考|Applications to Turbomachines

Typical applications of the balances of momentum and of angular momentum can be found in the theory of turbomachines. The essential element present in all turbomachines is a rotor equipped with blades surrounding it, either in the axial or radial direction.

When the fluid exerts a force on the moving blades, the fluid does work. In this case we can also speak of turbo force machines (turbines, wind wheels, etc.). If the moving blades exert a force on the fluid, and thus do work on it, increasing its energy, we speak of turbo work machines (fans, compressors, pumps, propellers).
Often the rotor has an outer casing, called stator, which itself is lined with blades. Since these blades are fixed, no work is done on them. Their task is to direct the flow either towards or away from the moving blades attached to the rotor. These blades are called guide blades or guide vanes. A row of fixed blades together with a row of moving blades is called a stage. A turbomachine can be constructed with one or more of these stages. If the cylindrical surface of Fig. $2.6$ at radius $r$ through the stage is cut and straightened, the contours of the blade sections originally on the cylindrical surface form two straight cascades. The set up shown consists of a

turbine stage where the fixed cascade is placed before the moving cascade seen in the direction of the flow.

Obviously the cascades are used to turn the flow. If the turning is such that the magnitude of the velocity is not changed, the cascade is a pure turning or constant pressure cascade, since then no change of pressure occurs through the cascade (only in the case of frictionless flow). In general the magnitude of the velocity changes with the turning and therefore also the pressure. If the magnitude of the velocity is increased we have an acceleration cascade, typically found in turbines, and if it is decreased we have a deceleration cascade, typically found in compressors. We shall consider the cascade to be a strictly periodic ordering of blades, that is, an infinitely long row of blades with exactly the same spacing $s$ between blades along the cascade. Because of this the flow is also strictly periodic.

物理代写|流体力学代写Fluid Mechanics代考|Balance of Energy

The fact that mechanical energy can be changed into heat and heat can be changed into mechanical energy shows that the balance laws of mechanics we have discussed up to now are not enough for a complete description of the motion of a fluid. As well as the two laws we have already treated, therefore a third basic empirical law, the balance of energy, appears:
The rate of change of the total energy of a body is equal to the power of the external forces plus the rate at which heat is transferred to the body.
This law can be “deduced” from the well known first law of thermodynamics together with a mechanical energy equation which follows from Cauchy’s Eq. (2.38a, 2.38b). However here we prefer to postulate the balance of the total energy, and to infer from it the more restrictive statement of the first law of thermodynamics.

We shall assume the fundamentals of classical thermodynamics as known. Thermodynamics is concerned with processes where the material is at rest and where all quantities appearing are independent of position (homogeneous), and therefore are only dependent on time. An important step to the thermodynamics of irreversible processes as they appear in the motion of fluids, consists of simply applying the classical laws to a material particle. If $e$ is the internal energy per unit

mass, then the internal energy of a material particle is given by $e \mathrm{~d} m$, and we can calculate the internal energy $E$ of a body, that is, the energy of a bounded part of the fluid, as the integral over the region occupied by the body
$$
E=\iiint_{(V(t))} e \varrho \mathrm{d} V
$$
In order to obtain the total energy of the fluid body under consideration, the kinetic energy which does not appear in the classical theory must be added to (2.109). The kinetic energy of the material particle is $\left(u^{2} / 2\right) \mathrm{d} m$, and the kinetic energy $K$ of the body is correspondingly
$$
K=\iiint_{(V(t))} \frac{u_{i} u_{i}}{2} \varrho \mathrm{d} V
$$
The applied forces which appear are the surface and body forces which were discussed in the context of the balance of momentum. The power of the surface force $\vec{t} \mathrm{~d} S$ is $\vec{u} \cdot \vec{t} \mathrm{~d} S$, while that of the body force $\varrho \vec{k} \mathrm{~d} V$ is $\vec{u} \cdot \vec{k} \varrho \mathrm{d} V$. The power of the applied forces is then
$$
P=\iiint_{(V(t))} \varrho u_{i} k_{i} \mathrm{~d} V+\iint_{(S(t))} u_{i} t_{i} \mathrm{~d} S
$$
In analogy to the volume flow $\vec{u} \cdot \vec{n} \mathrm{~d} S$ through an element of the surfacee, we introduce the heat flux through an element of the surface with $-\vec{q} \cdot \vec{n} \mathrm{~d} S$ and denote $\vec{q}$ as the heat flux vector. The minus sign is chosen so that inflowing energy ( $\vec{q}$ and $\vec{n}$ forming an obtuse angle) is counted as positive. From now we shall limit ourselves to the transfer of heat by conduction, although $\vec{q}$ can also contain other kinds of heat transfer, for example, heat transfer by radiation, via Poynting’s vector.

