behavior

JoVE行動学は、人間や動物の行動を理解するための観察および実験手法を公開しています。このセクションには、内外の刺激に対する遺伝的原因と生理学的反応を分析する方法と、関係する脳領域を調べる方法が含まれています。

行動学

biochemistry

JoVE生化学は、生体分子（タンパク質、核酸、炭水化物、脂質、代謝物など）の構造と機能、および生物学的プロセス中に起こるそれらの相互作用と変換についての理解を深める方法を出版しています。

生化学

bioengineering

JoVE生物工学は、物理学と生命科学を融合して基本的な生物学的プロセスと機能を理解する方法と技術を出版しています。このセクションでは、病気の測定、診断、治療を改善するための物理科学的ツールとアプローチについても特集します。

生物工学

biology

JoVE生物学は、細胞生物学、分子生物学、生命体生物学の分野で使用される方法を出版しています。これは、標準的な技法の新しいアプリケーションから、生物の基本的な生物学的機能を理解することを目的とした新規のアプローチにまで及びます。

生物学

cancer research

JoVEがん研究は、がん生物学の研究で使用される技術を出版しています。このセクションでは、発がん、薬剤耐性のメカニズム、診断、転移、革新的な治療法に取り組む研究方法論を取り上げます。

がん研究

chemistry

JoVE化学は、分析化学、有機化学、高分子化学、物理化学、無機化学など、幅広い分野の方法を出版しています。このセクションには、高度なまたはユニークなアプリケーション向けの材料および低分子の設計・調整も含まれています。

化学

developmental biology

JoVE発生生物学では、分子、細胞、組織、器官、および生物全体のレベルにおける、試験管内および/または生体内での生物発生を研究するのに使用される方法と技術を出版しています。

発生生物学

engineering

JoVE工学では、工学と応用物理学で利用される方法と技術を出版しています。方法には、機械、電気、化学のエンジニア、物理学者、材料科学者からの寄稿が含まれます。

工学

environment

JoVE環境学は、地球のプロセスと生態系を研究し、環境問題に対処するための研究方法と技術を出版しています。このセクションでは、農業および食品科学だけでなく、幅広い学際的な環境研究分野からの実験室およびフィールドベースの方法を取り上げます。

環境学

genetics

JoVE遺伝学は、ゲノミクス、遺伝子発現、遺伝子工学、後生遺伝学など、遺伝学のすべての分野（すべての生物）に取り組む方法を出版しています。このセクションでは、塩基配列決定技術とその応用の進歩についても特に取り上げます。

遺伝学

immunology and infection

JoVE免疫学と感染では、病原体に対する生物学的反応、感染に対する免疫反応、基本的な微生物学、および感染性微生物に対する新しい治療法を評価するための方法と技術を出版しています。

免疫・感染学

medicine

JoVE医学では、生物医学研究方法と臨床応用を出版しています。このセクションでは、疾患の動物モデル、医療処置、手術、患者のケーススタディ、および臨床試験の方法論について説明します。

医学

neuroscience

JoVE神経科学では、脳と神経系の構造、機能、生理学、および病態生理学を研究するための方法を出版しています。このセクションには、神経疾患および神経障害の潜在的な治療基盤と外科技術も含まれています。

神経科学

jove journal

JoVE Journal

科学ビデオジャーナル。査読された論文。学際的。

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Research

Pipe Flowrate Measurement

In pipe flow measurement, orifice, nozzle, and Venturi meters are commonly used to determine fluid flowrates by constricting the flow area, which increases fluid velocity and reduces pressure. This pressure difference, governed by Bernoulli&#39;s principle and adjusted for real-world conditions, is essential for calculating flowrate. Each meter type is suited to specific applications based on accuracy, efficiency, and compatibility with various flow conditions.
The orifice meter is a simple, cost-effective device consisting of a flat plate with a central hole that creates a measurable pressure drop. This device is popular in applications like water treatment, oil and gas processing, and general industrial use where moderate accuracy is acceptable. However, due to head loss from turbulent flow and area contraction, a discharge coefficient is used to correct the idealized flow equation. The flowrate through an orifice meter is proportional to the square root of the pressure difference, accounting for fluid density, orifice area, and the ratio of the hole diameter to the pipe diameter.
The nozzle meter improves on the orifice meter by using a contoured design that reduces flow separation and turbulence, resulting in a smoother flow and increased measurement accuracy. It is often used for high-velocity flows, such as in steam or gas pipelines, chemical processing, and power plants. With a higher discharge coefficient than the orifice meter, the nozzle meter provides improved precision with less energy loss.
The Venturi meter offers the highest accuracy among the three types. It is ideal for applications requiring minimal head loss and reliable measurements, such as water supply systems, natural gas pipelines, and wastewater management. Its smooth contraction and gradual expansion reduce flow separation, conserving energy and enabling accurate flowrate calculations even in low-pressure systems. The discharge coefficient for a Venturi meter, which depends on factors like the ratio of the throat to pipe diameter and flow characteristics, supports exact flow measurement but requires a more complex installation and is generally more costly.
Each meter type offers unique benefits, from essential flow monitoring to precise flow control, chosen based on the application&#39;s accuracy needs and specific conditions.

パイプ流量測定

Flow measurement devices&#8212;such as orifice, nozzle, and Venturimeters&#8212;operate by narrowing the flow area. This increases fluid velocity and ...

Pipe Flowrate Measurement: Problem Solving

A spray tank system is engineered to uniformly distribute a pest-control liquid across plants by using a pressurized mechanism. The tank, pressurized to 150 kPa, holds the pesticide at a height of 0.80 meters. Liquid flows from the tank through a 1.9 meter pipe with a diameter of 0.015 meters, angled at 0.698 radians, ultimately reaching a 0.007 meter nozzle that sprays the pesticide. Accurate calculation of the system&#39;s flow rate is crucial to ensure uniform application, and this is achieved by first determining the flow velocity within the connecting pipe.
The design requires an understanding of fluid mechanics principles. At the outset, the velocity of the fluid in the tank at Point 1 is zero, with the pressure set to 150 kPa. Point 2, located at the nozzle, is assumed to be open to the atmosphere, with a pressure of zero. The height difference between Points 1 and 2, calculated using the 0.698-radian pipe angle and pipe length, determines the elevation change component in the Bernoulli equation. This height difference is found by multiplying the pipe length by the sine of the inclination angle.
To connect the parameters at Points 1 and 2, a modified Bernoulli equation is used, accounting for energy losses due to friction and the nozzle&#39;s loss coefficient. The equation expresses the pressure, velocity, and elevation terms for both points as follows:
<img alt="Equation 1" src="/files/ftp_upload/18085/18085_PT_equation_1.svg" style="text-align: center; height: 30px;" />
Here, p represents pressure, &#961; the fluid density, V the velocity, g the gravitational acceleration, z1 the height of the pesticide inside the tank, and z2&#160; the nozzle height above the bottom of the tank. With values substituted for these terms, the flow velocity in the pipe at Point 1 is solved.
After calculating the pipe&#39;s flow velocity, the flow rate, Q, is determined by multiplying this velocity by the cross-sectional area A of the pipe:
<img alt="Equation 2" src="/files/ftp_upload/18085/18085_PT_equation_2.svg" style="text-align: center; height: 11px;" />
Where A is:
<img alt="Equation 3" src="/files/ftp_upload/18085/18085_PT_equation_3.svg" style="text-align: center; height: 25px;" />
This flow rate calculation ensures that the pesticide is delivered at a consistent and effective rate, optimizing pest control application.

パイプ流量測定:問題解決

Consider a spray tank system designed to evenly apply pest-control liquid to plants.
The system includes a pressurized tank at 150 kPa filled with ...

