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Research

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.

Пример проектирования: проектирование бытовой водопроводной системы

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

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.

Измерение расхода в трубе

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

Pipe Flowrate Measurement: Problem Solving

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

Измерение расхода в трубе: решение проблемы

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.

Однотрубные системы

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.

Незначительные потери в трубах

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.

Многотрубные системы

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.

Основные потери в трубах

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.

Турбулентное течение: решение проблем

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

Laminar Flow: Problem Solving

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

Ламинарный поток: решение проблем

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 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.

Общие характеристики Pipe Flow 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 ...

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.

Турбулентный поток

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

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.

Ламинарный поток

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

General Characteristics of Pipe Flow I

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

Общие характеристики течения в трубопроводе 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.

Пример проекта: создание гидравлической модели водосброса плотины

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 ...

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.

Корреляция экспериментальных данных

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

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.

Безразмерные группы в механике жидкости

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

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.

Типовые модельные исследования

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

Modeling and Similitude

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

Моделирование и подобие

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

Determination of Pi Terms

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

Определение членов числа Пи

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

The Buckingham Pi Theorem

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

Теорема Букингема о Пи

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

Dimensional Analysis

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

Размерный анализ

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

Navier&#8211;Stokes Equations

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

Уравнения Навье–Стокса

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.

Плоские потенциальные потоки

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.

Устойчивый, ламинарный поток между параллельными пластинами

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

Tree Identification: How To Use a Dichotomous Key

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
A dichotomous key is a tool that identifies items in nature, such as leaves. This method is based on the idea of choosing between two characteristics. The word dichotomous comes from two Greek words that mean &#8220;to divide into two parts.&#8221; In a dichotomous key for leaf identification, each pair of phrases describes different features of the leaf. Only one of the phrases correctly applies to the leaf being keyed out. The correct phrase leads to the next pair of phrases, or states the name of the tree from which the leaf came. Using a field guide to trees and the iTree National Tree Benefits Calculator helps to identify trees in a field investigation, which shows the significance of trees in terms of their environmental benefits, such as storm water management, increasing property value, energy efficiency, air quality, and carbon sequestration.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
A dichotomous key is a tool that identifies items in nature, such as ...

Tree Survey: Point-Centered Quarter Sampling Method

A number of methods are available for sampling forest communities. Point-centered quarter is one such method. It is used to gather information on the density, frequency, and coverage of tree species found in a forest. This information provides the ability to estimate the number of individual trees encountered, how often a certain tree occurs, how common the tree is compared to other trees, and the size of the tree. Compared to the standard plot analysis, the point-centered quarter method is more efficient, which is a major advantage. In a fixed-area plot sampling, a small portion of the total area of the forest is examined. In this small subsample, the density is determined directly by counting and identifying each tree. The ratio between size of the subplot and the overall forest size is used to determine the density for the entire forest.

A number of methods are available for sampling forest communities. Point-centered quarter is one such method. It is used to gather information on the ...

Using GIS to Investigate Urban Forestry

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Urban forests broadly include urban parks, street trees, landscaped boulevards, public gardens, river and coastal promenades, greenways, river corridors, wetlands, nature preserves, natural areas, shelterbelts of trees, and working trees at industrial brownfield sites. The history of urban trees begins with trees as landscape embellishment. Today, urban trees are seen as essential components of city infrastructure and critical to human life as food, housing, and other public utilities. Urban trees are now valued for the ecosystem services they provide (e.g., preventing erosion, air pollutant removal, oxygen, shade, etc.). Yet, to efficiently make use of these benefits, trees must reach maturity, as leaf number and size directly affect a tree&#8217;s ability to provide ecosystem services. Urban forestry has had to develop its own forestry methods to address the needs and challenges unique to urban trees as compared to their woodland counterparts.
The following excerpt from the USDA Forest Service illustrates the urban tree perspective and policies of federal government:

<blockquote>Urban forests are dynamic ecosystems that provide needed environmental services by cleaning air and water, helping to control storm water, and conserving energy. They add form, structure, beauty and breathing room to urban design, reduce noise, separate incompatible uses, provide places to recreate, strengthen social cohesion, leverage community revitalization, and add economic value to our communities... This natural life support system sustains clean air and water, biodiversity, habitat, nesting and travel corridors for wildlife, and connects people to nature.</blockquote>

