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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.

מדידת ספיקת צינור

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.

דוגמה עיצובית: תכנון מערכת אינסטלציה למגורים

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.

מדידת קצב זרימה בצנרת: פתרון בעיות

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.

מערכות צינור יחיד

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.

הפסדים קלים בצינורות

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.

מערכות צינורות מרובות

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.

הפסדים גדולים בצינורות

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.

זרימה טורבולנטית: פתרון בעיות

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.

זרימה טורבולנטית

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.

מאפיינים כלליים של זרימת צינור 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.

זרימה למינרית

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.

זרימה למינרית: פתרון בעיות

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.

מאפיינים כלליים של זרימת צינור 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.

דוגמה עיצובית: יצירת מודל הידראולי של מברץ סכר

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.

קבוצות חסרות ממד במכניקת זורמים

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.

קורלציה של נתוני ניסוי

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.

קביעת תנאי Pi

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.

דוגמנות ודמיון

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.

מחקרי מודל אופייניים

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.

אנליזה ממדית

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.

משפט בקינגהאם פי

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.

משוואות נאוויה-סטוקס

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.

זרימות פוטנציאליות מישוריות

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.

זרימה יציבה ולמינרית בין לוחות מקבילים

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

Imaging Biological Samples with Optical and Confocal Microscopy

Source: <a href="https://www.jove.com/author/Peiman_Shahbeigi-Roodposhti">Peiman Shahbeigi-Roodposhti</a> and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
Optical microscopes have been around for centuries, and while they reached their theoretical limitation of resolution decades ago, new equipment and techniques, such as confocal and digital image processing, have created new niches within the field of optical imaging. The best optical microscopes will typically have a resolution down to 200 nm in ideal conditions. However, optical microscopes are limited by the diffraction of waves, a function of the wavelength, which is around 500 nm for visible light. While the resolution of optical microscopes does not reach that of electron microscopes, they are the most valuable tools in the imaging of biological macrostructures and are a staple in any biological lab.
In conventional light microscopes, the signal produced from the imaged object is from the full thickness of the specimen, which does not allow most of it to be in focus to the observer. This causes the image to have &#34;out of focus blur&#34;. The confocal microscope, on the other hand, illuminates the sample through a pin-hole, and is therefore able to filter out the out-of-focus light from above and below the point of focus in the object.
This demonstration provides an introduction to image acquisition using optical and confocal microscopy methods. Here, a sectioned piece of mouse brain will be studied.&#160; Image acquisition and analysis, including the tools to generate topographical maps and composite images, will be covered. The advantages and disadvantages of different imaging methods as they relate to resolution, depth of focus and sample type will also be discussed. The purpose of this demonstration is to provide more information on optical and confocal microscopes to determine if these microscopy modules are the best fit for a type of biological sample.

Biological Sample Imaging with Optical and Confocal Microscopy

הדמיה דגימות ביולוגיות עם מיקרוסקופיה אופטית וקונפוקל

Source: Peiman Shahbeigi-Roodposhti and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
Optical ...

SEM Imaging of Biological Samples

Source: <a href="https://www.jove.com/author/Peiman_Shahbeigi-Roodposhti">Peiman Shahbeigi-Roodposhti</a> and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
A scanning electron microscope (SEM) is an instrument that uses an electron beam to nondestructively image and characterize conductive materials in a vacuum. As an analogy, an electron beam is to the SEM as light is to the optical microscope. The difference is that the electron microscope yields images of much higher resolution and magnification. The best optical microscopes typically have a resolution down to 200 nm, whereas SEMs usually claim a resolution of 0.5 nm. This is due to the fact that optical microscopes are limited by the diffraction of waves, a function of the wavelength, which is around 500 nm for visible light. Conversely, the SEM uses an energized electron beam, which as a wavelength of 1 nm. This characteristic makes them very dependable tools for the study of nano and microstructures. Electron microscopes also enable the study of biological samples with feature sizes too small for optical microscopy.
This demonstration provides an introduction to sample preparation and initial image acquisition of biological samples using a scanning electron microscope. In this case, a collagen-hydroxyapatite (HA) cellular scaffold will be studied. The vacuum environment of the SEM and the induced charging by the electron beam on non-conductive samples (such as organic matter) creates challenges that will be addressed in the preparation. The advantages and disadvantages of different imaging methods as they relate to resolution, depth of focus and sample type will also be discussed. The purpose of this demonstration is to give the participant more information on SEM to determine if this microscopy module is the best fit for a type of biological sample.

