Name: reynolds number and pipe flow
Uploaded: 2025-02-13T15:43:29.000Z
Duration: 1 min 27 s
Channel: JoVE

K12 Standards

Virginia  Standards of Learning

HIgh School

Biology

BIO.1

BIO.1.e

Dimensional Analysis

次元解析は、無次元グループを使用して流体の流れの問題を単純化し、複雑な変数をより理解しやすい用語に縮小するのに役立ちます。
パイプ システムの流体解析では、単位長さあたりの圧力損失がパイプの直径、流体速度、流体密度、粘度などの要因に依存します。
2つの無次元グループを形成することで、各因子を別々に分析することを避け、単位長さあたりの圧力損失とこれらの要因との関係を研究しやすくします。
1つのグループは、単位長さあたりの圧力損失と流体の動的特性との関係を捉え、もう1つのグループは粘度と流動特性に焦点を当てています。
これらのグループは、さまざまなパイプ サイズと流体タイプで機能する曲線を作成することにより、さまざまなシステムに実用的なソリューションを提供します。
寸法解析は、使用する測定単位に関係なく、有効な物理的解釈に重要な方程式の寸法一貫性を保つことを保証します。
また、ディメンション解析は、ダムや河川などの水理システムのスケールダウンモデルを作成するのにも役立ち、本格的なテストを行わなくても、水の流れ、浸食、洪水の挙動に関する洞察を得ることができます。
この方法は、水パイプラインや自然および人工のチャネルの流体の流れなどのシステムの結果を予測します。

次元解析

次元解析は、複雑な問題を次元のないグループにまとめることで簡素化する流体力学の貴重な手法です。これらのグループは、関係する変数間の重要な関係を捉え、研究者やエンジニアが各変数を個別に扱うことなく流体の流れを解析できるようにします。このアプローチにより、独立変数の数が減り、解析が容易になり、物理現象をよりよく理解できるようになります。

 流体力学では、次元解析を使用して、パイプライン、チャネル、土木工学で一般的なその他の構造物などのシステム内の流体の挙動を理解します。給水システムや下水道網の設計で一般的な、長く滑らかな壁の水平円形パイプを通る流体の流れの例を考えてみましょう。パイプに沿った単位長さあたりの圧力降下は、パイプの直径、流体の密度、流体の速度、粘度などの変数によって異なります。次元解析によると、圧力降下はこれらの変数の関数として表すことができます。

<img alt="Equation 1" src="/files/ftp_upload/18067/18067_Equation_1.svg" style="text-align: center; height: 12px;">

 この定式には 5 つの独立変数が含まれており、解析が複雑になる可能性があります。これを簡素化するために、次元解析を使用して変数の数を 2 つの無次元グループに減らし、問題を合理化することができます。この解析から得られる 2 つの重要な無次元グループは、流れの状態を特徴付けるレイノルズ数と、圧力降下と相関する摩擦係数です。

<img alt="Equation 2" src="/files/ftp_upload/18067/18067_Equation_2.svg" style="text-align: center; height: 30px;">

 エンジニアは、無次元グループを使用して、あらゆる滑らかな壁のパイプと非圧縮性のニュートン流体に適用される普遍曲線を生成します。この曲線を使用すると、考えられる組み合わせごとに多数の実験を実行することなく、さまざまなパイプサイズと流体の圧力降下を予測できます。

<img alt="Figure 1" src="/files/ftp_upload/18067/18067_PT_Figure.svg" style="text-align: center; height: 250px;">

 このアプローチにより、実験に必要な時間とコストが最小限に抑えられ、より簡単な設計決定が可能になります。配水ネットワークの設計であれ、灌漑システムの圧力損失の解析であれ、次元解析は土木エンジニアにとって非常に重要です。

次元解析は、無次元グループを使用して流体の流れの問題を単純化し、複雑な変数をより単純な用語に縮小します。

Education

JoVE Core

Civil Engineering

土木工学

Unit 1

ユニット1

Dimensional Analysis, Similitude, and Modeling

次元解析、相似則、およびモデリング

dimensional-analysis-similitude-and-modeling

KEY TERMS AND CONCEPTS

主要用語と概念

reynolds number and pipe flow

Dimensional analysis helps simplify pipe flow problems in fluid mechanics by turning several variables into dimensionless groups. These groups show the key relationships in the system without tracking every variable one by one. They also reduce the number of independent variables, which makes the problem easier to study and understand.

A common example is fluid flow through a long, smooth-walled, horizontal circular pipe. This kind of pipe appears in water distribution systems and sewage networks. In this case, the pressure drop per unit length depends on pipe diameter, fluid density, fluid velocity, and viscosity.

