behavior

JoVE Behavior documents observational and experimental techniques that seek to understand human and animal behavior. Work in this field includes analysis of genetic causes and physiological responses to internal or external stimuli as well as the implicated brain regions.

行为学

biochemistry

JoVE Biochemistry publishes experiments that investigate the structure, function, and interactions of biological molecules. The video articles in this section demonstrate methods to study nucleic acids, proteins, carbohydrates and lipids as well as enzyme function, protein folding, molecular interactions and biochemical reactions.

生物化学

bioengineering

JoVE Bioengineering merges both physical and life sciences to understand and predict biological processes. Applying physical science tools to life science questions allow for the discovery of better technologies to measure, diagnose, and clinically treat disease.

生物工程

biology

JoVE Biology welcomes all general biology research methodologies. Content in this section canvases all fields of cell, molecular, and organismal biology, ranging from new applications of standard techniques to novel approaches aimed at understanding the functions of life and living organisms. This diverse section includes, but is not limited to, techniques in physical biology, cellular biochemistry, genetics, physiology, systems biology and a combination of eukaryotic and prokaryotic model systems.

生物学

cancer research

JoVE Cancer Research illustrates experimental approaches in biomedical research and clinical practice aimed at understanding, detecting, treating and preventing cancer. The video articles in this section demonstrate methods to study the cellular and molecular mechanisms of cancer, animal models of cancer research, development of new therapies and diagnostics, tumor imaging, chemical and radiation treatments, surgical procedures and improvements in therapy. These video articles offer researchers and clinical practitioners an efficient way to learn the technologies and experimental methods in cancer research.

癌症研究

chemistry

JoVE Chemistry surveys a broad scope of chemical disciplines. This collection includes fundamental and applied research that investigates molecular interactions, properties, and structure spanning in the following core divisions: analytical, organic, organometallic, inorganic, bioinorganic, and biochemistry. This section also includes the design and preparation of materials and small molecules for advanced or unique applications.

化学

developmental biology

JoVE Developmental Biology publishes research methodologies in the field of developmental biology. This includes methods that are used to study biological development in vitro and in vivo at the molecular, cellular, tissue, organ and whole organism levels.

发育生物学

engineering

JoVE Engineering encompasses a broad range of experimental and instrumental techniques utilized in physics research. Investigations in this area strive to address and answer a broad range of scientific questions, such as device mechanisms and efficiencies, using physical tools. This approach often requires a combination of specialties, and research in this area tends to be interdisciplinary with contributions from mechanical, electrical, and chemical engineers.

工程学

environment

JoVE Environment is dedicated to research methodologies that address environmental concerns and seek to better understand Earth's ecosystem.  Special consideration is given to experimental methodologies that assess society’s impact on the environment, suggest solutions for protecting Earth’s resources, and develop sustainable fuel sources. Moving towards an environmentally conscious planet is a collaborative effort with contributions from both life and physical scientists.

环境科学

genetics

JoVE Genetics publishes video articles demonstrating experimental approaches to investigate gene function and regulation. This includes methods to study gene expression, mutagenesis, epigenetics, genetic determinants of development, genetic disorders, population genetics and evolution.

遗传学

immunology and infection

JoVE Immunology and Infection includes content from a variety of fields working toward a shared initiative of improving global health. Techniques evaluating the biological response to pathogens from the molecular to organismal level are presented as well as therapeutic agents and their efficacy in treating disease.

免疫与感染

medicine

JoVE Medicine serves as a connection between basic research and clinical applications. Articles may present medical procedures, case studies or clinical trial methodologies. Included studies are often modeled towards predictive, preventative, personalized, and practical approaches to treatment of disease. The goal of research methodologies in this section is to improve overall patient care and prognosis.

医学

neuroscience

JoVE Neuroscience is a multidisciplinary section devoted to investigations of the structure, function, physiology, and pathophysiology of the brain and nervous system. Included methodologies range from molecular and cellular level studies to full central and peripheral neural systems. Potential treatment platforms and surgical techniques for neurological diseases and disorders are also presented in this section.

神经科学

jove journal

JoVE Journal

经同行评审的多学科的科学视频期刊

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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.