Scanning Electron Microscopy: Operations and Sample Preparation

הדמיית SEM של דגימות ביולוגיות

Source: Peiman Shahbeigi-Roodposhti and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
A scanning ...

Biodistribution of Nano-drug Carriers: Applications of SEM

Source:&#160;<a href="https://www.jove.com/author/Peiman_Shahbeigi-Roodposhti">Peiman Shahbeigi-Roodposhti</a> and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
Nanoparticles have been increasingly used research towards targeted drug delivery and controlled drug release. While most of these particles have been developed as polymeric or liposomal particles because of their biocompatibility, there is a trend in current research toward the use of metallic and magnetic nanoparticles. These metallic nanoparticles were originally used as a contrast agent in imaging, but recent advances have shown how important they could be in drug and gene delivery and in therapeutics. Gold, silver, and paramagnetic nanoparticles have the greatest share in research being done. They have been shown to have good biocompatibility and certain varieties of magnetic nanoparticles have already been developed and distributed as therapeutic targeted drugs.&#160;&#160;
These heavy elements are typically imaged for research using fluorescence to evaluate delivery and distribution, but their atomic weights are good qualifications for increased contrast in backscatter electron analysis using a scanning electron microscope (SEM). Energy dispersive X-ray spectroscopy, which uses characteristic X-rays emitted upon electron beam interaction with the sample to identify chemical composition, can also be used with the SEM. These methods have the benefits of increased resolution and increased confidence in detection, as the EDS can ensure that the subject of an image is of the right composition, while current fluorescence methods can detach from the nanoparticles and can fade quickly while imaging.&#160;
This demonstration will examine the size-dependent metal nanoparticle distribution in organs of the body over time. Excised organs will be examined with SEM for various sizes of particles at a range of time points after particle delivery to the body.&#160;

Biodistribution of Nano Carriers: Imaging using SEM and EDS

ייחוס ביולוגי של נשאי ננו-תרופות: יישומים של SEM

Source:&#160;Peiman Shahbeigi-Roodposhti and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
...

High-frequency Ultrasound Imaging of the Abdominal Aorta

Source: Amelia R. Adelsperger, Evan H. Phillips, and <a href="https://www.jove.com/author/Craig+J._Goergen">Craig J. Goergen</a>, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
High-frequency ultrasound systems are used to acquire high resolution images. Here, the use of a state-of-the-art system will be demonstrated to image the morphology and hemodynamics of small pulsatile arteries and veins found in mice and rats. Ultrasound is a relatively inexpensive, portable, and versatile method for the noninvasive assessment of vessels in humans as well as large and small animals. These are several key advantages that ultraound offers compared to other techniques, such as computed tomography (CT), magnetic resonance imaging (MRI), and near-infrared fluorescence tomography (NIRF). CT requires ionizing radiation and MRI can be prohibitively expensive and even impractical in some scenarios. NIRF, on the other hand, is limited by the penetration depth of light required to excite the fluorescent contrast agents.
Ultrasound has limitations in terms of imaging depth; however, this may be overcome by sacrificing resolution and using a lower frequency transducer. Abdominal gas and excess body weight can severely diminish image quality. In the first case, the propagation of sound waves is limited, while in the latter case, they are attenuated by overlying tissues, such as fat and connective tissue. As a result, no contrast or faint contrast may be observed. Finally, ultrasound is a highly user-dependent technique, requiring the sonographer to be familiar with anatomy and to be able to work around issues, such as the appearance of imaging artifacts or acoustic interference.

High-frequency Ultrasound Imaging and Image Acquisition

הדמיית אולטרסאונד בתדר גבוה של אב העורקים בבטן

Source: Amelia R. Adelsperger, Evan H. Phillips, and Craig J. Goergen, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, 
...