Dimensional analysis can reduce this five-variable problem to two dimensionless groups. One is the Reynolds number, which describes the flow regime. The other is the friction factor, which relates to the pressure drop.

Engineers use these groups to build a universal curve for any smooth-walled pipe and incompressible Newtonian fluid. That curve can predict pressure drop for different pipe sizes and fluids without testing every possible case. It saves time and cost and supports better design choices in projects such as water distribution networks and irrigation systems.

Reynolds Number and Pipe Flow

dimensional analysis

Dimensional analysis helps simplify pipe flow problems in fluid mechanics by turning several variables into dimensionless groups. These groups show the key relationships in the system without tracking every variable one by one. They also reduce the number of independent variables, which makes the problem easier to study and understand. A common example is fluid flow through a long, smooth-walled, horizontal circular pipe. This kind of pipe appears in water distribution systems and sewage...

the buckingham pi theorem

Reynolds Number from Buckingham Pi

The Buckingham Pi theorem turns fluid flow variables into dimensionless terms. In a pipe flow example, the key variables are the pipe diameter, fluid velocity, density, and viscosity. These variables can be combined into one dimensionless group, the Reynolds number, which captures their relationship. Applying the theorem starts with identifying the fundamental dimensions of each variable. In fluid mechanics, these dimensions are mass, length, and time. The pipe diameter represents length,...

determination of pi terms

Buckingham Pi Terms for Wing Lift

Buckingham Pi terms help simplify the study of lift force on an airplane wing. Dimensional analysis is used to turn several related variables into dimensionless terms, which makes the problem easier to work with. The wing-lift example uses five variables: lift force, air density, wing area, aircraft velocity, and air viscosity. Each variable is written in fundamental dimensions of mass, length, and time. The Buckingham Pi theorem then shows that the number of Pi terms equals the total number...

dimensionless groups in fluid mechanics

Key Fluid Flow Ratios for Modeling

Dimensionless groups in fluid mechanics are key ratios that make fluid behavior easier to compare without using specific units. These numbers help simplify analysis across different flow situations. The Reynolds number, or Re, compares inertial forces to viscous forces. It helps show whether a flow is laminar or turbulent and is important in pipeline and aerodynamic surface design. Other dimensionless numbers describe how fluid flow responds to gravity, pressure, elasticity, and speed. The...

correlation of experimental data

Using Experimental Data in Dimensional Analysis

Dimensional analysis helps organize experimental data and test physical relationships. It can simplify a complex problem and point to the key dimensionless groups that matter. But it does not give a full solution by itself. Experimental data is needed to find the exact relationship and to check theoretical predictions. In the example of a spherical particle moving through a viscous fluid, dimensional analysis shows that drag force depends on the particle’s diameter, velocity, and the fluid’s...

modeling and similitude

Scaled Models for Testing Dams and Ships

Scaled models help engineers study large systems in a smaller, controlled setup. They are useful when a full-size test would cost too much or take too long. In civil infrastructure and hydrology, a scaled dam model can show how water flow, turbulence, and pressure will behave in the real structure. For a model to give useful results, it must keep similitude. Similitude means the model matches the prototype, or full-size system, in important ways. Geometric similarity keeps the shape and...

typical model studies

River and Spillway Model Design

River and spillway model design uses scaled systems to predict how fluid will behave in full-scale settings. These model studies help engineers study river flow, dam spillways, and structures that interact with open surfaces. For river models, Froude number similarity is important. The Froude number compares inertial and gravitational forces, and matching it helps copy surface flow features such as wave patterns and velocity. Practical limits can cause geometric distortion, which means the...

design example: creating a hydraulic model of a dam spillway

design-example-creating-a-hydraulic-model-of-a-dam-spillway

Testing Spillway Flow with a Scale Model

A scale model of a dam spillway is used to study how water moves over the structure. These hydraulic models are often built at a 1:15 ratio. They help show flow speed, flow patterns, and energy dissipation, which is the loss of water energy as flow moves through the spillway. Researchers use the model to watch how water behaves in a controlled setting. They can examine velocity distribution, wave formation, turbulence, and flow separation. These details help them see how the spillway performs...

key terms and concepts

Learn how dimensional analysis reduces pipe flow into Reynolds number and friction factor, helping engineers predict pressure drop in pipes and channels.

Reynolds Number and Pipe Flow | JoVE K12

JoVE Core Civil Engineering provides a foundational exploration of essential construction materials in civil engineering, focusing on bricks, stones, steel, wood, and concrete through easy-to-understand animated videos. This collection covers the properties, manufacturing processes, and practical applications of these materials. Additionally, the accompanied science-in-action videos demonstrate the research experiments performed in laboratories.

civil engineering

Chemistry

CH.1

CH.1.e

The Scientific Method

The scientific method is a detailed, empirical problem-solving process used by biologists and other scientists. This iterative approach involves ...

