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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Balance of Linear Momentum

The momentum equation in integral form applied to a control volume determines the integral flow quantities such as lift force, drag forces, average pressure, averaged temperature, and entropy. The motion of a material volume is descrihed hy the Newton’s second law of motion which states that mass times acceleration is the sum of all external forces acting on the system. In the absence of electrodynamic, electrostatic, and magnetic forces, the external forces can be summarized as the surface forces and the gravitational forces:
$$m \frac{D \boldsymbol{V}}{D t}=\boldsymbol{F}_S+\boldsymbol{F}_G$$

Equation (5.8) is valid for a closed system with a system boundary that may undergo deformation, rotation, expansion or compression. In an engineering component subjected to flow, however, there is no closed system with a defined system boundary. The mass is continuously flowing from one point within a component to another point. Thus, in general, we deal with mass flow rather than mass. Consequently, Eq. (5.8) must be modified in such a way that it is applicable to a predefined control volume with mass flow passing through it. This requires applying the Reynolds transport theorem to a control volume, as we already discussed in the previous section. For this purpose, we prepare Eq. (5.8) before proceeding with the Reynolds transport theorem. In the following steps, we add a zero-term to Eq. (5.8):
$$\frac{D m}{D t}=0, \quad V \frac{D m}{D t}=0$$
$$m \frac{D V}{D t}+\boldsymbol{V} \frac{D m}{D t}=\boldsymbol{F}_S+\boldsymbol{F}_G$$
Using the Leibnitz’s chain rule of differentiation, Eq. (5.10) can be rearranged as:
$$\frac{D}{D t}(m \boldsymbol{V})=\boldsymbol{F}_S+\boldsymbol{F}_G$$

## 物理代写|流体力学代写Fluid Mechanics代考|Balance of Moment of Momentum

One of the application field of conservation of moment of momentum is turbomachinery. This allows a better understanding of the physics in an illustrative manner. To establish the conservation law of moment of momentum for a time dependent material volume, we start from the second law of Newton, Eq. (5.18):
$$m \frac{D \boldsymbol{V}}{D t}=\sum \boldsymbol{F}=\boldsymbol{F}S+\boldsymbol{G}=\int{V(t)} \nabla \cdot \Pi d v+\boldsymbol{G}$$
The moment of the force given by Eq. (5.27) is then
$$m \boldsymbol{X} \times \frac{D \boldsymbol{V}}{D t}=\sum \boldsymbol{X} \times F$$
with $X$ as the position vector originating from a fixed point. To rearrange Eq. (5.28) for further analysis, its left-hand side is extended by adding the following zero-term identities:

$$\boldsymbol{V} \times \boldsymbol{V}=\frac{D \boldsymbol{X}}{D t} \times \boldsymbol{V}=m \frac{D \boldsymbol{X}}{D t} \times \boldsymbol{V}=0$$
and:
$$\frac{D m}{D t}=0=X \times V \frac{D m}{D t}=0$$
Introducing the identities (5.29) and (5.30) into Eq. (5.28), we arrive at:
$$m \boldsymbol{X} \times \frac{D \boldsymbol{V}}{D t}+m \frac{D \boldsymbol{X}}{D t} \times \boldsymbol{V}+\boldsymbol{X} \times \boldsymbol{V} \frac{D m}{D t}=\sum \boldsymbol{X} \times \boldsymbol{F}$$
Using the Leibnitz’s chain differential rule, a simple rearrangement of Eq. (5.31) allows the application of the Reynolds transport theorem as follows:
$$\frac{D(m \boldsymbol{X} \times \boldsymbol{V})}{D t}=\sum \boldsymbol{X} \times \boldsymbol{F} .$$
Since $m=\int_{v(t)} \rho d v$, Eq. (5.32) can be written as:
$$\frac{D}{D t} \int_{v_{(f)}}(\rho \boldsymbol{X} \times \boldsymbol{V}) d v=\sum \boldsymbol{X} \times \boldsymbol{F}$$
with $v(t)$ as the time dependent volume of the integral boundary. We apply the Reynolds transport theorem and the Gauss conversion theorem (Chap. 2) to the lefthand side of Eq. (5.33) and arrive at:
$$\frac{D}{D t} \int_{V_C}(\rho \boldsymbol{X} \times \boldsymbol{V}) d v=\int_{V_C}\left(\frac{\partial(\rho \boldsymbol{X} \times \boldsymbol{V})}{\partial t} d v\right)-\int_{S_C} \boldsymbol{n} \cdot(\rho \boldsymbol{V} \boldsymbol{V} \times \boldsymbol{X}) d S .$$

# 力学代考

## 物理代写|流体力学代写Fluid Mechanics代考|Balance of Linear Momentum

$$m \frac{D \boldsymbol{V}}{D t}=\boldsymbol{F}_S+\boldsymbol{F}_G$$

$$\frac{D m}{D t}=0, \quad V \frac{D m}{D t}=0$$

$$m \frac{D V}{D t}+\boldsymbol{V} \frac{D m}{D t}=\boldsymbol{F}_S+\boldsymbol{F}_G$$

$$\frac{D}{D t}(m \boldsymbol{V})=\boldsymbol{F}_S+\boldsymbol{F}_G$$

## 物理代写|流体力学代写Fluid Mechanics代考|Balance of Moment of Momentum

$$m \frac{D \boldsymbol{V}}{D t}=\sum \boldsymbol{F}=\boldsymbol{F} S+\boldsymbol{G}=\int V(t) \nabla \cdot \Pi d v+\boldsymbol{G}$$

$$m \boldsymbol{X} \times \frac{D \boldsymbol{V}}{D t}=\sum \boldsymbol{X} \times F$$

$$\boldsymbol{V} \times \boldsymbol{V}=\frac{D \boldsymbol{X}}{D t} \times \boldsymbol{V}=m \frac{D \boldsymbol{X}}{D t} \times \boldsymbol{V}=0$$

$$\frac{D m}{D t}=0=X \times V \frac{D m}{D t}=0$$

$$m \boldsymbol{X} \times \frac{D \boldsymbol{V}}{D t}+m \frac{D \boldsymbol{X}}{D t} \times \boldsymbol{V}+\boldsymbol{X} \times \boldsymbol{V} \frac{D m}{D t}=\sum \boldsymbol{X} \times \boldsymbol{F}$$

$$\frac{D(m \boldsymbol{X} \times \boldsymbol{V})}{D t}=\sum \boldsymbol{X} \times \boldsymbol{F}$$

$$\frac{D}{D t} \int_{v(f)}(\rho \boldsymbol{X} \times \boldsymbol{V}) d v=\sum \boldsymbol{X} \times \boldsymbol{F}$$

$$\frac{D}{D t} \int_{V_C}(\rho \boldsymbol{X} \times \boldsymbol{V}) d v=\int_{V_C}\left(\frac{\partial(\rho \boldsymbol{X} \times \boldsymbol{V})}{\partial t} d v\right)-\int_{S_C} \boldsymbol{n} \cdot(\rho \boldsymbol{V} \boldsymbol{V} \times \boldsymbol{X}) d S$$

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## 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。

assignmentutor™您的专属作业导师
assignmentutor™您的专属作业导师