The management of urban trees is an interdisciplinary practice involving architecture, landscaping, planning, development, horticulture, etc. One particular discipline involved in forestry is geography, especially through the use of geographical information systems (GIS). GIS is a broad name encompassing any type of database containing geographical or spatial data that can be used to create computer-generated visual representations (e.g., maps). GIS allows for extensive data collection and management through ever-improving user interfaces, increasing the user-friendly quality of very large sets of information that can be accessed by many users. GIS applications range from free software and open access protocols, such as Google Earth, to proprietary systems, like ESRI ArcGIS. Using GIS to create and store geographical information also allows for easy data maintenance, because maps can be quickly updated by adding new information to the database and regenerating the visual output.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Urban forests broadly include urban parks, street trees, landscaped ...

Proton Exchange Membrane Fuel Cells

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
The United States consumes a large amount of energy &#8211; the current rate is around 97.5 quadrillion BTUs annually. The vast majority (90%) of this energy comes from non-renewable fuel sources. This energy is used for electricity (39%), transportation (28%), industry (22%), and residential/commercial use (11%). As the world has a limited supply of these non-renewable sources, the United States (among others) is expanding the use of renewable energy sources to meet future energy needs. One of these sources is hydrogen.
Hydrogen is considered a potential renewable fuel source, because it meets many important criteria: it&#8217;s available domestically, it has few harmful pollutants, it&#8217;s energy efficient, and it&#8217;s easy to harness. While hydrogen is the most abundant element in the universe, it is only found in compound form on Earth. For example, it is combined with oxygen in water as H2O. To be useful as a fuel, it needs to be in the form of H2 gas. Therefore, if hydrogen is to be used as a fuel for cars or other electronics, H2 needs to be made first. Thusly, hydrogen is often called an &#8220;energy carrier&#8221; rather than a &#8220;fuel.&#8221;
Currently, the most popular way to make H2 gas is from fossil fuels, through steam reforming of hydrocarbons or coal gasification. This does not reduce dependence on fossil fuels and is energy intensive. A less-used method is by electrolysis of water. This also requires an energy source, but it can be a renewable source, like wind or solar power. In electrolysis, water (H2O) is split into its component parts, hydrogen gas (H2) and oxygen gas (O2), through an electrochemical reaction. The hydrogen gas made through the process of electrolysis can then be used in a Proton Exchange Membrane (PEM) fuel cell, generating an electric current. This electric current can be used to power motors, lights, and other electrical devices.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
The United States consumes a large amount of energy &#8211; the current ...

Biofuels: Producing Ethanol from Cellulosic Material

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
In this experiment, cellulosic material (such as corn stalks, leaves, grasses, etc.) will be used as a feedstock for the production of ethanol.&#160;The cellulosic material is first pretreated (ground and heated), digested with enzymes, and then fermented with yeast.&#160;Ethanol production is monitored using an ethanol probe.&#160;The experiment can be extended to optimize ethanol production by varying the feedstock used, pretreatment conditions, enzyme variation, yeast variation, etc.&#160;An alternative method of monitoring the reaction is to measure the carbon dioxide produced (using a gas sensor) instead of the ethanol.&#160;As a low-tech alternative, glucose meters (found in any drug store) can be used to monitor the glucose during the process, if an ethanol probe or carbon dioxide gas sensor is not available.
With an increased emphasis on &#8216;inquiry-based learning&#8221;, scientific probes are becoming more popular.&#160;Handheld devices like the Vernier Lab Quest used in conjunction with a variety of probes (such as those for conductivity, dissolved oxygen, voltage, and more) allow for less focus on collecting data and/or making graphs and more on analyzing the data and making predictions.&#160;Another advantage is that these are small and lightweight and can be taken into the field for measurements.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
In this experiment, cellulosic material (such as corn stalks, leaves, ...