Inductive Reasoning

Inductive reasoning is a form of logical thinking that uses related observations to arrive at a general conclusion. It is uncertain and operates in ...

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the ...

Correlation and Causation

Correlation and CausationStatistical tests can calculate whether there is a relationship, or correlation, between independent and dependent variables. A ...

The student will demonstrate an understanding of scientific and engineering practices by asking questions and defining problems
• ask questions that arise from careful observation of phenomena and/or
organisms, from examining models and theories, and/or to seek additional
information
• determine which questions can be investigated within the scope of the
school laboratory or field to determine relationships between independent
and dependent variables
• generate hypotheses based on research and scientific principles
• make hypotheses that specify what happens to a dependent variable when
an independent variable is manipulated

BIO.1.a

Case Studies

There are many research methods available to psychologists in their efforts to understand, describe, and explain behavior and the cognitive and biological ...

Naturalistic Observations

If you want to understand how behavior occurs, one of the best ways to gain information is to simply observe the behavior in its natural context. However, ...

Surveys

Often, psychologists develop surveys as a means of gathering data. Surveys are lists of questions to be answered by research participants, and can be ...

Archival Research

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Longitudinal Research

Sometimes we want to see how people change over time, as in studies of human development and lifespan. When we test the same group of individuals ...

Cross-Sectional Research

In cross-sectional research, a researcher compares multiple segments of the population at the same time. If they were interested in people&#39;s dietary ...

Group Design

The most basic experimental design involves two groups: the experimental group and the control group. The two groups are designed to be the same except ...

Factorial Design

Factorial Analysis is an experimental design that applies Analysis of Variance (ANOVA) statistical procedures to examine a change in a dependent variable ...

The Placebo Effect

The placebo effect occurs when people&#39;s expectations or beliefs influence or determine their experience in a given situation. In other words, simply ...

Blind Procedures

Ideally, the people who observe and record the children&rsquo;s behavior are unaware of who was assigned to the experimental or control group, in order to ...

Ethics in Research

Today, scientists agree that good research is ethical in nature and is guided by a basic respect for human dignity and safety. However, this has not ...

The student will demonstrate an understanding of scientific and engineering practices by planning and carrying out investigations
 • individually and collaboratively plan and conduct observational and experimental investigations 
 • plan and conduct investigations or test design solutions in a safe and ethical manner including considerations of environmental, social, and personal effects
• determine appropriate sample size and techniques 
 • select and use appropriate tools and technology to collect, record, analyze, and evaluate data

BIO.1.b

Introduction to Statistics

The science of statistics involves collecting, analyzing, interpreting, and presenting data. The method of collecting, organizing, and summarizing data is ...

How Data are Classified: Categorical Data

A variable, usually notated by capital letters such as X and Y, is a characteristic or measurement that can be determined for each member of a population. ...

How Data are Classified: Numerical Data

Data that are countable or measurable in specific units are called numerical or quantitative data. Quantitative data are always numbers. Quantitative data ...

Ogive Graph

An ogive graph is sometimes called a cumulative frequency polygon. It is one type of frequency polygon that shows cumulative frequency. In other words, ...

Histogram

The histogram is a graphical representation in the x-y form of data distribution in a data set. The horizontal x-axis is labeled with what the data ...

Relative Frequency Histogram

The relative frequency depicts the proportion of data points that have each value. The frequency tells the number of data points that have each value. ...

Scatter Plot

The most common and easiest way to display the relationship between two variables, x and y, is a scatter plot. A scatter plot shows the direction of a ...

Time-Series Graph

A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct ...

Bar Graph

A bar graph is also called a bar chart and consists of bars that are separated from each other. It either uses horizontal or vertical bars to show ...

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can ...

Pareto Chart

A Pareto chart is a bar graph or a combination of both line and bar graphs. The bar lengths represent the individual values or the frequency, while the ...

Pie Chart

A pie chart (or a pie graph) is a circular graphical chart or a pictorial representation of categorical data. It is divided into slices of pie each ...

What is Central Tendency?

Descriptive statistics describe or summarize relevant characteristics of a sample and aid in the analysis of data of interest. When analyzing large ...

Arithmetic Mean

The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the ...

Mean From a Frequency Distribution

Sometimes, data gathered from an experiment on a large sample or population are organized into concise tables. In such cases, the frequency of the ...

What is a Mode?

The mode is one of the commonly used measures of a central tendency. It is defined as the most frequent value in a data set.
There can be more than one ...