管道流量测量

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

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.

设计示例：设计住宅卫浴系统

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

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.

管道流量测量：问题解决

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 ...

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.

单管系统

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 ...

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.

管道中的局部损失

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.

多管道系统

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

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.

管道中的重大损失

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

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.

湍流：问题解决

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 ...

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.

湍流

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.

管道流 II 的一般特性

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.

层流

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

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.

层流：问题解决

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 ...

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.

管道流 I 的一般特性

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.

设计示例：创建大坝溢洪道的水力模型

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.

流体力学中的无量纲群

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.

实验数据的相关性

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

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.

确定 Pi 项

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

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.

建模和模拟

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

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.

典型模型研究

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

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.

尺寸分析

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

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.

白金汉 Pi 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 ...

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.

纳维-斯托克斯方程

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

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.

平面电位流

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

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.

平行板之间的稳定层流

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

Safety Checks and Five Rights of Medication Administration

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

According to the 1999 Institution of Medicine (IOM) report titled To Err is Human: Building a Safer Health System, medication errors are significant contributors to avoidable patient deaths in the hospital environment. Therefore, to maintain patient safety and to avoid medication errors, it is important that every nurse adheres to at least five &#34;rights&#34; of safe medication administration. These five &#34;rights&#34; refer to the right patient, right medication, right medication dose, right time of administration, and right route of administration. The nurse should check for these five &#34;rights&#34; at three different checkpoints points in the mediation administration process: 1) while comparing the Medication Administration Record (MAR) when withdrawing medications, 2) while comparing the MAR to acquired medications, and 3) while comparing the MAR to both the medication and patient identifiers at the bedside. This video will demonstrate the acquisition component of medication administration, which consists of performing the five &#34;rights&#34; during the first, second, and third checkpoints.
Prior to acquiring medications from a medication dispensing system (MDS), the nurse must consider whether the medication is appropriate, given the patient&#39;s medical conditions, medication allergies, and current clinical status and when previous doses of the medication were administered. In addition, certain medications may need preparation prior to administration and prior to the second medication safety check. There are different electronic MAR software, including hardcopy MARs, as well as different types of MDS. The general steps for each system are the same, and although this video illustrates the steps performed using one of these software tools, the safety checks highlighted in this section are universally applicable.

安全检查和用药五权利

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

According to the 1999 Institution of Medicine ...

Preparing and Administering Oral Tablet and Liquid Medications

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Oral medications are the route most preferred by patients and are one of the most commonly used routes of medication administration by providers. Most oral preparations are taken by mouth, swallowed with fluid, and absorbed via the gastrointestinal tract. Oral medications are available in solid forms (e.g., tablets, capsules, caplets, and enteric-coated tablets) and liquids forms (e.g., syrups, elixirs, spirits, and suspensions). Most oral medications have a slower onset of action and, in the case of liquids and swallowed oral medications, may also have a more prolonged effect. Enteric-coated tablets are covered with material that prevents dissolution and absorption until the tablet reaches the small intestine. Additional oral medication routes (not shown in this video) include sublingual administration, in which the preparation is placed under the tongue to dissolve, and buccal administration, which involves placing the medication in the cheek area between the gums and mucus membranes to dissolve.
When preparing and administering oral tablets and liquid medications, the nurse must consider whether the medication is appropriate given the patient&#39;s medical conditions, medication allergies, and current clinical status and when previous doses of the medication have been administered. Patients with altered gastrointestinal function (e.g., vomiting and nausea) should not be given oral medications, since they would not be able to retain them. Oral medications are contraindicated in patients that are unconscious, uncooperative, or unable to swallow due to a medical problem. Medication administration also requires the nurse to be knowledgeable about the medication purpose, adverse effects, and patient preferences. This demonstration will present how to prepare and administer oral medications in both tablet and liquid forms (most common), including the five &#34;rights,&#34; and will discuss medication documentation.

拟备及管理口腔片和液体药物，

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Oral medications are the route most preferred ...