物理代写|流体力学代写Fluid Mechanics代考|Momentum and Angular Momentum

流体力学代写

物理代写|流体力学代写Fluid Mechanics代考|Accelerating Frame

到目前为止我们讨论的动量和角动量的平衡仅在惯性参考系中有效。经典力学中的惯性参考系可以是笛卡尔坐标系,其轴在空间中是固定的(例如,相对于固定恒星),并且使用平均太阳日作为时间单位,这是我们所有年表的基础. 所有匀速运动的参考系,即在这个系统中不加速的,都是等价的,因此是惯性系。

上述平衡不适用于相对于惯性坐标系加速的坐标系。但是由坐标系的非均匀运动产生的惯性力通常很小,以至于参考坐标系可以被认为是近似惯性坐标系。另一方面,我们经常不得不使用不能忽略这种惯性力的参考系。

为了说明这一点,我们将看一个以角速度旋转的水平桌子Ω. 桌子上和它一起旋转的是一个观察者,他拿着一根绳子,绳子的末端是一块石头,躺在远处R从桌子的支点。观察者在弦中感受到一个力(离心力)。由于石头在他的坐标系中静止,因此他的参考坐标系中的加速度为零,动量变化率也必须为零,因此,根据动量平衡(2.9),弦中的力应该消失。然后观察者正确地得出结论,动量平衡在他的参考系中不成立。必须将旋转台视为非惯性参考系。对于站在旋转台旁边的观察者来说,绳子中的力的来源是显而易见的。他看到石头在圆周上运动,所以它向圆心加速,根据动量平衡,石头上一定有外力作用。Ω2R. 向内作用的力是向心力,其大小与旋转观察者所承受的离心力的大小完全相同。

在这个例子中,静止的观察者的参考系,即地球,可以作为惯性参考系。然而,在其他情况下,会出现与动量平衡预期的偏差。这是因为地球是自转的,因此动量平衡在与地球一起运动的参考系中严格不成立。对于相对于地球固定的框架,我们观察到,例如,自由落体向东的偏转,或者傅科摆的摆动平面的旋转方式。这些示例以及许多其他示例与选择为地球的参考系中动量平衡的有效性不兼容。然而,对于大多数地球事件来说,坐标系的原点位于地球中心,其轴指向固定的恒星,作为惯性参考系是有效的。上面提到的向东偏转可以通过以下事实来解释:由于地球的自转,物体在其初始位置的圆周速度比靠近地球中心的撞击点处的圆周速度稍高。为了解释傅科摆,我们注意到,与 (2.9) 一致,摆保持其相对于惯性系的振荡平面。附在地球上的参考系绕着这个平面旋转,实验室中的观察者经历了振荡平面相对于他的系统的旋转,周期为 24 小时。由于地球的自转,其圆周速度比靠近地球中心的撞击点要高一些。为了解释傅科摆,我们注意到,与 (2.9) 一致,摆保持其相对于惯性系的振荡平面。附在地球上的参考系绕着这个平面旋转,实验室中的观察者经历了振荡平面相对于他的系统的旋转,周期为 24 小时。由于地球的自转,其圆周速度比靠近地球中心的撞击点要高一些。为了解释傅科摆,我们注意到,与 (2.9) 一致,摆保持其相对于惯性系的振荡平面。附在地球上的参考系绕着这个平面旋转,实验室中的观察者经历了振荡平面相对于他的系统的旋转,周期为 24 小时。

