Mechanics of fluid henter 4
1 Mechanics of Fluid
流体力学
2
Chapter 4 Similarity principle and dimensional analysis §4-1 Introduction D84-2 Similarity Principle 84-3 Similarity Criterion §44 Model laws 当§4-5兀 Law and application of Dimensional Analysis Chapter 4 Exercise
3 Chapter 4 Similarity Principle and Dimensional Analysis §4–1 Introduction §4–2 Similarity Principle §4–3 Similarity Criterion §4–4 Model Laws §4–5 Law and Application of Dimensional Analysis Chapter 4 Exercise
第四章相似原理和量纲分析 §4-1引言 §4-2相似原理 §4-3相似准则 §4-4模型规律 §45丌定理和量纲分析的应用 第四章习题
4 第四章 相似原理和量纲分析 §4–1 引言 §4–2 相似原理 §4–3 相似准则 §4–4 模型规律 §4–5 定理和量纲分析的应用 第四章 习 题
a Chapter 4 Similarity Principle and Dimensional Analysis 84-1 Introduction Experiment is the basis of developing theories as well as the yardstick of proving theories, sometimes science and technology problems cant be solved without the cooperation of experiments There are mainly two kinds of experiments in engineering fluid mechanic a. model experiment of engineering. For the purpose of forecasting the flow situation of large-scale machine or water power engineering which are being built b exploratory observing experiment. For the purpose of searching unknown flow laws, the theoretical foundation to direct these experiments are similarity principle and dimension analyse
5 Chapter 4 Similarity Principle and Dimensional Analysis §4-1 Introduction Experiment is the basis of developing theories as well as the yardstick of proving theories, sometimes science and technology problems can’t be solved without the cooperation of experiments. a. model experiment of engineering. For the purpose of forecasting the flow situation of large-scale machine or water power engineering which are being built. b. exploratory observing experiment. For the purpose of searching unknown flow laws, the theoretical foundation to direct these experiments are similarity principle and dimension analyse. There are mainly two kinds of experiments in engineering fluid mechanics:
相似量筑分 第四章相似原理和量纲分析 §41引 实验既是发展理论的依据又是检验理论的准绳,解决科技 问题往往离不开实验手段的配合。 工程流体力学中的实验主要有两种: a、工程性的模型实验。目的在于预测即将建造的大型机械 或水工结构上的流动情况; b、探索性的观察实验。目的在于寻找未知的流动规律,指 导这些实验的理论基础就是相似原理和量纲分析
6 第四章 相似原理和量纲分析 §4-1 引言 实验既是发展理论的依据又是检验理论的准绳，解决科技 问题往往离不开实验手段的配合。 a、工程性的模型实验。目的在于预测即将建造的大型机械 或水工结构上的流动情况； b、探索性的观察实验。目的在于寻找未知的流动规律，指 导这些实验的理论基础就是相似原理和量纲分析。 工程流体力学中的实验主要有两种：
a 84-2 Similarity Principle When we design or manufacture some complex and huge hydraulic machines built water power engineering as well as search some complicated hydraulic phenomena, we often design and made a model which is reduced size according to similarity principle. Carrying out simulation experiment, deduce the flow situation and relative data of practicality through observing the flow situation of model defination: The basic theory which analyze and study the similitude relation between model and real object is called similarity pI rinciple Real object is called prototype too 7
7 §4-2 Similarity Principle When we design or manufacture some complex and huge hydraulic machines ,built water power engineering as well as search some complicated hydraulic phenomena ,we often design and made a model which is reduced size according to similarity principle. Carrying out simulation experiment, deduce the flow situation and relative data of practicality through observing the flow situation of model. The basic theory which analyze and study the similitude relation between model and real object is called similarity principle Real object is called prototype too. defination：
相似量筑分 §42相似原理 当设计制造某些复杂而庞大的水力机械,建造水利工程 以及研究某些复杂的水力现象时,往往要根据相似原理,设 计制造缩小了尺寸的模型。进行模拟实验,通过对模型的流 动状况观测来推断实物的流动状况及有关数据。 定义: 分析研究模型和实物间的相似关系的基本理论称为相似 理论 实物又称为原型
8 §4-2 相 似 原 理 当设计制造某些复杂而庞大的水力机械，建造水利工程 以及研究某些复杂的水力现象时，往往要根据相似原理，设 计制造缩小了尺寸的模型。进行模拟实验，通过对模型的流 动状况观测来推断实物的流动状况及有关数据。 分析研究模型和实物间的相似关系的基本理论称为相似 理论。 实物又称为原型。 定义：
Similarit Prineiple and Dimension l Analysis 1. Geometry similitude defination: The corresponding geometrical linear dimensions of prototype are in proportion to those of model and corresponding geometrical angles are that called geometry similitude Model parameter adds a subscript m and prototype parameter adds a subscript n to express Linear scale (4-1) a l Surface scale 6,= =o(42) Volume scale CA =d 4-3) 3
9 1. Geometry similitude Model parameter adds a subscript m and prototype parameter adds a subscript n to express. Linear scale m n l l l = （4—1） Surface scale 2 2 2 l m n m n l l = = = （4—2） Volume scale 3 3 3 l m n m n l l V V = = = （4—3） The corresponding geometrical linear dimensions of prototype are in proportion to those of model and corresponding geometrical angles are that called geometry similitude. defination：
一、几何相似 定义: 原型与模型中对应的几何线性尺寸成比例,对应的几何角 度相等,称为几何相似。 模型参数加脚码m,原型参数加脚码n表示。 线性比尺为 (4-1) 面积比尺为=△,1n=672(42) 体积比尺为 A =d 43) 3 10
10 一、几何相似 模型参数加脚码 m ，原型参数加脚码 n 表示。 线性比尺为 m n l l l = （4—1） 面积比尺为 2 2 2 l m n m n l l = = = （4—2） 体积比尺为 3 3 3 l m n m n l l V V = = = （4—3） 原型与模型中对应的几何线性尺寸成比例，对应的几何角 度相等，称为几何相似。 定义：