Preparing and Administering Topical Medications

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Topical medications are applied directly to the body surfaces, including the skin and mucous membranes of the eyes, ears, nose, vagina, and rectum. There are many classes of topical medications, such as creams, ointments, lotions, patches, and aerosol sprays. Medications that are applied to the skin to produce slow, controlled, systemic effect are also referred to as transdermal. Transdermal absorption can be altered if lesions, burns, or breakdowns are present at the application site. Many transdermal medications are delivered via adhesive patch to achieve the slow, controlled, systemic effect. The patch should be applied to clean and hairless skin areas that do not undergo excessive movement, such as the back of the shoulder or thigh. Other topical creams or eye ointments should be applied according to the packaging and manufacturer instructions using an application device. When instilling eardrop medications, never occlude the ear canal, as this may increase pressure and rupture the ear drum.
Medications that can be administered via a topical route include antibiotics, narcotics, hormones, and even chemotherapeutics. This requires adherence to the five &#34;rights&#34; of medication administration and three checks during the administration process to ensure the safe administration of these medications. Also, the administration of the topical medications requires wearing gloves to protect the healthcare provider from accidental exposure and absorption of the medication. Topical medications should never be applied with the bare hands. This video will demonstrate techniques of the safe administration of topical medications, including transdermal patch (skin), optical (eye), and otic (ear) application, within the context of the standards of safe medication practices.

Topical Transdermal Patch, Ophthalmic Medication and Otic Drop

拟备及管理局部药物

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Topical medications are applied directly to the ...

Preparing and Administering Inhaled Medications

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Inhaled medications are prescribed for conditions affecting the bronchi, which branch off of the trachea, and bronchioles, which are progressively smaller conducting airways spread throughout the lung tissue. These conditions can be classified as acute (i.e., temporary, with quick onset) or chronic (i.e., persistent and/or recurrent symptoms lasting months to years). Common acute conditions requiring inhaled medications include acute bronchitis, pneumonia, tuberculosis, pulmonary edema, and acute respiratory distress syndrome. Chronic conditions requiring inhaled medications encompass those classified as COPD (i.e., asthma, chronic bronchitis, and emphysema), as well as other chronic conditions, including cystic fibrosis, lung cancer, and pneumoconiosis.
These conditions often require medications to open airways, decrease airway inflammation, and promote airflow. The delivery of medications directly into the airways allows for a faster response when compared to systemically administered medications and decreases the impact of systemic side effects. Inhaled medications come in different forms and delivery devices. Common inhaled medications include short- and long-acting bronchodilators and corticosteroids. These may be delivered using various types of inhalation delivery devices, such as metered-dose inhalers, dry-powder inhalers, and breath-activated inhalers. These devices require either a chemical propellant, deep inhalation, or a fine mist to deliver the medication. Regardless of the type of delivery, the goal is the same: to deliver the medications to the lower bronchi and bronchioles. For those using metered-dose inhalers and who have difficulties inhaling the medications into the lower airways, a device called a spacer may be used to help coordinate breathing with medication release from the device.
Because these medications require administration that is coordinated with the breathing cycle, it is important to educate the patient about the procedure prior to administering the medication and for the patient to have a working understanding of the process before beginning inhaled medication administration. A thorough respiratory assessment should also be completed prior to administering any inhaled medication to ensure the appropriateness of the medication and delivery device and the ability to comply with administration procedure.
This demonstration will present the preparation and administration of inhaled medications using the metered-dose inhaler as the prototype delivery device.

Inhaled Medications: Bronchodilators and Corticosteroids

拟备及管理吸入的药物

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Inhaled medications are prescribed for ...

Preparing and Administering Subcutaneous Medications

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Subcutaneous medication administration is a parenteral approach to administer small amounts of medication (less than 2 mL) into the layer of tissue just below the skin. Common medications administered via the subcutaneous route include anticoagulant medications, such as heparin or enoxaparin; epinephrine administered for allergic reactions; insulin; and some immunizations.
Subcutaneous injection preparations are commonly provided in vials or ampules for withdrawal into a subcutaneous syringe. Subcutaneous needles have a shorter length and smaller diameter than syringes used for intramuscular injections, are typically less than 5/8th of an inch, and are 26 gauge or smaller. Medication absorption and onset is slower than for intravenous routes, with some absorption rates lasting 24 h or longer. This approach is selected for many medications that may be denatured or deactivated if given via the oral route, given the acidity of the gastrointestinal tract.
Subcutaneous injection preparations are commonly provided in vials or ampules for withdrawal into a subcutaneous syringe. The nurse should determine the appropriate medication dose according to the concentration provided on the container. This demonstration will present how to prepare and administer subcutaneous medications after the medication has been obtained from the medication dispensing device. The discussion also includes the five &#34;rights&#34; and the medication documentation in the electronic Medication Administration Record (MAR).

