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Research

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.

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 ...

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.

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.

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

Single Pipe Systems

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

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.

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

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.

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

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.

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

Turbulent Flow

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.

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

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.

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 ...

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.

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.

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.

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.

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.

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.

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.

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

Typical Model Studies

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

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.

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.

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

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.

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.

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.

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.

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.

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

The Split Brain

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
The study of how damage to the brain affects cognitive functioning has historically been one of the most important tools for cognitive neuroscience. While the brain is one of the most well protected parts of the body, there are many events that can affect the functioning of the brain. Vascular issues, tumors, degenerative diseases, infections, blunt force traumas, and neurosurgery are just some of the underlying causes of brain damage, all of which may produce different patterns of tissue damage that affect brain functioning in different ways.
The history of neuropsychology is marked by several well-known cases that led to advances in the understanding of the brain. For instance, in 1861 Paul Broca observed how damage to the left frontal lobe resulted in aphasia, an acquired language disorder. As another example, a great deal about memory has been learned from patients with amnesia, such as the famous case of Henry Molaison, known for many years in the neuropsychology literature as &#34;H.M.,&#34; whose temporal lobe surgery led to a profound deficit in forming certain kinds of new memories.
While the observation and testing of patients with focal brain damage has provided neuroscience with insight into the functioning of the brain, great care must be taken in designing tests to reveal the specific nature of the deficit. Also, because the brain is a complex network of interconnected neurons, damage to one brain region can affect functioning in regions far away from the damage. To demonstrate how brain damage can affect connections among brain regions, this video examines the case of the so-called split brain.
The corpus callosum is a large bundle of fibers that connects the left and right hemispheres of the brain. It is one of the largest white matter tracts in the brain and can be easily recognized on a sagittal view of the midline of the brain. In the 1960s, neurosurgeons discovered that cutting the corpus callosum could be a successful treatment for certain kinds of epilepsy, which involves uncontrollable neural activity spreading through the brain. People who underwent the split-brain operation had their two hemispheres surgically separated, such that the left and right hemispheres were no longer able to communicate. This condition allowed experimenters to probe the functions of the left and right hemisphere independently, to learn about the relative abilities, and about the nature of communication between them.
This video demonstrates how to test a split-brain patient to reveal some of the differences between the two hemispheres of the brain and to see some dramatic consequences of such a disconnection. The original versions of these experiments were developed by Michael Gazzaniga and colleagues1, 2 and later were elaborated upon by others;3 the version presented here incorporates more recent modernizations of the methodology.

Testing Cognitive Abilities in Split-brain Patients Using Visual Stimuli

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
The study of how damage to the brain affects cognitive ...

Motor Maps

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
One principle of brain organization is the topographic mapping of information. Especially in sensory and motor cortices, adjacent regions of the brain tend to represent information from adjacent parts of the body, resulting in maps of the body expressed on the surface of the brain. The primary sensory and motor maps in the brain surround a prominent sulcus known as the central sulcus. The cortex anterior to the central sulcus is known as the precentral gyrus and contains the primary motor cortex, while the cortex posterior to the central sulcus is known as the postcentral gyrus and contains the primary sensory cortex (Figure 1).
<img alt="Figure 1" src="/files/ftp_upload/10175/10175fig1.jpg" /> 
Figure 1: Sensory and motor maps around the central sulcus. The primary motor cortex, which contains a motor map of the body&#39;s effectors, is anterior to the central sulcus, in the precentral gyrus of the frontal lobe. The primary somesthetic (sensory) cortex, which receives touch, pain, and temperature information from the external parts of the body, is located posterior to the central sulcus, in the postcentral gyrus of the parietal lobe.
In this experiment, functional neuroimaging is used to demonstrate the motor map in the precentral gyrus. This map is often called the motor homunculus, which is Latin for &#34;little man,&#34; because it is as if there is a little version of one&#39;s self represented in this part of a person&#39;s brain. One interesting property of this map is that more cortical space is devoted to body parts requiring finer control, such as the hands and mouth, which results in disproportionate representation of those appendages in the cortex. Also, because of the anatomy of the motor system, the neurons that control the right side of the body are in the left primary motor cortex, and vice versa. Therefore, when a participant in the experiment is asked to move their right hand or foot, an increased activation on their left precentral gyrus is expected.
In this experiment, participants are asked to alternately move their hands and feet, on the left and right sides, while their brain activity is measured with fMRI. Since the fMRI signal relies on changes in blood oxygenation, which are slow in comparison to the movements the participants make, the periods of movement are separated with periods of stillness to ensure that the various conditions can be distinguished from each other and from the resting baseline. To achieve precise timing of the movements, participants are instructed on when to begin and end each movement with a visual cue. The methods in this video are similar to those used by several fMRI studies that have demonstrated somatotopy in primary motor cortex.1,2

Studying Brain Activation and Motor Maps Using fMRI

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
One principle of brain organization is the topographic ...

Perspectives on Neuropsychology

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212; University of Southern California
Neuropsychology is a complex field, as it investigates how mental processes are executed in the brain&#8212;events that integrate concepts from biochemistry, biology, psychology, and neuroscience. Although the multidisciplinary nature of neuropsychology prepares young learners for a variety of careers, it also poses a challenge in that it forces students to study concepts outside of their comfort zone. For example, a psychology major may have difficulty grasping neuroanatomy&#8212;a challenging topic in itself&#8212;given that the brain is a complicated, three-dimensional organ that is typically represented two-dimensionally in textbooks.
This JoVE collection in Neuropsychology introduces major concepts and methods in the field, and showcases how advances in imaging technology have allowed us to look inside the brain and visualize its structure and function. Importantly, these videos are also meant to reassure students that you don&#8217;t need to be an expert in all aspects of neuropsychology to understand how the brain shapes our experiences, behaviors, and social interactions in everyday life. For instance, the video "Decision-making and the Iowa Gambling Task" explores how damage to a specific region of the brain can affect an individual&#8217;s proclivity for risky decisions, like stealing.
These JoVE videos in Neuropsychology provide the perfect introduction to this complex topic, and also explore some of the potential, exciting future directions in this field. With further advances in technology, one day researchers might even be able to visualize dynamic changes in a person&#8217;s brain outside of a laboratory setting&#8212;for example, when they are sitting in a classroom listening to a lecture on neuropsychology.