Design Example: Designing a Residential Plumbing System

The design of residential plumbing systems requires carefully evaluating water demand, flow rates, and pressure dynamics to ensure both efficiency and reliability. The nature of water flow within pipes is defined by its Reynolds number, which classifies flow as either laminar (smooth) or turbulent.
<img alt="Equation 1" src="/files/ftp_upload/18086/18086_Equation_1.svg" style="text-align: center; height: 42px;" />
This dimensionless value depends on factors such as water velocity and pipe. Residential plumbing systems are designed to meet specific water demand and flow rate requirements based on occupancy and fixture needs.
Determining the nature of water flow &#8212; laminar or turbulent &#8212; requires calculating the Reynolds number, which depends on variables like pipe diameter and water velocity. In residential settings, flow is often turbulent, leading to higher energy loss due to friction, which impacts system efficiency. Energy losses, or head losses, arise as water moves through pipes. These losses are classified as either major or minor. Major losses from friction along pipe walls are calculated using the Darcy-Weisbach equation.
<img alt="Equation 2" src="/files/ftp_upload/18086/18086_Equation_2.svg" style="text-align: center; height: 42px;" />
The Darcy-Weisbach equation requires a friction factor, which is obtained from the Moody chart. This chart accounts for pipe roughness and flow characteristics, which significantly affect turbulent flow friction levels. Minor losses, in contrast, are caused by fittings, bends, and valves, each of which contributes resistance to flow. Each fitting is assigned a loss coefficient that quantifies its resistance and is factored into the total head loss.
<img alt="Equation 3" src="/files/ftp_upload/18086/18086_Equation_3.svg" style="text-align: center; height: 48px;" />
By adding major and minor losses, the overall head loss can be determined and managed so as to maintain adequate pressure, avoiding potential leaks or damage. Flow measurement devices like Venturi or orifice meters ensure the plumbing system provides the necessary flow rates. These meters measure flow rates by detecting pressure differences across constrictions in the pipe, confirming that water flow meets design specifications and household needs.

設計例: 住宅用配管システムの設計

The residential plumbing system is designed by assessing the building&#39;s water demand and flow rate needs based on occupancy and fixture requirements.
...

Single Pipe Systems

In pipe flow analysis, problems are typically categorized into three types &#8212; Type I, Type II, and Type III &#8212; based on the known parameters and the desired outcome. Each type of problem addresses specific engineering requirements using fluid properties, pipe characteristics, and operational conditions.
In a Type I problem, fluid properties (density and viscosity), pipe characteristics (including diameter, length, and surface roughness), and the flow rate or average velocity are known. The objective is calculating the pressure drop or head loss needed to maintain the specified flow rate. For instance, in a heating system circulating hot water at 0.32 liters per second, knowing the system&#39;s fluid and pipe specifications allows engineers to determine the required pressure to achieve steady flow. Type I problems are common in designing HVAC systems, where maintaining consistent flow is essential for effective temperature control.
A Type II problem provides the applied pressure, fluid properties, and pipe details, to calculate the resulting flow rate. This type of analysis is used in applications such as garden irrigation, where engineers need to determine the water flow rate in a sprinkler system operating at a specified pressure, such as 276 kilopascals. Knowing the pipe dimensions and roughness, the flow rate reaching each sprinkler can be calculated to ensure adequate water distribution.
In a Type III problem, the known parameters include the pressure drop and desired flow rate, to determine the optimal pipe diameter to support efficient flow. This scenario is typical in cooling systems or industrial piping design, where engineers must size the pipe to achieve a flow rate of 0.19 liters per second, balancing efficiency with minimal energy loss. Choosing an appropriate pipe diameter in Type III problems ensures the required flow rate while minimizing pressure losses and pump energy demands.
By systematically categorizing pipe flow problems, engineers can streamline analysis and ensure optimal design and performance for fluid transport systems in heating, irrigation, and industrial applications.

シングルパイプシステム

In pipe flow problems, scenarios are grouped by known information and desired calculation and are typically classified as Type I, II, or III.
In a Type I ...

Major Losses in Pipes

When a fluid flows through a pipe, it experiences energy losses due to frictional resistance along the pipe walls, known as major losses. These energy losses result in a pressure drop, which varies based on the flow conditions &#8212; whether laminar or turbulent &#8212; and the specific physical properties of the fluid and pipe.
Fluid flow can be classified as laminar or turbulent, primarily based on the Reynolds number. This dimensionless number reflects the relative influence of inertial to viscous forces in the fluid. In laminar flow (Re &#60; 2000), the fluid flows in parallel layers, or streamlines, with minimal cross-stream mixing. Here, the pressure drop mostly depends on the fluid&#39;s viscosity and is generally lower. In contrast, turbulent flow (Re &#62; 4000) is characterized by chaotic eddies and swirling motions. In this regime, the pressure drop is influenced not only by viscosity but also by the roughness of the pipe wall, as these irregularities disrupt the flow further, increasing energy losses.
The pressure drop in a pipe depends on several factors: fluid properties, flow velocity, pipe characteristics, and dimensionless numbers.
The Darcy-Weisbach equation is the standard approach for quantifying the pressure drop due to frictional losses in pipe flow:
<img alt="Equation 1" src="/files/ftp_upload/18080/18080_Equation_1.svg" style="text-align: center; height: 30px;" />
Where:
<ol style="list-style-type: circle;">
	<li>&#916;P is the pressure drop,</li>
	<li>f is the friction factor,</li>
	<li>L is the length of the pipe,</li>
	<li>D is the pipe diameter,</li>
	<li>&#961; is the fluid density,</li>
	<li>v is the flow velocity.</li>
</ol>
The friction factor f is crucial for calculating pressure drops, especially in turbulent flow. It depends on the Reynolds number and the relative roughness of the pipe. Engineers often refer to the Moody chart, which provides empirical values of friction factors across flow regimes and roughness levels.
The Colebrook equation
<img alt="Equation 2" src="/files/ftp_upload/18080/18080_Equation_2.svg" style="text-align: center; height: 30px;" />
Where:
<ol style="list-style-type: circle;">
	<li>f is the friction factor,</li>
	<li>&#1013;/D is the relative roughness</li>
	<li>Re is the Reynolds number.</li>
</ol>
offers a precise method to calculate f for smooth and moderately rough pipes, but it is implicit and requires iterative solutions. To avoid iteration, approximations like the Haaland equation:
<img alt="Equation 3" src="/files/ftp_upload/18080/18080_Equation_3.svg" style="text-align: center; height: 30px;" />
Where:
<ol style="list-style-type: circle;">
	<li>f is the friction factor,</li>
	<li>&#1013;/D is the relative roughness</li>
	<li>Re is the Reynolds number.</li>
</ol>
are commonly used in practice, providing reasonably accurate friction factor values without extensive calculation. Understanding these dynamics enables engineers to design pipe systems that manage flow efficiently, compensating for potential pressure losses over time as pipe roughness increases.

パイプの主な損失

Consider &#160;a fluid flowing through a pipe; it encounters frictional resistance, causing energy losses known as major losses, resulting in a pressure ...

Minor Losses in Pipes

In pipe systems, minor losses refer to energy losses arising from components such as valves, bends, fittings, expansions, and other features that disrupt the steady flow of fluid. These disturbances cause energy dissipation through turbulence and resistance, which engineers quantify to manage system efficiency effectively.
Valves play a significant role in generating minor losses by obstructing or redirecting the fluid flow. When a valve is closed or partially closed, it restricts the flow path, creating additional resistance and inducing turbulence. The resulting energy dissipation depends on the valve&#39;s geometry, position, and flow path design. To quantify this effect, engineers use a loss coefficient, K, which scales with the square of the fluid velocity V as follows:
<img alt="Equation 1" src="/files/ftp_upload/18081/18081_Equation_1.svg" style="text-align: center; height: 30px;" />
where:
<ol style="list-style-type: circle;">
	<li>hLminor is the head loss due to the component,</li>
	<li>KL is the loss coefficient specific to the component geometry,</li>
	<li>V is the fluid velocity</li>
	<li>g is the acceleration due to gravity.</li>
</ol>
For ease of calculation, engineers often represent minor losses from fittings and valves as an equivalent length of straight pipe that would produce the same head loss.
At the entry point of a pipe, sharp edges or abrupt changes in flow area can cause the fluid to separate from the wall, creating turbulence and energy dissipation through viscous effects. This entrance loss contributes to the overall energy loss, depending on the pipe geometry and the flow velocity. When fluid exits a pipe, the kinetic energy disperses into the surrounding environment, creating an exit loss characterized by a unity loss coefficient, as all the kinetic energy is lost from the system.
Sudden expansions in the pipe create high-velocity jets that decelerate as they expand, dissipating energy through viscous effects. These expansions lead to additional energy losses as the fluid experiences abrupt pressure and velocity changes. Bends in the pipe also contribute to head loss, primarily due to flow separation and swirling motions induced by centripetal forces as the fluid changes direction. The frictional resistance over the length of the bend adds further to the overall head loss, with the degree of loss depending on the bend angle and radius.
Understanding these minor losses allows engineers to design pipe systems that manage energy dissipation effectively, optimizing flow efficiency and minimizing pressure drops across the system.

パイプの軽微な損失

Minor losses in pipe systems arise from components like valves, bends, and fittings that disrupt fluid flow, causing energy dissipation through turbulence ...