Subcutaneous Injections: Anticoagulant, Epinephrine and Insulin

拟备及管理皮下药物

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Subcutaneous medication administration is a ...

Preparing and Administering Intramuscular Injections

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Intramuscular (IM) injections deposit medications deep into the muscle tissue. Since muscle fibers are well perfused, this route of administration provides quick uptake of the medication and allows for the administration of relatively large volumes. Skeletal muscles have fewer pain-sensing nerves than subcutaneous tissue, which allows for the less painful administration of irritating drugs (e.g., chlorpromazine, an anti-psychotic). IM injections are recommended for patients unable to take oral medications and for uncooperative patients. Some examples of medications that are commonly delivered by IM injections include antibiotics, hormones, and vaccinations.
As in any other route of administration, the nurse must consider if the medication is appropriate, given the patient&#39;s medical conditions, allergies, and current clinical status. In addition, specifically for IM injections, it is important to assess the patient&#39;s muscle mass to determine the appropriate needle size. Also, if the patient has already received this injection, it is necessary to verify the injection site that was previously used and to ensure that the previous dose did not result in any adverse reactions.
The sites that are most commonly utilized for IM injections include the deltoid muscle of the shoulder; the vastus lateralis of the thigh; and the ventrogluteal, gluteus medius, or dorsogluteal muscles of the hip. It is best to avoid administering IM injections into the dorsogluteal muscle, because this location is associated with an increased risk of hitting a blood vessel, nerve, or bone.
This video will focus on the essential steps that every nurse should follow in order to correctly prepare and administer an IM injection.

Intramuscular Injection: Antibiotics, Hormones and Vaccinations

准备和肌内注射

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

Intramuscular (IM) injections deposit ...

Preparing and Administering Enteric Tube Medications

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

An enteric tube is a tube that is inserted and passed into the stomach or intestines. Enteric tubes serve multiple purposes, including stomach decompression (through the removal of air, gastric contents, and secretions), enteric feeding, and/or the administration of medications or oral contrast. Enteric tubes are indicated for patients with impaired swallowing and for patients with neurological or other conditions associated with an increased risk of aspiration, or when the patient is unable to maintain adequate oral intake of fluid or calories. There are multiple types of enteric tubes, with their generic names assigned according to the insertion site and the gastrointestinal termination point. For instance, one of the common tube types is the nasogastric tube, which is inserted through a nostril and passed along the upper gastrointestinal tract into the stomach.
When administering medications through an enteric tube, it is important to ensure that the tube terminates in the intended gastrointestinal location. When enteric tubes are initially placed, the position of the tube is verified by X-ray. However, due to gastric peristalsis, enteric tubes may migrate out of their intended termination location. Thus, it is important to confirm the appropriate tube location before administering the medications. Medications administered through an enteric tube are typically oral preparations that must either be crushed into powder by the nurse or prepared in suspension or liquid form by the pharmacy. Prior to crushing any oral medications, it is important to confirm that it is appropriate and safe to do so. For example, administering crushed extended-release medications can lead to toxic medication levels, and crushing medications with cytotoxic or carcinogenic properties can harm the healthcare worker. It is also important to consider the tube lumen size when administering medications, because smaller-bore tubes are more likely to become clogged if the medications are not prepared properly or are not flushed with an appropriate amount of fluid.
This video presents the process of assessing enteric tube placement and administering medications through an enteric tube.

Enteric Tube: Stomach Decompression, Feeding, Oral Medication

拟备及管理肠溶管药物

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT

An enteric tube is a tube that is inserted and ...