Quantitative Strain Mapping of an Abdominal Aortic Aneurysm

Source: Hannah L. Cebull1, Arvin H. Soepriatna1, John J. Boyle2 and <a href="https://www.jove.com/author/Craig+J._Goergen">Craig J. Goergen</a>1 
1Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
2Mechanical Engineering &#38; Materials Science, Washington University in St. Louis, St Louis, Missouri
The mechanical behavior of soft tissues, such as blood vessels, skin, tendons, and other organs, are strongly influenced by their composition of elastin and collagen, which provide elasticity and strength. The fiber orientation of these proteins depends on the type of soft tissue and can range from a single preferred direction to intricate meshed networks, which can become altered in diseased tissue. Therefore, soft tissues often behave anisotropically on the cellular and organ level, creating a need for three-dimensional characterization. Developing a method for reliably estimating strain fields within complex biological tissues or structures is important to mechanically characterize and understande disease. Strain represents how soft tissue relatively deforms over time, and it can be described mathematically through various estimations.
Acquiring image data over time allows deformation and strain to be estimated. However, all medical imaging modalities contain some amount of noise, which increases the difficulty of accurately estimating in vivo strain. The technique described here successfully overcomes these issues by using a direct deformation estimation (DDE) method to calculate spatially varying 3D strain fields from volumetric image data.
Current strain estimation methods include digital image correlation (DIC) and digital volume correlation. Unfortunately, DIC can only accurately estimate strain from a 2D plane, severely limiting the application of this method. While useful, 2D methods such as DIC have difficulty quantifying strain in regions that undergo 3D deformation. This is because out-of-plane motion creates deformation errors. Digital volume correlation is a more applicable method that divides the initial volume data into regions and finds the most similar region of the deformed volume, thereby reducing out-of-plane error. However, this method proves to be sensitive to noise and requires assumptions about the mechanical properties of the material.
The technique demonstrated here eliminates these issues by using a DDE method, thus making it very useful in the analysis of medical imaging data. Furthermore, it is robust to high or localized strain. Here we describe the acquisition of gated, volumetric 4D ultrasound data, its conversion into an analyzable format, and the use of a custom Matlab code to estimate 3D deformation and corresponding Green-Lagrange strains, a parameter that better describes large deformations. The Green-Lagrange strain tensor is implemented in many 3D strain estimation methods because it allows for F to be calculated from a Least Squares Fit (LSF) of the displacements. The equation below represents the Green-Lagrange strain tensor, E, where F and I represent the deformation gradient and second order identity tensor, respectively.
<img alt="Equation 1" src="/files/ftp_upload/10480/10480eq1v2.jpg" /> (1)

4-D Ultrasound &amp; Quantitative Strain Mapping in Abdominal Aortic Aneurysm

מיפוי מאמץ כמותי של מפרצת באבי העורקים בבטן

Source: Hannah L. Cebull1, Arvin H. Soepriatna1, John J. Boyle2 and Craig J. Goergen1 
1Weldon School of Biomedical Engineering, Purdue University, West ...

Photoacoustic Tomography to Image Blood and Lipids in the Infrarenal Aorta

Source: Gurneet S. Sangha and <a href="https://www.jove.com/author/Craig+J._Goergen">Craig J. Goergen</a>, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
Photoacoustic tomography (PAT) is an emerging biomedical imaging modality that utilizes light generated acoustic waves to obtain compositional information from tissue. PAT can be used to image blood and lipid components, which is useful for a wide variety of applications, including cardiovascular and tumor imaging. Currently used imaging techniques have inherent limitations that restrict their use with researchers and physicians. For example, long acquisition times, high costs, use of harmful contrast, and minimal to high invasiveness are all factors that limit the use of various modalities in the laboratory and clinic. Currently, the only comparable imaging techniques to PAT are emerging optical techniques. But these also have disadvantages, such as limited depth of penetration and the need for exogenous contrast agents. PAT provides meaningful information in a rapid, noninvasive, label-free manner. When coupled with ultrasound, PAT can be used to obtain structural, hemodynamic, and compositional information from tissue, thereby complementing currently used imaging techniques. The advantages of PAT illustrate its capabilities to make an impact in both the preclinical and clinical environment.

Photoacoustic Tomography and Laser-ultrasound Coupling

טומוגרפיה פוטואקוסטית לדם תמונה ולומנים בבטורה האינפרא-רנאלית

Source: Gurneet S. Sangha and Craig J. Goergen, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
Photoacoustic ...