Multiple Pipe Systems

Multipipe systems consist of complex configurations of interconnected pipes designed to transport fluids efficiently across intricate networks. They are essential in engineering applications requiring precise control over flow distribution, pressure, and head loss. They are categorized into series, parallel, loop, and network configurations, each distinguished by unique flow characteristics and applications.
Series Configuration
In a series configuration, fluid flows sequentially from one pipe segment to the next, maintaining a constant flow rate throughout. This setup means each segment experiences the same flow rate, although head losses accumulate progressively across each section. The total head loss from an entry point A to an exit point B is the cumulative sum of head losses in each pipe, governed by the Darcy-Weisbach equation for head loss or similar empirical relationships. This configuration suits applications requiring a consistent flow rate along a fixed path, such as in specific water treatment processes.
Parallel Configuration
Parallel multipipe systems divide fluid flow across multiple paths, enabling a higher overall flow rate and reducing resistance across the network. Here, the total flow rate is the sum of the individual flow rates in each branch. However, a critical feature of parallel systems is that all paths experience the same pressure drop. Consequently, fluid particles in each path encounter identical head losses, regardless of the path taken. This arrangement is effective in systems needing efficient fluid distribution, such as in heating and cooling systems, where multiple paths ensure temperature control across large areas.
Loop and Network Configurations
In loop systems, the flow rate within one pipe is balanced by the combined flow rates of the other connected pipes, enabling fluid redistribution based on demand changes or localized resistance variations, such as in urban water distribution systems. Network configurations represent the most complex setup, involving numerous interconnected pipes with multiple inlets and outlets,such as in oil and gas pipeline networks. This flexibility allows for multiple flow directions, enhancing transport efficiency and adaptability to dynamic system demands.
Applications of Multipipe Systems
Multipipe systems are indispensable in several engineering sectors. Municipal water supply networks often use network configurations to ensure consistent pressure and reliable delivery across urban areas. In deepwater oil and gas pipelines, multipipe systems help manage the challenging pressures and flow conditions of underwater environments. Additionally, industrial cooling systems benefit from the controlled fluid distribution provided by parallel configurations, which improve heat dissipation and maintain optimal temperatures in manufacturing processes.

マルチパイプシステム

Multiple pipe systems consist of interconnected pipes that regulate fluid flow across complex networks.
They can be arranged in series, parallel, loop, or ...

Turbulent Flow: Problem Solving

Carbonation is a process used to dissolve carbon dioxide gas in a liquid, commonly used in the production of carbonated beverages. Achieving efficient carbonation requires careful control of temperature, pressure, and flow conditions. By adjusting these parameters, carbonation efficiency can be maximized, producing a higher concentration of CO2&#160;in the liquid.
Temperature is a key factor in CO2 solubility. In this case, the CO2 gas and the liquid are cooled to 20&#176;C. Lower temperatures enhance the solubility of CO2, enabling a greater volume of gas to dissolve within the liquid. At this temperature, the CO2&#160;gas is pressurized to approximately 550 kPa. Elevated pressure increases the partial pressure of CO2&#160;over the liquid, further driving dissolution.
CO2 is pumped through a connecting pipe between two tanks, where the flow characteristics are crucial for maintaining steady carbonation. The high Reynolds number, defined as greater than 4000, indicates that the flow is turbulent rather than laminar. Turbulent flow improves gas-liquid contact by promoting mixing, which enhances CO2&#160;dissolution in the liquid. The Reynolds number (Re) is calculated using the equation:
<img alt="Equation 1" src="/files/ftp_upload/18079/18079_Equation_1.svg" style="text-align: center; height: 30px;" />
where:
<ol style="list-style-type: circle;">
	<li>&#961; is the density of CO2,</li>
	<li>v is the velocity of flow,</li>
	<li>D is the pipe diameter,</li>
	<li>&#956; is the dynamic viscosity of CO2.</li>
</ol>
The flow rate of CO2&#160;in this system is controlled by the pipe&#39;s cross-sectional area and the velocity of the gas. To maintain turbulent conditions, the flow velocity v is adjusted based on the desired Reynolds number, which allows the required pipe diameter to be calculated.
The Reynolds number equation can be rearranged to determine the pipe diameter for the required turbulent flow. The&#160;dynamic viscosity &#956; of CO2&#160;at 20&#176;C are obtained using physical property tables. The optimal pipe diameter can be calculated by substituting these values along with the target Reynolds number and flow velocity into the equation. This configuration ensures efficient CO2&#160;transport through the system, optimizing the liquid&#39;s carbonation conditions.

乱流:問題解決

Consider a liquid that needs to be carbonated. Both the liquid and the carbon dioxide gas are cooled. The temperature is selected as 20 degrees Celsius to ...

Laminar Flow: Problem Solving

Laminar flow occurs when a fluid moves smoothly in parallel layers with minimal mixing and turbulence. In fluid mechanics, ensuring laminar flow within a pipe is essential for precise control of flow characteristics, especially in engineering applications. The key factor in determining whether flow remains laminar is the Reynolds number, a dimensionless quantity that depends on the fluid&#39;s velocity, density, viscosity, and the pipe&#39;s diameter. A Reynolds number of 2100 or lower indicates laminar flow, while higher values lead to turbulence.
For air flowing through a pipe at standard atmospheric conditions and a given mass flow rate, the velocity of the fluid must be controlled to maintain laminar conditions. Since velocity depends on the flow rate and the cross-sectional area of the pipe, the pipe diameter plays a crucial role. By substituting the velocity expression into the Reynolds number formula and solving for the diameter, it is possible to determine the minimum required pipe size.
Using standard values for air density and viscosity at 300 Kelvin, the volumetric flow rate can be computed. This, in turn, allows for the calculation of the necessary pipe diameter. To ensure a Reynolds number of 2100 or lower, the minimum allowable diameter for the pipe is found to be approximately 0.46 meters. This calculation ensures that the flow remains smooth and predictable, avoiding turbulence that could disrupt performance.

層流:問題解決

Consider air flowing through the pipe at 300 Kelvin at standard atmospheric pressure, with a mass flowrate of 0.0163 kilograms per second. If the flow is ...

Turbulent Flow

Turbulent flow is characterized by unpredictable fluctuations in velocity and pressure, which result in a chaotic fluid movement distinct from the orderly patterns of laminar flow. While laminar flow is governed by smooth, parallel layers with minimal mixing, turbulent flow exhibits highly irregular, three-dimensional patterns. This behavior arises due to instabilities in the fluid&#39;s velocity profile, and amplifies as the flow velocity increases. Minor disturbances, known as turbulent spots, appear once the flow reaches a critical speed. When the Reynolds number &#8212; a dimensionless quantity expressing the ratio of inertial to viscous forces in a fluid &#8212; exceeds a threshold of around 4,000, these spots coalesce, generating fully developed turbulence.
Structure of Turbulent Flow in Pipes
In pipe systems, turbulent flow comprises three distinct regions: the viscous sublayer, the buffer layer, and the outer layer. The viscous sublayer forms close to the pipe wall, a thin boundary where viscous forces dominate, and the flow behaves similarly to laminar flow. Here, velocity follows a near-linear profile influenced by fluid viscosity, providing a stable region within the otherwise chaotic turbulent flow.
Above the viscous sublayer lies the buffer layer, a transitional zone where viscous and turbulent forces contribute to fluid motion. This region is marked by a logarithmic velocity profile that conforms to the logarithmic law of the wall, representing a balance between viscous and turbulent interactions. Further from the wall, turbulent eddies drive fluid movement in the outer layer, promoting rapid mixing and random motion across the flow.
Engineering Applications of Turbulent Flow
The chaotic nature of turbulent flow makes it advantageous in numerous engineering applications where mixing and energy dissipation are crucial. For instance, wastewater treatment systems rely on turbulent flow to enhance the mixing of chemicals, promoting efficient contaminant removal. In hydraulic engineering, turbulent flow dissipates energy in spillways, preventing structural damage by controlling water velocity. The turbulent mixing process also reduces river sediment buildup, maintaining navigable waterways and protecting aquatic ecosystems.

乱流

Turbulent flow is a fluid movement marked by chaotic shifts in pressure and velocity.
Unlike laminar flow, turbulent flow displays complex, irregular ...