Testing For Genetically Modified Foods

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Genetic modification of foods has been a controversial issue due to debated concerns over health and environmental safety. This experiment demonstrates technical understanding of how food DNA is genetically identified, allowing for educated decision making about the safety and potential dangers of using genetically modified organisms (GMOs) in food supplies.
Polymerase Chain Reaction (PCR) is used to amplify food DNA to test for the presence of genetically modified DNA in food products. Presence of specific DNA bands is detected by using gel electrophoresis to pull extracted food DNA through a 3% agarose gel, a concentration dense enough to separate the bands of DNA containing the genetically modified DNA. Several controls are used in the electrophoresis procedure to ensure DNA is successfully extracted from test foods (plant primer), and to provide known examples of both genetically modified DNA (purchased genetically modified DNA) and non-genetically modified DNA (purchased certified non-GMO food control).

Identifying Genetically Modified Foods Using PCR

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Genetic modification of foods has been a controversial issue due to debated ...

Turbidity and Total Solids in Surface Water

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Turbidity and total solids are related measurements addressing clarity of surface waters. Turbidity is an indirect measure of water clarity that determines the amount of light that can pass through the water. Total solids is a direct measurement of solid particles suspended in water determined by weight.
High levels of turbidity and total solids are caused by soil erosion, waste discharge, runoff, or changes in ecological communities including algal growth or abundance of benthic organisms that can disrupt sediments up into the water. Higher levels of turbidity and suspended solids can lower water quality by absorbing heat causing an increase in water temperature and a decrease in oxygen levels (warm water holds less oxygen). These conditions can also cause a decrease in photosynthesis as less sunlight penetrates the water, making the water unable to support some aquatic life. Suspended solids can also clog gills, smother eggs, reduce growth rates, and disrupt microhabitats of many aquatic organisms.
One method of measuring turbidity includes using a Secchi disk. A Secchi disk is a metal disk with alternate black and white quarters (Figure 1). It is attached to a rope that has one-foot markings along it. The disk is dropped into water until it can no longer be seen (Figure 2). The drawback of this method is that it must be done in the field and ideal protocol requires sunny conditions and that the testing area be shaded. In addition, if there is a large distance between the riverbank and the water level, it is difficult to use the Secchi disk. By using turbidity tubes, one can collect water and then perform the turbidity measurements back in the laboratory.
<img alt="Figure 1" src="/files/ftp_upload/10015/10015fig1.jpg" /> 
Figure 1. The modified Secchi disk design used in freshwater.
<img alt="Figure 2" src="/files/ftp_upload/10015/10015fig2.jpg" /> 
Figure 2. Different kinds of Secchi disk. A marine style one on the left and the freshwater version on the right

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Turbidity and total solids are related measurements addressing clarity of ...

Dissolved Oxygen in Surface Water

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Dissolved oxygen (DO) measurements calculate the amount of gaseous oxygen dissolved in surface water, which is important to all oxygen-breathing life in river ecosystems, including fish species preferred for human consumption (e.g. bluegill and bass), as well as decomposer species critical to the recycling of biogeochemical materials in the system.
The oxygen dissolved in lakes, rivers, and oceans is crucial for the organisms and creatures living in it. As the amount of dissolved oxygen drops below normal levels in water bodies, the water quality is harmed and creatures begin to die. In a process called eutrophication, a body of water can become hypoxic and will no longer be able to support living organisms, essentially becoming a &#8220;dead zone.&#8221;
Eutrophication occurs when excess nutrients cause algae populations to grow rapidly in an algal bloom. The algal bloom forms dense mats at the surface of the water blocking out two essential inputs of oxygen for water: gas exchange from the atmosphere and photosynthesis in the water due to the lack of light below the mats. As dissolved oxygen levels decline below the surface, oxygen-breathing organisms die-off in large amounts, creating an increase in organic matter. The excess organic matter causes an increase in the oxygen-breathing decomposer populations in the benthic zone, which further depletes the remaining dissolved oxygen levels during the metabolic decomposition activity. Once the oxygen levels become this low, mobile oxygen-breathing species (e.g. fish) will move away, leaving no aerobic life in the water and creating a dead zone.
The Azide-Winkler titration method uses titration to determine the concentration of an unknown in a sample. Specifically, sodium thiosulfate is used to titrate iodine, which can be stoichiometrically related to the amount of dissolved oxygen in a sample.

Measuring Dissolved Oxygen in Water by Azide-Winkler Method

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Dissolved oxygen (DO) measurements calculate the amount of gaseous oxygen ...