Bias

Bias refers to any tendency that prevents a question from being considered unprejudiced. In research, bias occurs when one outcome or answer is selected ...

Median

Besides mean, the median is a widely used measure of central tendency. Typically, median is defined as the central or middle value of a data set, measured ...

Blinding

Blinding is a commonly used method of not telling participants which treatment a subject is receiving. Blinding is a critical part of a randomized control ...

Midrange

A somewhat easy to compute quantitative estimate of a data set&#8217;s central tendency is its midrange, which is defined as the mean of the minimum and ...

Clinical Trials

Clinical trials are prospective experimental studies conducted on humans to determine the safety and efficacy of treatments, drugs, diet methods, and ...

What is Variation?

Apart from the measures of central tendency, distribution, outliers, and the changing characteristics of data with time, an important characteristic of ...

Range

The range is one of the measures of variation. It can be defined as the difference between a dataset&#39;s highest and lowest values. For example, in the ...

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The ...

Standard Error of the Mean

The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is ...

Calculating Standard Deviation

The standard deviation is the most common measure of variation. It is a value that tells us how far a data value is from the mean value in a dataset. ...

Crossover Experiments

Crossover experiments, also called the repeated-measurements design, is a study design in which all experimental units are exposed to all treatments in ...

Controls in Experiments

When conducting an experiment, it is crucial to have control to reduce bias and accurately measure the dependent variables. It also marks the results more ...

The student will demonstrate an understanding of scientific and engineering practices by interpreting, analyzing, and evaluating data 
 • construct and interpret data tables showing independent and dependent variables, repeated trials, and means
 • construct, analyze, and interpret graphical displays of data
 • use data in building and revising models, supporting an explanation for phenomena, or testing solutions to problems
 • analyze data using tools, technologies, and/or models to make valid and reliable scientific claims or determine an optimal design solution

BIO.1.c

What is a Hypothesis?

A hypothesis can be a simple sentence or statement about a property or any phenomenon observed or predicted for a population. It is usually a claim about ...

Null and Alternative Hypotheses

The actual hypothesis testing begins by considering two hypotheses. They are termed&#160; the null hypothesis and the alternative hypothesis. These ...

critical-region-critical-values-and-significance-level

Critical Region, Critical Values and Significance Level

The critical region, critical value, and significance level are interdependent concepts crucial in hypothesis testing.
In hypothesis testing, a sample ...

P-value

P-value is one of the most crucial concepts in statistics.
P-value stands for the probability value. &#160;P-value is the probability that, if the null ...

Types of Hypothesis Testing

There are three types of hypothesis tests: right-tailed, left-tailed, and two-tailed.
When the null and alternative hypotheses are stated, it is observed ...

The student will demonstrate an understanding of scientific and engineering practices by  constructing and critiquing conclusions and explanations
• make quantitative and/or qualitative claims regarding the relationship between dependent and independent variables 
• construct and revise explanations based on valid and reliable evidence obtained from a variety of sources including students' own investigations, models, theories, simulations, and peer review 
• apply scientific ideas, principles, and/or evidence to provide an explanation of phenomena and design solutions 
• compare and evaluate competing arguments or design solutions in light of currently accepted explanations and new scientific evidence
• construct arguments or counterarguments based on data and evidence differentiate between a scientific hypothesis and theory

BIO.1.d

Dimensional analysis helps simplify fluid flow problems by using dimensionless groups, reducing complex variables into simpler terms that are easier to ...

Modeling and Similitude

A scaled model of a dam is tested in a controlled environment to observe how it will manage water flow, turbulence, and pressure.
This setup predicts the ...

Typical Model Studies

Typical model studies analyze scaled-down systems to predict fluid behavior, focusing on interactions with free surfaces and flow around immersed bodies.
...

The student will demonstrate an understanding of scientific and engineering practices by  developing and using models
• evaluate the merits and limitations of models
• develop, revise, and/or use models based on evidence to illustrate or predict relationships 
• develop and/or use models to generate data to support explanations, predict phenomena, analyze systems, and/or solve problems

Communication Process

The communication process is the transmission and reception of messages or information from one sender to the receiver.
It involves the sender encoding an ...

Communication Objectives

Marketing communication objectives refer to the strategic goals that guide promotional activities.
They set the stage for messaging strategies, content ...

The student will demonstrate an understanding of scientific and engineering practices by  obtaining, evaluating, and communicating information 
• compare, integrate, and evaluate sources of information presented in different media or formats to address a scientific question or solve a problem
• gather, read, and evaluate scientific and/or technical information from multiple authoritative sources, assessing the evidence and credibility of each source
• communicate scientific and/or technical information about phenomena in multiple formats

BIO.1.f

Reynolds Number and Pipe Flow

Description

Transcript

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