General Characteristics of Pipe Flow II

When fluid enters a pipe, it first passes through the entrance region, where the velocity profile adjusts due to viscous effects. In this region, a boundary layer forms along the pipe walls and grows until it fully occupies the pipe&#39;s cross-section. Once the boundary layer merges, the flow becomes fully developed, with a steady velocity profile that remains consistent along the pipe&#39;s length.
The distance to reach a fully developed flow is called the entrance length and depends on the flow regime (laminar or turbulent) and the Reynolds number. Laminar flow typically has a shorter entrance length due to its smooth, gradual profile development, whereas turbulent flow requires a longer entrance length due to enhanced mixing and chaotic motion.
A pressure difference along the pipe&#39;s length drives fully developed flow in a constant-diameter pipe. In horizontal pipes, this pressure difference overcomes viscous forces, ensuring steady motion. The entrance region has a higher pressure gradient to account for acceleration as the velocity profile evolves. Once fully developed, the pressure gradient stabilizes, reflecting the energy needed to overcome viscosity.
Shear stress behaves differently in laminar and turbulent flows. In laminar flow, shear stress arises from molecular momentum transfer, resulting in smooth, orderly layers. Turbulent flow stems from momentum exchange between more significant, irregularly moving fluid particles, making it a macroscopic effect. These differences influence pressure distribution and flow characteristics.
For inclined pipes, gravity modifies the pressure gradient. Depending on the pipe&#39;s orientation, gravity can assist or resist flow, altering the force balance required for steady motion. The viscosity, pressure, and gravity interplay determine fluid behavior within the pipe.

パイプフローの一般特性II

As fluid enters a pipe, it first flows through an entrance region where the velocity profile adjusts, forming a boundary layer along the walls. This ...

Laminar Flow

Laminar flow represents a smooth, orderly fluid motion where particles move along parallel paths, resulting in minimal mixing between layers. Streamlined particle paths characterize this flow regime and occur under conditions where viscous forces dominate over inertial forces. The distinction between laminar, transitional, and turbulent flow is primarily determined by the Reynolds number, a dimensionless quantity calculated as:
<img alt="Equation 1" src="/files/ftp_upload/18076/18076_Equation 1.svg" style="text-align: center; height: 30px;" />
where &#961; is the fluid density, v is the flow velocity, D is the pipe diameter, and &#956; is the dynamic viscosity. A Reynolds number below approximately 2100 indicates laminar flow, while values above 4000 denote turbulent flow. Transitional flow occurs between these ranges as the fluid shifts from laminar to turbulent.
Velocity Profile and Entrance Length
In a pipe, fluid initially entering develops a velocity profile over a length known as the entrance length. During this phase, the flow transitions from a uniform profile at the inlet to a fully developed parabolic profile, where the velocity is highest at the center and gradually decreases toward the pipe walls due to viscous forces. The entrance length is a function of the Reynolds number and pipe characteristics, typically shorter in turbulent flow and longer in laminar flow. Once fully developed, the parabolic velocity profile remains stable unless disrupted by changes in pipe geometry, allowing consistent analysis of flow behavior along the pipe&#39;s length.
Energy Loss and Hagen-Poiseuille Law
Laminar flow is advantageous in minimizing energy loss, as the pressure drop along the pipe is dominated by viscous forces rather than turbulence. The relationship between pressure drop and flow rate in a fully developed laminar flow is defined by the Hagen-Poiseuille equation:
<img alt="Equation 2" src="/files/ftp_upload/18076/18076_Equation 2.svg" style="text-align: center; height: 30px;" />
where &#916;P is the pressure drop, &#956; is the dynamic viscosity, L is the pipe length, Q is the volumetric flow rate, and R is the pipe radius. This equation shows that the pressure drop in laminar flow is directly proportional to flow rate and fluid viscosity and inversely proportional to the fourth power of the pipe radius, highlighting the significant impact of pipe diameter on energy efficiency.
Applications of Laminar Flow
Laminar flow conditions are essential in applications that require smooth, predictable fluid motion with minimal mixing. Wastewater treatment systems, for example, benefit from laminar flow to avoid excessive energy loss and facilitate controlled fluid handling. In canal designs for irrigation, laminar flow promotes even distribution without turbulent disturbances, enhancing water delivery efficiency. Hydropower systems can also leverage laminar flow for more efficient energy conversion, particularly in sections where consistent, low-energy flow is needed.

層流

Laminar flow refers to the smooth, orderly motion of fluid particles in which each particle follows parallel paths with minimal mixing between layers.
The ...

General Characteristics of Pipe Flow I

Pipe flow refers to the movement of fluids within fully enclosed conduits, typically cylindrical in shape, such as water pipes or hydraulic hoses. These conduits are designed to withstand high-pressure gradients that drive fluid movement, contrasting with open-channel flows, where gravity is the primary driving force. Rectangular conduits, like air conditioning and heating ducts, generally operate at lower pressures and are less suited for high-pressure applications.
The classification of fluid flow in pipes was pioneered by Osborne Reynolds through his foundational dye injection experiments. Reynolds identified three flow regimes &#8212; laminar, transitional, and turbulent &#8212; based on fluid velocity. At low velocities, the dye maintained a smooth streakline, indicating laminar flow, where fluid particles follow orderly, parallel paths. As velocity increased, the dye began to oscillate, marking the transitional regime, and at higher velocities, it dispersed unpredictably in the turbulent regime, where random, chaotic motion dominates.
These observations led to the development of the Reynolds number, a dimensionless quantity that indicates the balance of inertial and viscous forces in the flow. The Reynolds number is calculated based on fluid velocity, density, viscosity, and pipe diameter and serves as an indicator of flow type: laminar for values below 2100, turbulent for values above 4000, and transitional in the range between. In laminar flow, velocity remains steady over time, while turbulent flow exhibits unsteady, fluctuating velocities with random components perpendicular to the pipe axis. By calculating the Reynolds number, engineers can predict flow behavior in pipe systems, aiding in the design and optimization of pipelines, hydraulic systems, and fluid transport networks across various industries.

パイプフローの一般的な特性I

Pipe flow describes fluid movement through enclosed, fully-filled conduits, typically cylindrical pipes like water pipes or hydraulic hoses, engineered to ...

Design Example: Creating a Hydraulic Model of a Dam Spillway

Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
<img alt="Equation 1" src="/files/ftp_upload/18074/18074_Equation_1.svg" style="text-align: center; height: 38px;" />
Through this controlled setup, researchers can closely examine how water flows over the spillway, supporting a detailed analysis of its performance. A fundamental principle behind these models is using Froude number similarity, which preserves the proper balance between gravitational and inertial forces.
<img alt="Equation 2" src="/files/ftp_upload/18074/18074_Equation_2.svg" style="text-align: center; height: 38px;" />
This similarity is essential, as it ensures that free-surface flow characteristics, including wave formation, turbulence, and flow separation, behave as they would in the full-sized structure. By achieving this accurate representation, scaled models provide valuable insights into how water interacts with spillway features, helping to pinpoint areas where the design might benefit from adjustments to enhance safety or flow efficiency.
In the scaled model, adjustments are also applied to discharge rates, flow velocities, and timing to reflect real-world conditions without requiring extensive water volumes or prolonged test durations. The discharge rate, for example, is reduced by the scale factor to maintain manageable flow rates, enabling safe experimentation.
<img alt="Equation 3" src="/files/ftp_upload/18074/18074_Equation_3.svg" style="text-align: center; height: 36px;" />
Additionally, time is compressed so that events unfolding over an entire day in the full-scale structure can be examined in just a few hours within the model.
<img alt="Equation 4" src="/files/ftp_upload/18074/18074_Equation_4.svg" style="text-align: center; height: 48px;" />
This efficient scaling supports rapid testing and analysis of different flow conditions and potential structural responses. Overall, scaled modeling of spillways is crucial for assessing designs, identifying potential vulnerabilities, and confirming that the full-scale structure will perform reliably under various water flow conditions.

設計例: ダムの余水吐の水理モデルの作成

A hydraulic model of a dam spillway is often created by scaling down the design, typically to a 1:15 ratio, to replicate key flow characteristics such as ...

Dimensionless Groups in Fluid Mechanics

Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in open-channel flows and coastal engineering.
The Euler number (Eu) indicates the ratio of pressure forces to inertial forces and is used to calculate pressure drops in systems such as pipelines and across valves. The Cauchy number (Ca), representing the ratio of inertial to elastic forces, is critical in compressible fluid flow analysis and the study of shockwaves. The Mach number (Ma) compares the flow speed to the speed of sound, making it crucial for studies in supersonic flight and aeroelasticity.
The Strouhal number (St), which compares oscillatory frequency to inertial forces, finds applications in resonance studies, particularly vortex shedding around structures like bridge piers. Lastly, the Weber number (We), showing the ratio of inertial to surface tension forces, is vital in analyzing droplet formation, spray dynamics, inkjet printing, and fuel atomization processes. These groups enable the comparison of fluid behaviors across different scales and systems, supporting a broad range of fluid dynamics applications.

流体力学における無次元群

The dimensionless groups in fluid mechanics are ratios of physical quantities used to describe and analyze fluid behavior independently of units of ...