Cardiac Magnetic Resonance Imaging

Source: Frederick W. Damen and <a href="https://www.jove.com/author/Craig+J._Goergen">Craig J. Goergen</a>, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
In this video, high field, small-bore magnetic resonance imaging (MRI) with physiological monitoring is demonstrated to acquire gated cine loops of the murine cardiovascular system. This procedure provides a basis for assessing left-ventricular function, visualizing vascular networks, and quantifying motion of organs due to respiration. Comparable small animal cardiovascular imaging modalities include high-frequency ultrasound and micro-computed tomography (CT); however, each modality is associated with trade-offs that should be considered. While ultrasound does provide high spatial and temporal resolution, imaging artifacts are common. For example, dense tissue (i.e., the sternum and ribs) can limit imaging penetration depth, and hyperechoic signal at the interface between gas and liquid (i.e., pleura surrounding the lungs) can blur contrast in nearby tissue. Micro-CT in contrast does not suffer from as many in-plane artifacts, but does have lower temporal resolution and limited soft-tissue contrast. Furthermore, micro-CT uses X-ray radiation and often requires the use of contrast agents to visualize vasculature, both of which are known to cause side effects at high doses including radiation damage&#160; and renal injury. Cardiovascular MRI provides a nice compromise between these techniques by negating the need for ionizing radiation and providing the user with the ability to image without contrast agents (although contrast agents are often used for MRI).
This data was acquired with a triggering Fast Low Angle SHot (FLASH) MRI sequence that was gated off of the R-peaks in the cardiac cycle and expiratory plateaus in respiration. These physiological events were monitored through subcutaneous electrodes and a pressure-sensitive pillow that was secured against the abdomen. To ensure the mouse was properly warmed, a rectal temperature probe was inserted and used to control the output of a MRI-safe heating fan. Once the animal was inserted into the bore of the MRI scanner and navigation sequences were run to confirm positioning, the gated FLASH imaging planes were prescribed and data acquired. Overall, high field MRI is a powerful research tool that can provide soft tissue contrast for the study of small animal disease models.

Cardiac MRI: Principle and Imaging

הדמיית תהודה מגנטית לבבית

Source: Frederick W. Damen and Craig J. Goergen, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
In this video, high ...

Computational Fluid Dynamics Simulations of Blood Flow in a Cerebral Aneurysm

Source: Joseph C. Muskat, Vitaliy L. Rayz, and Craig J. Goergen, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
The objective of this video is to describe recent advancements of computational fluid dynamic (CFD) simulations based on patient- or animal-specific vasculature. Here, subject-based vessel segmentations were created, and, using a combination of open-source and commercial tools, a high-resolution numerical solution was determined within a flow model. Numerous studies have demonstrated that the hemodynamic conditions within the vasculature affect the development and progression of atherosclerosis, aneurysms, and other peripheral artery diseases; concomitantly, direct measurements of intraluminal pressure, wall shear stress (WSS), and particle residence time (PRT) are difficult to acquire in vivo.
CFD allow such variables to be assessed non-invasively. In addition, CFD is used to simulate surgical techniques, which provides physicians better foresight regarding post-operative flow conditions. Two methods in magnetic resonance imaging (MRI), magnetic resonance angiography (MRA) with either time of flight (TOF-MRA) or contrast-enhanced MRA (CE-MRA) and phase-contrast (PC-MRI), allow us to obtain vessel geometries and time-resolved 3D velocity fields, respectively. TOF-MRA is based on the suppression of the signal from static tissue by repeated RF pulses that are applied to the imaged volume. A signal is obtained from unsaturated spins moving into the volume with the flowing blood. CE-MRA is a better technique for imaging vessels with complex recirculating flows, as it uses a contrast agent, such as gadolinium, to increase the signal.
Separately, PC-MRI utilizes bipolar gradients to generate phase shifts that are proportional to a fluid&#39;s velocity, thus providing time-resolved velocity distributions. While PC-MRI is capable of providing blood flow velocities, the accuracy of this method is affected by limited spatiotemporal resolution and velocity dynamic range. CFD provides superior resolution and can assess the range of velocities from high-speed jets to slow recirculating vortices observed in diseased blood vessels. Thus, even though the reliability of CFD depends on the modeling assumptions, it opens up the possibility for high quality, comprehensive depiction of patient-specific flow fields, which can guide diagnosis and treatment.

סימולציות דינמיקה של נוזל חישובי של זרימת דם במפרצת מוחית

Source: Joseph C. Muskat, Vitaliy L. Rayz, and Craig J. Goergen, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
The ...