Peripheral Intravenous Catheter Insertion

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
The purpose of peripheral intravenous catheter (PIV) insertion is to infuse medications, perform intravenous (IV) fluid therapy, or inject radioactive tracers for special examination procedures. Placing a PIV is an invasive procedure and requires the use of an aseptic, no-touch technique. 
Common IV venipuncture sites are the arms and hands in adults and the feet in children. According to the Intravenous Nurses Society (INS), the feet should be avoided in the adult population because of the risk of thrombophlebitis. Venipuncture sites should be carefully assessed for contraindications, such as pain, wounds, decreased circulation, a previous cerebral vascular accident (CVA), dialysis fistulas, or a mastectomy on the same side. The median cubital vein and the cephalic vein in the wrist area should be avoided when possible. The cephalic vein has been associated with nerve damage when used for IV placements. The most distal site available on the hand or arm is preferred so that future venipuncture sites may be used if infiltration or extravasation occurs.
This video will demonstrate the insertion of a PIV, including the preparation and attachment of an IV extension set. Although a PIV securement device is used here to stabilize the IV catheter, according to INS recommendations, some facilities may not elect to purchase these devices, and the alternate chevron or U-shaped taping method may also be used.

Peripheral Intravenous Catheter Insertion: No Touch Technique

外周静脉导管插入

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
The purpose of peripheral intravenous catheter ...

Assessing and Flushing a Peripheral Intravenous Line

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
After peripheral intravenous (IV) access is initiated, it is important to assess and maintain the IV catheter according to institutional policies and nursing standards of practice. The regular assessment of the insertion site and the surrounding areas for signs of complications is necessary to prevent IV catheter complications, including infiltration, phlebitis, infection, extravasation, or catheter dislodgement. Routine IV maintenance is equally important to preserve line patency and to reduce the risk of occlusion, thrombosis, and thrombophlebitis. According to the CDC, peripheral IV catheters (PIV) may be kept in place for as long as 96 h, with proper care and maintenance. In addition, according to the Infusion Nurses Society (INS), a pediatric patient IV catheter may be kept in place until the IV line is no longer patent or it demonstrates complications. Routine rotation every 96 h is not indicated in the pediatric population due to increased anxiety caused by needle sticks. 
This video demonstrates the assessment and maintenance of peripheral IV lines, including general considerations before initiating the procedure, assessing the injection site for associated complications, and maintaining catheter patency by flushing it with the normal saline solution.

评估和法拉盛周边的静脉行

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
After peripheral intravenous (IV) access is ...

Initiating Maintenance IV Fluids

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Hospitalized patients frequently require the administration of intravenous (IV) fluids to maintain their fluid and electrolyte balance. Certain medical conditions that preclude oral fluid intake may necessitate IV fluid administration, with or without electrolytes, to prevent hypovolemia, dehydration, and electrolyte imbalances. Pre-surgical and pre-procedure patients who require anesthesia are often required to be NPO (i.e., nil per os; Latin for &#34;nothing by mouth&#34;) to prevent aspiration and to maintain hydration during the procedure. Post-surgical and post-procedure patients may also require IV fluid administration to increase intravascular volume following surgical blood loss.
IV fluids can be delivered by different types of administrations sets: gravity flow infusion devices, which rely on gravitation force to push the fluid to the patient&#39;s bloodstream, or infusion pumps, which use a pump mechanism that generates positive pressure. While administering maintenance IV fluids using an infusion pump is the most common approach, facility policy; availability of infusion pump equipment; and other limitations, such as a power outage, may necessitate the use of IV gravity tubing. This video describes the approach to initiate maintenance IV fluids using gravity tubing, as well as how to calculate and set the infusion drip rates.

Calculating and Setting Dip Rate of Intravenous Fluids

启动维护四流体

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Hospitalized patients frequently require the ...