Correlation of Experimental Data

Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle&#39;s diameter, velocity, and the fluid&#39;s viscosity. These variables are grouped into dimensionless terms to form a relationship, but experimental data is needed to determine the exact nature of this relationship.
Researchers measure drag force while varying velocity to correlate the dimensionless groups, such as the Reynolds number. This correlation allows the relationship between drag and velocity to be expressed as a constant. Multiple tests verify this constant, confirming the dependency of drag on velocity.
If drag depends only on diameter, velocity, and viscosity, the relationship should be universal for any spherical particle in any fluid under consistent conditions. Multiple tests with different particles and fluids verify this universality, reducing the need for further experiments, as the derived constant remains valid under the specified conditions.

実験データの相関

A key use of dimensional analysis is to efficiently manage, interpret, and correlate experimental data.
Dimensional analysis alone cannot fully solve a ...

Typical Model Studies

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
<img alt="Equation 1" src="/files/ftp_upload/18073/18073_Equation_1.svg" style="text-align: center; height: 48px;" />
Practical constraints, however, can introduce geometric distortions, impacting how accurately these models represent the real system. Adjustments, such as increased model roughness, help bridge this gap, aligning flow behaviors between the model and the actual river environment.
For hydraulic structures like spillways, the focus shifts to achieving high Reynolds numbers to maintain dynamic similarity. This approach emphasizes balancing inertial and gravitational forces to replicate the prototype&#39;s behavior closely.
<img alt="Equation 2" src="/files/ftp_upload/18073/18073_Equation_2.svg" style="text-align: center; height: 45px;" />
Larger models are generally preferred, as they capture critical force interactions more effectively in full-scale designs. Although exact similarity across all scales may not be feasible due to physical and financial limitations, these larger models still allow close approximations of essential conditions.
Verification tests and prototype comparisons are key for refining model accuracy. Adjusting variables and calibrating outcomes ensure that the model reliably mirrors actual fluid flow behaviors. This predictive capability supports planning and design adaptations, making these models indispensable tools for assessing performance before moving to full-scale implementation.

典型的なモデルスタディ

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

Modeling and Similitude

Scaled modeling is a fundamental technique in engineering, enabling the study of large and complex systems by creating smaller, manageable replicas that recreate critical characteristics of the original. In hydrology and civil infrastructure, for example, scaled models of dams help analyze water flow, turbulence, and pressure. This method allows for accurate predictions of real-world behavior within a controlled environment, significantly reducing the cost and time involved in full-scale testing, which is often impractical. These models provide valuable insights into system performance under various conditions by ensuring that essential design elements match.
For the model to yield valid insights, it must maintain similitude, meaning the replica accurately reflects the prototype&#39;s behavior through geometric, kinematic, and dynamic similarity. Geometric similarity ensures the scaled model retains the same proportional dimensions as the actual structure, while kinematic similarity requires that motion characteristics match between model and prototype. Dynamic similarity further demands that forces acting within the model accurately replicate those in the real system, accounting for any scaling effects.
In fluid dynamics, the Froude number is a key dimensionless parameter that matches scaled models to their full-sized counterparts, especially for applications like ship design. The Froude number is defined as:
<img alt="Equation 1" src="/files/ftp_upload/18072/18072_Equation_1.svg" style="text-align: center; height: 60px;" />
where V represents velocity, g is the gravitational acceleration, and L is a characteristic length, often the ship&#39;s length. By equating the Froude numbers for both the model and the full-scale ships, the gravitational and inertial forces align, allowing the scaled model to accurately predict behaviors such as maneuverability, stability, and wave formation.

モデリングと類似性

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 ...

Determination of Pi Terms

The Buckingham Pi theorem is a valuable method in dimensional analysis, reducing complex relationships between variables into dimensionless terms. Relevant variables in analyzing the lift force on an airplane wing include lift force, air density, wing area, aircraft velocity, and air viscosity. Expressing each variable in terms of fundamental dimensions &#8212; mass, length, and time &#8212; provides a consistent foundation for constructing these dimensionless terms.
The theorem indicates that the number of Pi terms equals the total variables minus the number of fundamental dimensions. In this example, five variables and three dimensions result in two Pi terms. Air density, velocity, and wing area are selected as repeating variables, as they independently cover all dimensions. These repeating variables combine with lift force and viscosity to form dimensionless Pi terms.
<img alt="Equation 1" src="/files/ftp_upload/18069/18069_Equation_1.svg" style="text-align: center; height: 100px;" />
The first Pi term expresses the efficiency of lift generation, representing how lift depends on density, velocity, and area. The second Pi term accounts for the relative impact of viscosity, revealing how viscous forces interact with the wing in relation to inertia.
Each Pi term is verified as dimensionless, allowing complex aerodynamic behavior to be represented in simplified expressions. This approach enables the prediction and optimization of lift under various conditions, capturing the essential dynamics without needing to examine each factor individually.

円周率の用語の決定

To determine Pi terms using the Buckingham Pi theorem, consider the example of analyzing lift force on an airplane wing.
Relevant variables here include ...

The Buckingham Pi Theorem

The Buckingham Pi theorem provides a structured method to simplify fluid dynamics problems by reducing complex systems of variables to dimensionless terms.
<img alt="Equation 1" src="/files/ftp_upload/18068/18068_Equation_1.svg" style="text-align: center; height: 34px;" />
In analyzing flow through a pipe, variables that define the system include the pipe&#39;s diameter, the fluid&#39;s velocity, its density, and viscosity. These can be combined into a single dimensionless term, the Reynolds number (Re), which captures their essential relationship.
<img alt="Equation 2" src="/files/ftp_upload/18068/18068_Equation_2.svg" style="text-align: center; height: 38px;" />
The first step in applying the Buckingham Pi theorem is identifying the fundamental dimensions of each variable. In fluid mechanics, these are typically mass, length, and time. Here, the diameter represents length, velocity combines length and time, density encompasses mass and volume, and viscosity incorporates mass, length, and time.
<img alt="Equation 3" src="/files/ftp_upload/18068/18068_Equation_3.svg" style="text-align: center; height: 140px;" />
The theorem suggests that the number of independent dimensionless groups, known as Pi terms, is the difference in the number of variables k and the number of fundamental dimensions r. Only one dimensionless term is needed with four variables and three dimensions, simplifying analysis.
<img alt="Equation 4" src="/files/ftp_upload/18068/18068_Equation_4.svg" style="text-align: center; height: 32px;" />
This single term, the Reynolds number, compares inertial forces to viscous forces in the fluid. Establishing this ratio reveals whether the flow is likely to be smooth and orderly, known as laminar flow, or chaotic and irregular, known as turbulent flow. Lower values indicate laminar flow, where viscous forces dominate, and the fluid moves in parallel layers. Higher values reflect turbulent flow, where inertial forces lead to chaotic motion. The Buckingham Pi theorem&#39;s application in this context reduces complex interactions to a single term, making it easier to generalize flow behavior under varying conditions.

バッキンガム円周率の定理

Consider the flow through a pipe, where key variables include the pipe&#39;s diameter D, fluid velocity V, density &#961;, and viscosity &#956;.
To ...

Dimensional Analysis

Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional analysis is used to understand the behavior of fluids in systems such as pipelines, channels, and other structures common in civil engineering. Consider the example of fluid flow through a long, smooth-walled, horizontal circular pipe, which is typical in the design of water distribution systems or sewage networks. The pressure drop per unit length along the pipe depends on variables such as pipe diameter, fluid density, fluid velocity, and viscosity. According to dimensional analysis, the pressure drop can be expressed as a function of these variables:
<img alt="Equation 1" src="/files/ftp_upload/18067/18067_Equation_1.svg" style="text-align: center; height: 12px;" />
This formulation involves five independent variables, which can complicate the analysis. To simplify this, we can use dimensional analysis to reduce the number of variables into two dimensionless groups, thus streamlining the problem. Two important dimensionless groups that emerge from this analysis are the Reynolds number, which characterizes the flow regime, and the friction factor, which correlates with the pressure drop.
<img alt="Equation 2" src="/files/ftp_upload/18067/18067_Equation_2.svg" style="text-align: center; height: 30px;" />
Engineers use the dimensionless groups to generate a universal curve that applies to any smooth-walled pipe and incompressible Newtonian fluid. This curve would allow them to predict the pressure drop for different pipe sizes and fluids without performing numerous experiments for each possible combination.
<img alt="Figure 1" src="/files/ftp_upload/18067/18067_PT_Figure.svg" style="text-align: center; height: 250px;" />
This approach minimizes the time and cost required for experimentation and allows for more straightforward design decisions. Whether designing water distribution networks or analyzing pressure losses in irrigation systems, dimensional analysis is critical for any civil engineer.