Near-infrared Fluorescence Imaging of Abdominal Aortic Aneurysms

Source: Arvin H. Soepriatna1, Kelsey A. Bullens2, and <a href="https://www.jove.com/author/Craig+J._Goergen">Craig J. Goergen</a>1
1 Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana
2 Department of Biochemistry, Purdue University, West Lafayette, Indiana
Near-infrared fluorescence (NIRF) imaging is an exciting optical technique that utilizes fluorescent probes to visualize complex biomolecular assemblies in tissues. NIRF imaging has many advantages over conventional imaging methods for noninvasive imaging of diseases. Unlike single photon emission computed tomography (SPECT) and positron emission tomography (PET), NIRF imaging is rapid, high-throughput, and does not involve ionizing radiation. Furthermore, recent developments in engineering target-specific and activatable fluorescent probes provide NIRF with high specificity and sensitivity, making it an attractive modality in studying cancer and cardiovascular disease. The presented procedure is designed to demonstrate the principles behind NIRF imaging and how to conduct in vivo and ex vivo experiments in small animals to study a variety of diseases. The specific example shown here employs an activatable fluorescent probe for matrix metalloproteinase-2 (MMP2) to study its uptake in two different rodent models of abdominal aortic aneurysms (AAAs).

הדמיית פלואורסצנטיות כמעט אינפרא אדום של מפרצות באבי העורקים בבטן

Source: Arvin H. Soepriatna1, Kelsey A. Bullens2, and Craig J. Goergen1
1 Weldon School of Biomedical Engineering, Purdue University, West Lafayette, ...

Noninvasive Blood Pressure Measurement Techniques

Source: Hamna J. Qureshi and <a href="https://www.jove.com/author/Craig+J._Goergen">Craig J. Goergen</a>, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana

Here we will highlight the key similarities and differences of noninvasive blood pressure measurement techniques between humans and rodents and examine the engineering principles that govern blood pressure. The principles that govern current cuff technology to acquire systolic and diastolic pressures will also be discussed.
Commercially available cuffs that connect with mobile devices are typically compact and portable, thereby allowing measurements to be taken virtually anywhere. Noninvasive, portable blood pressure cuffs are especially useful for patients with hypertension and other cardiovascular problems that require careful monitoring and early detection of any changes in blood pressure.
Similarly, noninvasive blood pressure measurement systems are also available for rodents. This technology is used in laboratory settings and is useful for monitoring animal health throughout a study. While radiotelemetry is the gold standard of blood pressure measurement for rodents, this technique is invasive and can lead to animal mortality if done incorrectly. Noninvasive methods, therefore, are convenient for taking measurements in animals as they can provide valuable data without the need for device implantation. A commercially available system will be used to demonstrate how blood pressure can be measured in humans outside of a clinical setting. This technique allows patients to monitor their own blood pressure periodically without having to visit a clinic each time they want these measurements taken.
The methods described here take advantage of blood flow through the tail of the rodent by using pressure sensors and occlusion cuffs. Both mobile blood pressure cuffs for humans and noninvasive tail-cuff methods for rodents take advantage of similar hemodynamic principles to acquire blood pressure measurements that can provide useful data for users, including clinicians, researchers, and patients.

Wireless and Noninvasive Blood Pressure Measurement System

טכניקות למדידת לחץ דם לא פולשניות

Source: Hamna J. Qureshi and Craig J. Goergen, Weldon School of Biomedical Engineering, Purdue University, West Lafayette, Indiana

Here we will highlight ...