Nutrients in Aquatic Ecosystems

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Nitrogen and phosphorus are essential plant nutrients found in aquatic ecosystems and both are monitored as a part of water quality testing because in excess amounts they can cause significant water quality problems.&#160;
Nitrogen in water is measured as the common form nitrate (NO3-) that is dissolved in water and readily absorbed by photosynthesizers such as algae. The common form of phosphorus measured is phosphate (PO43-), which is strongly attracted to sediment particles as well as dissolved in water. In excess amounts, both nutrients can cause an increase in aquatic plant growth (algal bloom, Figure 1) that can disrupt the light, temperature, and oxygen levels in the water below and lead to eutrophication and hypoxia (low dissolved oxygen in water) forming a &#8220;dead zone&#8221; of no biological activity. Sources of nitrates and phosphorus include wastewater treatment plants, runoff from fertilized lawns and agricultural lands, faulty septic systems, animal manure runoff, and industrial waste discharge.
<img alt="Figure 1" src="/files/ftp_upload/10023/10023fig1.jpg" /> 
Figure 1. Algal bloom 
Taken in 2011, the green scum shown in this image was the worst algae bloom Lake Erie has experienced in decades. Record torrential spring rains washed fertilizer into the lake, promoting the growth of microcystin producing cyanobacteria blooms. Vibrant green filaments extend out from the northern shore.

Eutrophication, Measuring Nitrate and Phosphate in Water

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Nitrogen and phosphorus are essential plant nutrients found in aquatic ...

Measuring Tropospheric Ozone

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Ozone is a form of elemental oxygen (O3), a molecule of three oxygen atoms bonded in a structure that is highly reactive as an oxidizing agent. Ozone occurs in both the stratosphere and the troposphere levels of the atmosphere. When in the stratosphere (located approximately 10-50 km from the earth&#8217;s surface), ozone molecules form to the ozone layer and help prevent harmful UV rays from reaching Earth&#8217;s surface. In lower altitudes of the troposphere (surface - approximately 17 km), ozone is harmful to human health and is considered an air pollutant contributing to photochemical smog (Figure 1). Ozone molecules can cause damage directly by harming respiratory tissue when inhaled or indirectly by harming plant tissues (Figure 2) and softer materials including tires on automobiles.
Outdoor tropospheric ozone is formed at ground level when nitrogen oxides (NOx) and volatile organic compounds (VOCs) from automobile emissions are exposed to sunlight. Consequently, health concerns over ozone concentrations escalate in sunny conditions or when and where automobile use is increased.
Reaction: NO2 + VOC + sunlight &#8594;&#160;O3 (+ other products)
Indoor tropospheric ozone is formed when electrical discharges from equipment using high voltages (e.g. ionic air purifiers, laser printers, photocopiers) break down the chemical bonds of the atmospheric oxygen (O2) in the air surrounding the equipment:
O2 &#8594; 2 O
The free radicals of oxygen in and around electrical discharge recombine to create ozone (O3).
2 O + 2 O2&#8594; 2 O3
<img alt="Figure 1" src="/files/ftp_upload/10024/10024fig1.jpg" /> 
Figure 1: Golden Gate Bridge panorama
Characteristic coloration for smog in California in the beige cloud bank behind the Golden Gate Bridge. The brown coloration is due to the NOx in the photochemical smog.
<img alt="Figure 2" src="/files/ftp_upload/10024/10024fig2.jpg" /> 
Figure 2: Plants damaged by ozone. Top row is normal, bottom row has been exposed to ozone.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Ozone is a form of elemental oxygen (O3), a molecule of three oxygen atoms ...