寸法解析

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

Navier&#8211;Stokes Equations

For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting tangential stress to velocity differences between layers. Normal and shear stresses define the internal forces within a fluid that influence its movement.
The Navier-Stokes equations are derived by incorporating these stress relationships into differential equations of motion.
<img alt="Equation 1" src="/files/ftp_upload/18062/18062_Equation_1.svg" style="text-align: center; height: 106px;" />
These equations balance inertial, pressure, and gravitational forces in a viscous fluid and are fundamental to predicting fluid behavior under various conditions. The inertia term in the Navier-Stokes equations accounts for fluid acceleration, representing the fluid&#39;s resistance to changes in velocity. This term is critical in capturing the momentum conservation of a moving fluid, as it demonstrates how fluids resist sudden shifts in speed or direction.
The pressure gradient term within the Navier-Stokes equations drives fluid movement by creating a net force from areas of high pressure to low pressure. Meanwhile, the viscous terms represent internal friction arising from molecular interactions within the fluid. Depending on the velocity gradients present, these viscous forces act to slow down the fluid movement.
Each directional Navier-Stokes equation captures internal forces like viscous stress and external forces like gravity. These equations allow for predicting fluid motion in various conditions, from simple to complex flows. For steady or laminar flow scenarios, where flow is smooth and orderly, the equations become more manageable, enabling more straightforward analysis. This simplification is useful in controlled scenarios like boundary layer flow, where flow near a surface has a structured layer, and in Couette flow, describing fluid between two parallel surfaces moving at different velocities.

Navier–Stokes 方程式

In fluid motion under viscous conditions, shear stress is directly proportional to fluid deformation. In incompressible Newtonian fluids, this stress ...

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.
Considering two horizontal plates aligned along the x-axis and spaced a distance &#39;2h&#39; apart, with the y-axis perpendicular to the plates, fluid motion is assumed to be parallel. Here, the continuity equation indicates no change in velocity along the x-axis, and the Navier-Stokes equations reduce as follows:
<img alt="Equation 1" src="/files/ftp_upload/18063/18063_Equation_1.svg" style="text-align: center; height: 30px;" />
The equations in the y and z directions show no pressure gradient along these axes, indicating that pressure varies hydrostatically in the y-direction, allowing integration to yield:
<img alt="Equation 2" src="/files/ftp_upload/18063/18063_Equation_2.svg" style="text-align: center; height: 12px;" />
For parallel plates with a pressure gradient along the x-axis, the equation simplifies:
<img alt="Equation 3" src="/files/ftp_upload/18063/18063_Equation_3.svg" style="text-align: center; height: 30px;" />
By integrating twice and applying boundary conditions (u = 0 at y = +h and y = -h), we obtain:
<img alt="Equation 4" src="/files/ftp_upload/18063/18063_Equation_4.svg" style="text-align: center; height: 30px;" />
This expression reveals that the velocity profile across the gap between the plates is parabolic, with maximum velocity at y = 0, midway between the plates. The volumetric flow rate through a unit width of the plates is obtained by integrating the velocity profile across the gap.
Understanding laminar flow between parallel plates has practical applications in groundwater flow, wastewater treatment, and lubrication. For instance, this model can approximate flow in soil layers, where water moves between soil particles like flow between plates. Knowing the flow rate and velocity distribution helps engineers design efficient drainage systems and predict groundwater movement.

平行プレート間の安定した層流

Steady, laminar flow between two parallel plates describes fluid movement in a narrow, confined channel, often used to model simple fluid systems.
For ...

Plane Potential Flows

Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, &#981;, representing the flow speed in a given direction, and a stream function, &#968;, that visualizes the flow path, both governed by Laplace&#39;s equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform Flow
Uniform flow represents the simplest form of potential flow, with fluid moving in a straight line at a constant velocity. Streamlines are straight, parallel, and evenly spaced, clearly visualizing flow across channels or pipes with constant velocity. This flow type is essential in designing canals, pipelines and drainage systems, where the assumption of constant velocity aids in flow rate estimation and hydraulic design.
Source and Sink Flows
Source and sink flows describe radially symmetric flows originating from or converging to a point. In a source flow, fluid moves radially outward from a central point, while in a sink flow, it converges inward. These flows are modeled using a flow rate parameter to represent the strength of the source or sink. This model is widely used in groundwater hydrology, where source flows represent groundwater recharge, such as that from an injection well, and sink flows represent groundwater extraction in a pumping well.&#160; represent groundwater extraction from a pumping well., and sink flows simulate groundwater recharge .
Vortex Flow
Vortex flow involves fluid circulating a central point and appears in two forms: free and forced. In a free vortex, particles move in circular paths around a center point without external force, creating a whirlpool effect often observed in natural bodies of water. This model is used to design spillways and drainage systems that manage spiraling water flow to prevent clogging or turbulence. In a forced vortex, an external force drives the fluid&#39;s rotation, creating a scenario where the fluid rotates as a rigid body. Forced vortices are used in sedimentation tanks and certain hydraulic devices where uniform rotation aids in sediment separation and fluid mixing.
Flow Nets
In flow nets, streamlines represent the fluid flow path, while equipotential lines mark points of equal hydraulic potential. These lines intersect perpendicularly, creating a grid pattern that aids in identifying pressure distributions and potential seepage paths around structures. Flow nets are constructed to assess seepage in soil or porous media. Seepage rates are estimated by carefully analyzing the spacing and orientation of these lines and identifying potential areas of erosion or structural weakness.

平面ポテンシャル フロー

Plane potential flows simplify fluid motion by assuming irrotational and incompressible flow, governed by a velocity potential function and a stream ...

General Approach to the Physical Exam

Source: <a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
The examination of the body is fundamental to the practice of medicine. Since the Roman Empire, physicians have described the connection between alterations in function of specific parts of the body and specific disease states and have sought to further scientific understanding to improve bedside diagnosis. However, in this modern age of increasing technology within medical diagnostics, it is important to consider the role that physical examination plays today. It is misguided to believe that physical examination holds all the answers, and much has been written about the questionable utility of certain maneuvers previously held in high regard. It is equally misguided to suggest that physical examination plays little role in the modern patient encounter.
Physical examination remains a valuable diagnostic tool; there are many diagnoses that can only be made by physical examination. A diagnosis made by labs or imaging is rarely done in the absence of findings detectable at the bedside. As the provider conducts a history and physical, they are actively generating and testing hypotheses to explain the patient&#39;s condition. The information one gathers may not replace the need for testing, but having firm hypotheses in place allows the provider to order tests more judiciously and ask better questions of those tests. This, in turn, has the potential to reduce risk to the patient and save cost for the health care system. Finally, physical examination plays a critical role in the therapeutic relationship. By engaging in the time-honored ritual of physical examination, the clinician has the opportunity to develop rapport (by demonstrating attention and sensitivity) and promote healing through the deliberate and responsible use of touch.

Preliminary Diagnosis/Prognosis through Physical Examination

身体検査の一般的なアプローチ

Source: Jaideep S. Talwalkar, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
The examination of the body is fundamental to ...

Observation and Inspection

Source: <a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Observation and inspection is fundamental to physical examination and begins at the first point of contact with a patient. While observation and inspection are often used interchangeably, observation is a general term that refers to the careful use of one&#39;s senses to gain information. Inspection is an act limited to what one can observe visually, and when referring to physical examination, typically refers to findings on the surface of the body, rather than to behaviors. Skilled clinicians utilize all of their senses to assist with gaining an understanding of their patients, relying on vision, touch (percussion and palpation), and hearing (percussion and auscultation) primarily. Smell can also provide important diagnostic information during the patient encounter (e.g., personal hygiene, substance use, or metabolic diseases). Fortunately the sense of taste is largely a historical relic in medicine, though it is interesting to note that diabetes mellitus was diagnosed for many centuries by the sweet taste of the urine. Through experience, clinicians develop an important sixth sense - the gut instinct - that can only be gained through deliberate practice of clinical skills on thousands of patients over many years. The clinician&#39;s gut instinct, which is based largely on bedside observations, has been shown to be a strong predictor of serious illness. This video and the others in the clinical skills video collection are steps on the way to learning this level of mastery.

Inspection of the Skin, Eyes, Ears, Scalp and Medical History

観察・検査

Source: Jaideep S. Talwalkar, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Observation and inspection is fundamental to ...