Acquisition and Analysis of an ECG (electrocardiography) Signal

Source: <a href="https://www.jove.com/author/Peiman_Shahbeigi-Roodposhti">Peiman Shahbeigi-Roodposhti</a> and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
An electrocardiograph is a graph recorded by electric potential changes occurring between electrodes placed on a patient&#39;s torso to demonstrate cardiac activity. An ECG signal tracks heart rhythm and many cardiac diseases, such as poor blood flow to the heart and structural abnormalities. The action potential created by contractions of the heart wall spreads electrical currents from the heart throughout the body. The spreading electrical currents create different potentials at points in the body, which can be sensed by electrodes placed on the skin. The electrodes are biological transducers made of metals and salts. In practice, 10 electrodes are attached to different points on the body. There is a standard procedure for acquiring and analyzing ECG signals. A typical ECG wave of a healthy individual is as follows:
<img alt="Figure 1" src="/files/ftp_upload/10473/10473fig1v2.jpg" /> 
Figure 1. ECG wave.
The &#34;P&#34; wave corresponds to atrial contraction, and the &#34;QRS&#34; complex to the contraction of the ventricles. The &#34;QRS&#39; complex is much larger than the &#34;P&#34; wave due to the relative dfference in muscle mass of the atria and ventricles, which masks the relaxation of the atria. The relaxation of the ventricles can be seen in the form of the &#34;T&#34; wave.
There are three main leads responsible for measuring the electrical potential difference between arms and legs, as shown in Figure 2. In this demonstration, one of the limb leads, lead I, will be examined, and the electrical potential difference between two arms will be recorded. As in all ECG lead measurements, the electrode connected to the right leg is considered the ground node. An ECG signal will be acquired using a biopotential amplifier and then displayed using instrumentation software, where a gain control will be created to adjust its amplitude. Finally, the recorded ECG will be analyzed.
<img alt="Figure 2" src="/files/ftp_upload/10473/10473fig2v2.jpg" /> 
Figure 2. ECG limb leads.

Acquisition and Analysis of an ECG electrocardiography Signal

רכישה וניתוח של אות אק"ג (אלקטרוקרדיוגרפיה)

Source: Peiman Shahbeigi-Roodposhti and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
An ...

Tensile Strength of Resorbable Biomaterials

Source: <a href="https://www.jove.com/author/Peiman_Shahbeigi-Roodposhti">Peiman Shahbeigi-Roodposhti</a> and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
For over 4000 years, sutures have been used as a medical intervention. The earliest records indicate linen was the biomaterial of choice. Catgut, which is still in use today, was reportedly used to treat gladiators around 150 AD. Today, there are numerous materials being used for sutures. Sutures are classified by their composition (natural or synthetic) and their absorption (non-resorbable or resorbable).
Resorbable (or absorbable) sutures degrade in the body through either enzymatic degradation or programmed degradation caused by the interaction of water with specific groups in the polymer chain. These sutures are often created from synthetic materials, such as polyglycolic acid, polydioxanone, and polycaprolactone, or natural biomaterials, such as silk. They are usually used for certain internal procedures, like general surgery. Resorbable sutures will hold the wound together for a time frame long enough for healing, but then they eventually disintegrate by the body. On the other hand, non-resorbable sutures do not degrade and must be extracted. They are usually derived from polypropylene, nylon, and stainless-steel. These sutures are usually implemented for orthopedic and cardiac surgery and require a medical professional to remove them at a later date.
Here, the tensile strength of two types of resorbable sutures will be tested after exposing them to neutral, acidic, and alkaline solutions, which correspond to the different pH environments found within the human body. The test will consist of two parts. First, control samples will be prepared and analyzed via tensile testing. Then, samples will be tested after the continuous exposure to solutions of varying pH over the course of several weeks.

Tensile Strength and Loss Profile of Resorbable Biomaterials

חוזק מתיחה של ביו-חומרים הניתנים למיחזור

Source: Peiman Shahbeigi-Roodposhti and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
For over ...

Micro-CT Imaging of a Mouse Spinal Cord

Source:&#160;<a href="https://www.jove.com/author/Peiman_Shahbeigi-Roodposhti">Peiman Shahbeigi-Roodposhti</a> and Sina Shahbazmohamadi, Biomedical Engineering Department, University of Connecticut, Storrs, Connecticut
It&#39;s a little-known fact that the discovery and (inadvertent) use of X-rays garnered the first ever Nobel Prize in Physics. The famous X-ray image of Dr. R&#246;ntgen&#39;s wife&#39;s hand from 1895 that sent shock waves through the scientific community looks like most modern day 2D medical X-ray images. Though it is not the newest technology, X-ray absorption imaging is an indispensable tool and can be found in the world&#39;s top R&#38;D and university labs, hospitals, airports, among other places. Arguably the most advanced uses of X-ray absorption imaging involve attaining information like the kind found in a 2D medical X-ray but realized in 3D through a computed tomography (CT or micro-CT). By taking a series of 2D X-ray projections, advanced software is capable of reconstructing data to form a 3D volume. The 3D information can, and most likely will include information from the inside of the probed object without having to be cut open. Here, a micro-CT scan will be obtained, and the major factors impacting image quality will be discussed.

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