物理代写|流体力学代写Fluid Mechanics代考|Applications to Turbomachines

动量平衡和角动量平衡的典型应用可以在涡轮机理论中找到。存在于所有涡轮机中的基本元件是配备有沿轴向或径向围绕它的叶片的转子。

当流体对动叶片施加作用力时,流体会做功。在这种情况下,我们也可以说涡轮机(涡轮机、风轮等)。如果动叶片对流体施加作用力,从而对其做功,从而增加其能量,我们称之为涡轮做功机(风扇、压缩机、泵、螺旋桨)。
转子通常有一个外壳,称为定子,它本身衬有叶片。由于这些刀片是固定的,因此无需对它们进行任何操作。他们的任务是引导流动朝向或远离连接到转子的移动叶片。这些叶片称为导向叶片或导向叶片。一排定叶片和一排动叶片合称为一个级。涡轮机可以由这些级中的一个或多个构成。如果图的圆柱面2.6在半径r通过阶段的切割和矫直,原来在圆柱面上的叶片截面轮廓形成两个直的叶栅。所示的设置包括一个

从流动方向看,固定叶栅位于移动叶栅之前的涡轮级。

显然,级联是用来改变流动的。如果转向使得速度的大小没有改变,则叶栅是纯转向或恒压叶栅,因为那时通过叶栅不会发生压力变化(仅在无摩擦流动的情况下)。一般来说,速度的大小会随着转向而变化,因此也会随着压力而变化。如果速度的大小增加,我们就会有一个加速级联,通常出现在涡轮机中,如果速度降低,我们就会有一个减速级联,通常出现在压缩机中。我们将把级联看作是叶片的严格周期性排序,即具有完全相同间距的无限长的叶片排s沿级联的叶片之间。因此,流动也是严格周期性的。

物理代写|流体力学代写Fluid Mechanics代考|Balance of Energy

机械能可以转化为热,热可以转化为机械能这一事实表明,到目前为止我们所讨论的力学平衡定律不足以完整地描述流体的运动。除了我们已经讨论过的两个定律之外,还出现了第三个基本经验定律,即能量平衡:
物体总能量的变化率等于外力的功率加上外力的变化率。热量传递到身体。
该定律可以从众所周知的热力学第一定律以及从柯西方程得出的机械能方程“推导出”。(2.38a,2.38b)。然而,在这里我们更愿意假设总能量的平衡,并从中推断出热力学第一定律的更具限制性的陈述。

我们将假定已知的经典热力学的基本原理。热力学关注的是材料处于静止状态并且所有出现的量都与位置无关(均匀)的过程,因此只取决于时间。流体运动中出现的不可逆过程的热力学的一个重要步骤是简单地将经典定律应用于材料粒子。如果和是每单位的内能

质量,则物质粒子的内能由下式给出和 d米,我们可以计算内能和物体的能量,即流体有界部分的能量,作为物体占据的区域上的积分

和=∭(在(吨))和ϱd在
为了获得所考虑的流体的总能量,必须将经典理论中没有出现的动能添加到(2.109)中。物质粒子的动能为(在2/2)d米, 和动能ķ身体的相应

ķ=∭(在(吨))在一世在一世2ϱd在
出现的施加力是在动量平衡的背景下讨论的表面力和体力。表面力的力量吨→ d小号是在→⋅吨→ d小号, 而体力的ϱķ→ d在是在→⋅ķ→ϱd在. 那么所施加的力的功率为

磷=∭(在(吨))ϱ在一世ķ一世 d在+∬(小号(吨))在一世吨一世 d小号
类似于体积流量在→⋅n→ d小号通过表面的一个元素,我们通过表面的一个元素引入热通量−q→⋅n→ d小号并表示q→作为热通量向量。选择减号是为了使流入的能量 (q→和n→形成钝角)计为正数。从现在开始,我们将限制自己通过传导来传递热量,尽管q→还可以包含其他类型的传热,例如,通过坡印廷矢量的辐射传热。

物理代写|流体力学代写Fluid Mechanics代考 请认准statistics-lab™

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金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

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