Palpation

Source: <a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
The physical examination requires the use of all of the provider&#39;s senses to gain information about the patient. The sense of touch is utilized to obtain diagnostic information through palpation.
The specific parts of the examiner&#39;s hand used for palpation differ based on the body part being examined. Because of their dense sensory innervation, the finger pads are useful for fine discrimination (e.g., defining the borders of masses, lymph nodes) (Figure 1). The dorsal surface of the hand provides a rough sense of relative temperature (Figure 2). The palmar surfaces of the fingers and hands are most useful for surveying large areas of the body (e.g., abdomen) (Figure 3). Vibration is best appreciated with the ulnar surface of the hands and 5th fingers (e.g., tactile fremitus) (Figure 4).
While palpation is fundamental to the diagnostic aspect of the physical exam, it is also important to acknowledge the role that touch plays in communicating caring and comfort during the patient encounter. Patients generally perceive touch from a healthcare provider in a positive light, and their perceptions of a healthcare provider can be shaped by the skilled use of touch during clinical encounters.1 Physical contact has been associated with alterations in hormonal and neurotransmitter levels, specifically decreases in cortisol and increases in serotonin.2
Therefore, through the careful use of palpation, and touch in general, during the physical examination, the clinician has the opportunity to gain important diagnostic information, while developing rapport and promoting healing.
<img alt="Figure 1" src="/files/ftp_upload/10143/10143fig1.jpg" /> 
Figure 1. Lymph node examination with finger pads. 
<img alt="Figure 2" src="/files/ftp_upload/10143/10143fig2.jpg" /> 
Figure 2. Using the dorsum of hand to assess for warmth.
<img alt="Figure 3" src="/files/ftp_upload/10143/10143fig3.jpg" /> 
Figure 3. Abdominal palpation with palmar surface of fingers and hands. 
<img alt="Figure 4" src="/files/ftp_upload/10143/10143fig4.jpg" /> 
Figure 4. Using the ulnar surface of the hand to assess for tactile fremitus.

Palpation for Lymph Nodes, Abdomen and Tactile Fremitus

触診

Source: Jaideep S. Talwalkar, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
The physical examination requires the use of ...

Percussion

Source: <a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Simply stated, percussion refers to the striking of one object against another to produce sound. In the early 1700s, an Austrian inn-keeper&#39;s son, named Leopold Auenbrugger, discovered that he could take inventory by tapping his father&#39;s beer barrels with his fingers. Years later, while practicing medicine in Vienna, he applied this technique to his patients and published the first description of the diagnostic utility of percussion in 1761. His findings faded into obscurity until the prominent French physician Jean-Nicolas Corvisart rediscovered his writings in 1808, during an era in which great attention was focused on diagnostic accuracy at the bedside.1
There are three types of percussion. Auenbrugger and Corvisart relied on direct percussion, in which the plexor (i.e. tapping) finger strikes directly against the patient&#39;s body. An indirect method is used more commonly today. In indirect percussion, the plexor finger strikes a pleximeter, which is typically the middle finger of the non-dominant hand placed against the patient&#39;s body. As the examiner&#39;s finger strikes the pleximeter (or directly against the surface of the patient&#39;s body), sound waves are generated. If using indirect percussion, important information is gained from the vibration in the pleximeter finger, as well.2 The third type of percussion, auscultatory percussion, relies on the clinician using a stethoscope to discern differences in sounds created by the plexor finger.
The density of the structure underlying the site of percussion determines the tone of the percussion note; the denser the structure, the quieter the note. Notes differ in relative intensity, pitch, and duration, and help the examiner determine what lies below the skin surface. Knowledge of what particular locations on the body should sound like, in conjunction with the particulars of a specific clinical situation, can help a clinician determine if percussion notes in a particular patient are normal or not.

Clinical Percussion Examination: Direct, Indirect and Auscultatory

パーカッション

Source: Jaideep S. Talwalkar, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Simply stated, percussion refers to the ...

Auscultation

Source: <a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Through auscultation, the clinician is able &#34;to eavesdrop on the workings of the body&#34; to gain important diagnostic information.1 Historically, the term &#34;auscultation&#34; was synonymous with &#34;immediate auscultation,&#34; in which the examiner&#39;s ear was placed directly against the patient&#39;s skin. Although this was standard practice for centuries, the method proved inadequate in nineteenth-century France, due to social norms and suboptimal diagnostic yield. This led Ren&#233; La&#235;nnec to invent the first stethoscope in 1816 (Figure 1), a tool that has since become inseparable from auscultation in modern clinical practice, and patients hold it as a symbol of honor and trustworthiness among those who carry them.2
<img alt="Figure 1" src="/files/ftp_upload/10153/10153fig1.jpg" /> 
Figure 1. A representative illustration of the first stethoscope invented by Ren&#233; La&#235;nnec.
The stethoscope has undergone many technologic advances since La&#235;nnec&#39;s initial hollow wooden tube. Practically speaking, the provider must understand the difference between the two sides of the modern stethoscope&#39;s chest piece: the diaphragm and the bell (Figure 2).
<img alt="Figure 2" src="/files/ftp_upload/10153/10153fig2.jpg" /> 
Figure 2. Parts of a modern stethoscope.
When applied firmly against the patient&#39;s skin, the diaphragm transmits high frequency sounds. Sounds from within the patient vibrate the membrane of the diaphragm. These vibrations result in the propagation of sound through the column of air inside the stethoscope and into the examiner&#39;s ears. Conversely, when applied lightly, the bell transmits low frequency sounds. The bell acts as a cup that directly transmits sounds from within the patient through the tubing of the stethoscope. Pressing more firmly with the bell can stretch the underlying skin, essentially turning it into a diaphragm. Auscultation is used in a wide variety of clinical settings. It most commonly plays a role in the examination of the chest, heart, abdomen, and vasculature.

Auscultation and Working Mechanism of a Stethoscope

聴診

Source: Jaideep S. Talwalkar, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Through auscultation, the clinician is able ...

Proper Adjustment of Patient Attire during the Physical Exam

Source: <a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, and Joseph Donroe, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
In order to optimize the predictive value of the physical examination, the provider must perform maneuvers correctly. The proper use of drapes is an important component of correctly performing physical examination maneuvers. Skin lesions are missed when &#34;inspection&#34; occurs through clothing, crackles are erroneously reported when the lungs are examined through a t-shirt, and subtle findings on the heart exam go undetected when auscultation is performed over clothing. Accordingly, the best practice standards call for examining with one&#39;s hands or equipment in direct contact with the patient&#39;s skin (i.e., do not examine through a gown, drape, or clothing). In addition to its clinical value, the correct draping technique is important for improving the patient&#39;s comfort level during the encounter.
Like all other aspects of the physical exam, it takes deliberate thought and practice to find the right balance between draping, which is done to preserve patient modesty, and exposure, which is necessary to optimize access to the parts that need examination. Individual provider styles in the use of gowns and drapes vary considerably based on the site of practice, resource availability, and discipline within medicine. This video provides a general overview of some of the most common techniques used, combining techniques that utilize common draping approaches.

Patient Attire During Physical Exam; Use of Gowns and Drapes

身体検査中に患者の服装の適切な調整

Source: Jaideep S. Talwalkar, MD, and Joseph Donroe, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
In order to optimize the ...

Blood Pressure Measurement

Source: Meghan Fashjian, ACNP-BC, Beth Israel Deaconess Medical Center, Boston MA
The term blood pressure (BP) describes lateral pressures produced by blood upon the vessel walls. BP is a vital sign obtained routinely in hospital and outpatient settings, and is one of the most common medical assessments performed around the world. It can be determined directly with the intra-arterial catheter or by indirect method, which is a non-invasive, safe, easily reproducible, and thus most used technique. One of the most important applications of BP measurements is the screening, diagnosis, and monitoring of hypertension, a condition that affects almost one third of the U.S. adult population and is one of the leading causes of the cardiovascular disease.
BP can be measured automatically by oscillometry or manually by auscultation utilizing a sphygmomanometer, a device with an inflatable cuff to collapse the artery and a manometer to measure the pressure. Determination of the pulse-obliterating pressure by palpation is done prior to auscultation to give a rough estimate of the target systolic pressure. Next, the examiner places a stethoscope over the brachial artery of the patient, inflates the cuff above the expected systolic pressure, and then auscultates while deflating the cuff and observing the manometer readings. When the pressure in the cuff falls below the pressure in the brachial artery, the turbulent blood flow in a partially squeezed artery produces the Korotkoff audible sounds. The first audible Korotkoff sound signifies the maximum arterial pressure during systole. When the pressure in the cuff is reduced further and falls below the minimal arterial pressure (during diastole), the Korotkoff sounds become no longer audible. The reading at this point signifies the diastolic blood pressure. The blood pressure is measured in mmHg and recorded as a fraction (systolic BP/ diastolic BP).
In most instances, the vital signs are initially measured by a health care assistant or registered nurse (RN). The physician may choose to repeat the vital signs and blood pressure measurement after completion of the patient interview. Repeated measurement of blood pressure is especially important given the potential measurement errors and blood pressure variations.