Determination Of NOx in Automobile Exhaust Using UV-VIS Spectroscopy

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
In the troposphere, ozone is naturally formed when sunlight splits nitrogen dioxide (NO2):
NO2 + sunlight &#8594; NO + O
O + O2 &#8594; O3
Ozone (O3) can go on to react with nitric oxide (NO) to form nitrogen dioxide (NO2) and oxygen:
NO + O3 &#8594; NO2 + O2
This results in no net gain of ozone (O3). However, with the anthropogenic production of ozone forming precursors (NO, NO2, and volatile organic compounds) through the combustion of fossil fuels, elevated levels of ozone in the troposphere have been found. Motor vehicle exhaust is a significant source of these ozone forming precursors: NO, NO2, and volatile organic compounds (VOCs). For example, mobile sources make up nearly 60% of NO + NO2 emissions.
At the high temperatures found in a car&#8217;s combustion chamber, nitrogen and oxygen from the air react to form nitric oxide (NO) and nitrogen dioxide (NO2):
N2(g) + O2 (g)&#8594; 2 NO(g)
2 NO(g) + O2(g)&#8594; 2 NO2(g)
The nitric oxide (NO) emitted in the car exhaust is gradually oxidized to nitrogen dioxide (NO2) in ambient air. This mixture of NO and NO2 is often referred to as NOx. When NOx reacts with volatile organic compounds in the atmosphere in the presence of sunlight, tropospheric ozone forms, as seen in this simplified chemical reaction:
NOx + VOCs + sunlight &#8594; O3 + other products
This noxious mixture of air pollution, which can include aldehydes, peroxyacetyl nitrates, ozone, VOCs, and NOx, is called photochemical smog. Ozone is the largest component of photochemical smog. This smog is found in all modern cities, but it&#8217;s found especially in cities with sunny, warm, dry climates and large numbers of motor vehicles. The yellow-brown color of smog in the air is due in part to the nitrogen dioxide present, since this gas absorbs visible light near 400 nm (Figure 1).
Short-term NO2 exposure (30 min to 1 day) leads to adverse respiratory effects in healthy people and increased respiratory symptoms in people with asthma. NOx reacts with ammonia and other compounds to form particulates. These small particles can penetrate the lungs and cause respiratory problems, including emphysema and bronchitis. Individuals who spend a lot of time on the road or who live near a roadway experience considerably higher exposure to NO2.
Due to the impact it has on human health and the environment, the U.S. Environmental Protection Agency (EPA) has classified NO2 as a criteria pollutant and has set the primary standard at 100 ppb (98th percentile of 1-h daily maximum concentrations, averaged over 3 years) and 53 ppb (annual mean). Considering that on-road vehicles account for approximately 1/3 of NOx emissions in the U.S., automobile emissions are therefore regulated through the Clean Air Act. The U.S. EPA established emission standards that automobile manufacturers must follow when producing cars. Currently, Tier 2 emission standards set that manufacturers must have fleet average NOx emissions of no more than 0.07 g/mile.
One way manufacturers meet this standard is by using catalytic converters on their cars. This device is placed between the engine and the tailpipe. The exhaust stream passes through the catalytic converter and is exposed to a catalyst. A reduction catalyst of platinum and rhodium is used to reduce the NOx concentration in the exhaust. When an NO or NO2 molecule in the exhaust contacts the catalyst, the nitrogen atom is grabbed off the molecule and held onto by the catalyst. The oxygen is freed and forms O2. The nitrogen atom on the catalyst binds with another nitrogen atom held on the catalyst to form N2.
Catalytic converters have greatly reduced the emissions of NOx from car exhaust &#8211; up to 80% reduction, when performing properly. However, they only work when they have reached a fairly high temperature. Therefore, when doing a cold start of a car, the catalytic converter is removing virtually no NOx. It isn&#8217;t until the catalytic converter reaches higher temperatures that it effectively removes the NOx from the exhaust stream. Catalytic converters do not work on diesel passenger cars due to the lean conditions under which they operate. In addition, the sulfur in diesel fuel also deactivates the catalyst. The NOx in diesel engines are reduced mainly through the exhaust gas recirculation (EGR) valve, which cools the temperature of the combustion gases. As a result, diesel cars generally emit more NOx than gasoline cars.
<img alt="Figure 1" src="/files/ftp_upload/10076/10076fig1.jpg" /> 
Figure 1. Characteristic coloration for smog in California in the beige cloud bank behind the Golden Gate Bridge. The brown coloration is due to the NOx in the photochemical smog.

Determination Of NOx in Automobile Exhaust Using UV-VIS Spectroscopy

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
In the troposphere, ozone is naturally formed when sunlight splits nitrogen ...