Preparing and Administering IV Push Medications

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Intravenous (IV) push is the rapid administration of a small volume of medication into a patient&#39;s vein via a previously inserted IV catheter. Preparations for IV push administration are commonly provided in vials or ampules for withdrawal into a syringe. This method is used when a rapid response to a medication is required, or when the medication cannot be administered via the oral route. For instance, medications commonly administered via IV push are the ones used to treat moderate or severe pain.
Before administrating IV push, it is important to confirm the correct placement of the IV catheter, because the push medication can cause irritation and damage to the lining of the blood vessel and to surrounding tissues. Since IV push medications act quickly, the patients need to be closely monitored after the drug has been administered, and any error can be especially dangerous. It is imperative that the nurse adheres to the five &#34;rights&#34; and three checks of safe medication administration and is knowledgeable about the medication purpose and adverse effects. The nurse should determine the appropriate medication dose, based upon the medication concentration in the container. If the patient receives other IV medications, the nurse needs to ensure the compatibility of the IV push medication with other fluids present in the IV line and should understand the proper IV push administration rate of the medication. The following video will demonstrate how to prepare and administer an IV push injection.

拟备及管理四推药物

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Intravenous (IV) push is the rapid ...

Preparing and Administering Intermittent Intravenous Medications with an Infusion Pump

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Primary intermittent intravenous (IV) infusions are delivered alone as volume-controlled infusions, while secondary infusions are delivered with another IV fluid, usually maintenance fluids. Intermittent infusions are delivered over a specific amount of time, which is dictated by the type of medication, such as IV antibiotics. High-volume IV medications, anywhere from 50- to 500-mL infusions, are typically delivered using an infusion pump as either primary or secondary infusions. Infusion pumps deliver IV fluids in a volume-controlled manner, keeping medication side effects to a minimum and helping to prevent nurse medication errors. Careful review of the medication compatibility with maintenance fluids using an approved medication drug guide, pharmacy recommendations in the Medication Administration Record (MAR), and physician orders must be assessed prior to delivering an IV medication. This review will determine if primary or secondary delivery is appropriate based on the risk for patient harm, such as for concentrated electrolyte preparations like potassium.
Certain medical conditions that preclude oral fluid intake, specific medication preparations, or situations that require an increase in the blood concentration of the medication that is faster than possible through the GI tract may require IV medication administration. This video describes the approach to administer primary intermittent IV infusion medications using an IV infusion pump, including acquiring primary intermittent IV infusion medication, priming the IV tubing, preparing the patient, and programming the infusion pump. The infusion pump consists of a main pump PC unit (i.e., the brain) and interlocking modules or channels in which the IV tubing is contained. While the procedure outlines the steps for a specific brand of infusion pumps, the general concepts and principles are consistent across infusion pump brands, although the steps may vary slightly from brand to brand.

Administering Intermittent Intravenous Medications with an Infusion Pump

拟备及管理间歇静脉药物输液泵

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Primary intermittent intravenous (IV) infusions ...

Preparing and Administering Secondary Intermittent Intravenous Medications

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Secondary intravenous (IV) infusions are a way to administer smaller volume-controlled amounts of IV solution (25-250 mL). Secondary IV infusions are delivered over longer periods of time than IV push medications, which reduces the risks associated with rapid infusions, such as phlebitis and infiltration. In addition, some antibiotic medications are only stable for a limited time in solution. 
The secondary IV medication tubing is connected to the primary macrobore (large internal diameter) IV tubing and is therefore "secondary" to the primary infusion. The secondary solution bag is typically hung higher than the primary infusion bag and is subsequently "piggybacked" on top of the primary IV infusion. This higher position places greater gravitational pressure on the secondary IV solution. As a result, the primary infusion is temporarily paused until the secondary infusion volume has been delivered. This approach ensures that the medication is completely infused due to an immediate return of maintenance IV infusion in the IV line. The secondary IV infusion can be safely delivered when the patient's fluid volume status permits temporarily pausing the delivery of maintenance fluid and in hypervolemia patients. 
This video demonstrates the administration of secondary intermittent IV infusion medications using an infusion pump and using gravity tubing without an infusion pump. This will include a review of acquiring the intermittent secondary IV infusion medication, priming the secondary IV tubing, preparing the patient, calculating the medication administration rate, and setting the secondary IV drip rate.

Administering Secondary Intermittent Intravenous Medications

拟备及管理二级间歇静脉药物

Source: Madeline Lassche, MSNEd, RN and Katie Baraki, MSN, RN, College of Nursing, University of Utah, UT
Secondary intravenous (IV) infusions are a way ...

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