Blood Pressure Measurement Using a Sphygmomanometer

血圧測定

Source: Meghan Fashjian, ACNP-BC, Beth Israel Deaconess Medical Center, Boston MA
The term blood pressure (BP) describes lateral pressures produced by ...

Measuring Vital Signs

Source: Meghan Fashjian, ACNP-BC, Beth Israel Deaconess Medical Center, Boston MA
The vital signs are objective measurements of a patient&#39;s clinical status. There are five commonly accepted vital signs: blood pressure, heart rate, temperature, respiratory rate, and oxygen saturation. In many practices, pain is considered the sixth vital sign and should regularly be documented in the same location as the other vital signs. However, the pain scale is a subjective measurement and, therefore, has a different value according to each individual patient.
The vital signs assessment includes estimation of heart rate, blood pressure (demonstrated in a separate video), respiratory rate, temperature, oxygen saturation, and the presence and severity of pain. The accepted ranges for vital signs are: heart rate (HR), 50-80 beats per minute (bpm); respiratory rate (RR), 14-20 bpm; oxygen saturation (SaO2), &#62; 92%; and average oral temperature, ~98.6 &#176;F (37 &#176;C) (average rectal and tympanic temperatures are ~1&#176; higher, and axillary temperature is ~1&#176; lower compared to the average oral temperature).
Vital signs serve as the first clue that something may be amiss with a patient, especially if the patient is unable to communicate. Although there are quoted normal ranges, each patient should be considered as an individual and not treated without taking into account the entire clinical picture.

Vital Signs: BP, Heart Rate, Temperature, Respiratory Rate and Oxygen Saturation

バイタル サインの測定

Source: Meghan Fashjian, ACNP-BC, Beth Israel Deaconess Medical Center, Boston MA
The vital signs are objective measurements of a patient&#39;s clinical ...

Respiratory Exam I: Inspection and Palpation

Source: <a href="https://www.jove.com/author/Suneel_Dhand">Suneel Dhand</a>, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Disorders of the respiratory system with a chief complaint of shortness of breath are among the most common reasons for both outpatient and inpatient evaluation. The most obvious visible clue to a respiratory problem will be whether the patient is displaying any signs of respiratory distress, such as fast respiratory rate and/or cyanosis. In a clinical situation, this will always require emergent attention and oxygen therapy.
Unlike pathology in other body systems, many pulmonary disorders, including chronic obstructive pulmonary disease (COPD), asthma, and pneumonia, can be diagnosed by careful clinical examination alone. This starts with a comprehensive inspection and palpation. Keep in mind that in non-emergency situations the patient&#39;s complete history will have been taken already, gaining important insight into exposure histories (e.g., smoking), which could give rise to specific lung diseases. This history can then confirm physical findings as the examination is performed.

Respiratory Exam I: Palpation, Chest and Peripheral Examination

呼吸試験 i: 検査と触診

Source: Suneel Dhand, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Disorders of the respiratory system with a chief ...

Respiratory Exam II: Percussion and Auscultation

Source: <a href="https://www.jove.com/author/Suneel_Dhand">Suneel Dhand</a>, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Learning the proper technique for percussion and auscultation of the respiratory system is vital and comes with practice on real patients. Percussion is a useful skill that is often skipped during everyday clinical practice, but if performed correctly, it can help the physician to identify underlying lung pathology. Auscultation can provide an almost immediate diagnosis for a number of acute pulmonary conditions, including chronic obstructive pulmonary disease (COPD), asthma, pneumonia, and pneumothorax.
The areas for auscultating the lungs correspond to the lung zones. Each lung lobe can be pictured underneath the chest wall during percussion and auscultation (Figure 1). The right lung has three lobes: the superior, middle, and inferior lobes. The left lung has two lobes: the superior and inferior lobes. The superior lobe of the left lung also has a separate projection known as the lingual.
<img alt="Figure 3" src="/files/ftp_upload/10041/10041fig1.jpg" /> 
Figure 1. Anatomy of lungs with respect to the chest wall. An approximate projection of lungs and their fissures and lobes to the chest wall anteriorly. RUL - right upper lobe; RML - right middle lobe; RLL - right lower lobe; LUL - left upper lobe; LLL - left lower lobe.

Respiratory Exam II: Percussion, Auscultation, Lung Lobes and Breath Sounds

呼吸試験 II: 打診と聴診

Source: Suneel Dhand, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Learning the proper technique for percussion and ...

Cardiac Exam I: Inspection and Palpation

Source: <a href="https://www.jove.com/author/Suneel_Dhand">Suneel Dhand</a>, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
The cardiac assessment is one of the core examinations performed by almost every physician whenever encountering a patient. Disorders of the cardiac system are among the most common reasons for hospital admission, with conditions ranging from myocardial infarction to congestive heart failure. Learning a complete and thorough cardiac examination is therefore crucial for any practicing physician.
If there is pathology in the heart or circulatory system, the consequences can also be manifested in other bodily areas, including the lungs, abdomen, and legs. Many physicians instinctively reach straight for their stethoscopes when performing cardiac exams. However, a large amount of information is gained before auscultation by going through the correct sequence of examination, starting with inspection and palpation.

Cardiac Exam I: Palpation, Chest and Peripheral Examination

心臓試験 i: 検査と触診

Source: Suneel Dhand, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
The cardiac assessment is one of the core ...

Cardiac Exam II: Auscultation

Source: <a href="https://www.jove.com/author/Suneel_Dhand">Suneel Dhand</a>, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Proficiency in the use of a stethoscope to listen to heart sounds and the ability to differentiate between normal and abnormal heart sounds are essential skills for any physician. Correct placement of the stethoscope on the chest corresponds to the sound of cardiac valves closing. The heart has two main sounds: S1 and S2. The first heart sound (S1) occurs as the mitral and tricuspid valves (atrioventricular valves) close after blood enters the ventricles. This represents the start of systole. The second heart sound (S2) occurs when the aortic and pulmonary valves (semilunar valves) close after blood has left the ventricles to enter the systemic and pulmonary circulation systems at the end of systole. Traditionally, the sounds are known as a &#34;lub-dub.&#34;
Auscultation of the heart is performed using both diaphragm and bell parts of the stethoscope chest piece. The diaphragm is most commonly used and is best for high-frequency sounds (such as S1 and S2) and murmurs of mitral regurgitation and aortic stenosis. The diaphragm should be pressed firmly against the chest wall. The bell best transmits low-frequency sounds (such as S3 and S4) and the murmur of mitral stenosis. The bell should be applied with a light pressure.

Cardiac Exam II: Auscultation and Lub-dub Heart Sounds

心臓試験 II: 聴診

Source: Suneel Dhand, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Proficiency in the use of a stethoscope to listen ...

Cardiac Exam III: Abnormal Heart Sounds

Source: <a href="https://www.jove.com/author/Suneel_Dhand">Suneel Dhand</a>, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Having a fundamental understanding of normal heart sounds is the first step toward distinguishing the normal from the abnormal. Murmurs are sounds that represent turbulent and abnormal blood flow across a heart valve. They are caused either by stenosis (valve area too narrow) or regurgitation (backflow of blood across the valve) and are commonly heard as a &#34;swishing&#34; sound during auscultation. Murmurs are graded from 1 to 6 in intensity (1 being the softest and 6 the loudest) (Figure 1). The most common cardiac murmurs heard are left-sided murmurs of the aortic and mitral valves. Right-sided murmurs of the pulmonary and tricuspid valves are less common. Murmurs are typically heard loudest at the anatomical area that corresponds with the valvular pathology. Frequently, they also radiate to other areas.
<img alt="Figure 1" src="/files/ftp_upload/10135/10135fig1.jpg" /> 
Figure 1. The Levine scale used to grade murmur intensity. 
In addition to the two main heart sounds, S1 and S2, which are normally produced by the closing of heart valves, there are two other abnormal heart sounds, known as S3 and S4. These are also known as gallops, because of the &#34;galloping&#34; nature of more than two sounds in a row. S3 is a low-pitched sound heard in early diastole, caused by blood entering the ventricle. S3 is a sign of advanced heart failure, although it can be normal in some younger patients. S4 is heard in late diastole and represents ventricular filling due to atrial contraction in the presence of a stiff ventricle. S4 is also heard in heart failure and left ventricular hypertrophy.

Cardiac Exam III: Abnormal Heart Sounds and Levine Scale

心臓試験 III: 異常な心臓の音

Source: Suneel Dhand, MD, Attending Physician, Internal Medicine, Beth Israel Deaconess Medical Center
Having a fundamental understanding of normal heart ...

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

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Science Education (臨床技術科学)

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Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)

Science Education (臨床技術科学)