Lead Analysis of Soil Using Atomic Absorption Spectroscopy

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Lead occurs naturally in soil, in levels ranging from 10-50 ppm. However, with the widespread use of lead in paint and gasoline in addition to contamination by industry, urban soils often have concentrations of lead significantly greater than background levels &#8211; up to 10,000 ppm in some places. Ongoing problems arise from the fact that lead does not biodegrade, and instead remains in the soil.
Serious health risks are associated with lead poisoning, where children are particularly at risk. Millions of children in the U.S. are exposed to soil containing lead. This exposure can cause developmental and behavioral problems in children. These problems include learning disabilities, inattention, delayed growth, and brain damage. The Environmental Protection Agency has set a standard for lead in soil at 400 ppm for play areas and 1,200 ppm for non-play areas.
Lead is also of concern in soil, when it&#8217;s used for gardening. Plants take up lead from the soil. Therefore, vegetables or herbs grown in contaminated soil can lead to lead poisoning. In addition, contaminated soil particles can be breathed in while gardening or brought into the house on clothing and footwear. It is recommended that soils with lead levels greater than 400 ppm should not be used for gardening. It is further recommended that soil with lead levels between 100 and 400 ppm not be used for leafy vegetables or herbs, because lead can be stored in the leaves. On a similar note, root vegetables should not be grown in this soil, because lead can also accumulate in plant roots.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Lead occurs naturally in soil, in levels ranging from 10-50 ppm. However, ...

Carbon and Nitrogen Analysis of Environmental Samples

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Elemental Analysis is a method used to determine elemental composition of a material. In environmental samples such as soils, scientists are particularly interested in the amounts of two ecologically important elements, nitrogen and carbon. Elemental analysis by the flash combustion technique works by oxidizing the sample with a catalyst through combustion in a high-temperature chamber. The products of combustion are then reduced to N2 and CO2 and detected with a thermal conductivity detector.
Unlike other methods for total nitrogen determination (Kjeldahl method) and total carbon determination (Walkley-Black, Heanes or Leco methods), the flash combustion technique does not use toxic chemicals and is therefore much safer to use.
This video will demonstrate combustion-based elemental analysis using the Flash EA 1112 instrument from Thermo Fisher Scientific.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Elemental Analysis is a method used to determine elemental composition of a ...

Soil Nutrient Analysis: Nitrogen, Phosphorus, and Potassium

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
In this experiment, three soil macronutrients are chemically extracted, combined with color-based reagents, then analyzed using color to determine the nutrient concentration present in the soil sample.
Nitrogen, phosphorus, and potassium are the main components of soil fertilizer. These methods isolate each nutrient from the soil into a solution that can be analyzed using turbidity and color to determine the concentration of nutrients present in the soil sample. Knowing present concentration informs environmental scientists of a nutrient deficiency or surplus in soils used to support plant production, and also provides general insight into basic biogeochemical cycles of an ecosystem.

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
In this experiment, three soil macronutrients are chemically extracted, ...

Analysis of Earthworm Populations in Soil

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Using mustard, Lumbricus terrestris earthworm populations can be sampled directly from soil depths without landscape disturbance or toxicity. Earthworms can then be counted for data and statistical analysis using a bar graph and student&#8217;s t-test.
Monitoring earthworm populations is a vital technique for environmental scientists, as multiple species of earthworms (most notably those from the suborder Lumbricina) have been invasively spreading throughout North America and South America. Exotic earthworms can be found on nearly every land mass and in nearly every ecosystem on the planet, and where and when these species become invasive has been a focus of international environmental research.1
Ecological invasion typically lowers biodiversity of an ecosystem by directly outcompeting, endangering, or otherwise contributing to the extirpation of native species. As ecosystem engineers, invasive earthworm species alter the cycling of nutrients through decomposition rates of organic matter on the upper horizons of soil, where plant roots mine for nutrients. Invasive Lumbricus species have both extirpated native earthworm species and have been shown to increase the available nitrogen concentration and rates of nitrogen in invaded soils.2 In a positive feedback loop, accelerated levels of nitrogen in turn make the system more hospitable to invasive plant species that are adapted to high levels of nitrogen compared to native plant species, and will outcompete natives in a phenomenon known as &#8220;invasion meltdown.&#8221; An invasion meltdown relationship has been proposed for invasive earthworm species Lumbricus terrestris (European earthworm) and an invasive plant species Rhamnus cathartica (European Buckthorn).3

Quadrat Sampling and Earthworm Population Analysis in Soil

Source: Laboratories of Margaret Workman and Kimberly Frye - Depaul University
Using mustard, Lumbricus terrestris earthworm populations can be sampled ...

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