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212; University of Southern California
Neuropsychology is a complex field, as it ...

Decision-making and the Iowa Gambling Task

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Decision-making is an important component of human executive function, in which a choice about a course of action or cognition is made from many possibilities. Damage to the inferior parts of the frontal lobes can affect a person's ability to make good decisions. However, while decision-making deficits can have a large impact on one's life, these deficits can be difficult to quantify in the laboratory. In the mid-1990s, a task was designed to mimic real life decision-making in the laboratory. This task, known as the Iowa Gambling Task (IGT), is a cognitively complex task used widely in research and clinical studies as a highly sensitive measure of decision-making ability.1-3
In the IGT, a participant is shown four decks of cards and chooses to reveal a card from one deck on each turn. When a card is turned over, the participant will receive some money, but sometimes will also be required to pay a penalty. Two of the decks have higher payoffs, but also have high penalties such that choosing from these decks leads to a net loss in the long term. The other two decks have lower payoffs, but also present smaller penalties, so that choosing from these decks leads to a net gain. Thus, to make an advantageous choice, participants must integrate information about losses and gains over time.
This video demonstrates how to administer the IGT to compare the performance of patients with damage to the ventromedial prefrontal cortex to a group of matched control subjects, revealing the unique contribution of this brain region to decision-making.

Decision-making and the Iowa Gambling Task- Effect of VMPFC Damage

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Decision-making is an important component of human ...

Executive Function in Autism Spectrum Disorder

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Attention, working-memory, planning, impulse control, inhibition, and mental flexibility are important components of human cognition that are often referred to as executive functions. Autism spectrum disorder is a developmental disorder that is characterized by impairments in social interaction, communication, and repetitive behaviors. It is a disorder that lasts a lifetime, and is thought to affect 0.6% of the population. The symptoms of autism suggest a deficit in executive function, which may be assessed by specialized neuropsychological tests. By employing several tests that each emphasize different aspects of executive function, we can gain a more complete picture of the cognitive profile of the disorder. 
One such task, known as the Wisconsin Card Sorting Test (WCST), is a cognitively complex task used widely in research and clinical studies as a highly sensitive measure of deficits in executive function. It tests a person's ability to shift attention and tests their flexibility with changing rules and reinforcement.1 In the WCST, a participant is presented with four stimulus cards, incorporating three stimulus parameters: color, shape, and number. The participant is asked to sort response cards according to different principles, changing their sorting criteria based on feedback from the experimenter. Participants try out different rules until they find the correct method for sorting the cards. Patients with executive dysfunction tend to get stuck in the card sorting task, unable to change their sorting strategy. This persistence with an incorrect strategy is called perseveration. 
A second task, The Tower of London (ToL) is a test dependent on complex planning, re-evaluation, and updating of planned moves. Individuals with autism have been reported to be impaired on tasks involving planning.2 In the ToL task, individuals must move disks from a prearranged sequence on three pegs to match a goal state in as few moves as possible, following specific rules. 
A third task, known as the Stroop test, targets cognitive inhibition. In this task participants are shown a name of a color, written in a different color, and are asked to identify the color the word is written in. For example, in an incongruent condition, the word blue would be written in green. Individuals with inhibition difficulty should not perform as well as typically developing individuals on this task involving inhibition of the written word.
In this video, we show how to administer the WCST, ToL, and Stroop task to compare flexibility, planning, and inhibition in children with autism spectrum disorder and typically developing counterparts, and explore how each of these groups performs on these different aspects of executive function.

Behavioral Tests to Assess Executive Functions in Children with ASD

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Attention, working-memory, planning, impulse control, ...

Anterograde Amnesia

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Anterograde amnesia is the loss of the ability to form new memories. This can be distinguished from retrograde amnesia, which is the loss of old memories. Anterograde amnesia can result from damage to structures in the brain that are involved in the formation of new memories. Patients who have damage to the structures of the medial temporal lobe, including the hippocampus, amygdala, and the surrounding cortices, often have severe deficits in the formation of certain kinds of memories. These cases can be informative as to how memory is organized in the brain, and how different systems support different kinds of memories. 
In this video, we will test a patient with medial temporal lobe damage on a series of memory tasks designed to distinguish between different forms of memory. First, we will test short-term or working memory, which is the process we use to keep information in mind temporarily. Next, we will test two different forms of long-term memory: explicit and implicit memory. Explicit memories are conscious and easy to verbalize. For example, memories of facts or episodes from our lives are explicit memories. We can easily tell someone what we ate for breakfast, or what city is the capital of France. Implicit memory involves knowledge we gain from experience but that is not easily expressible. For example, knowing how to do things, or becoming habituated to a stimulus are forms of implicit memory. 
These procedures are based in part on studies of the famous patient Henry Molaison, also known by his initials H.M., who had severe anterograde amnesia as a result of a surgery for intractable epilepsy in which parts of both temporal lobes were resected.1 We will perform a test of digit span, which measures short-term memory, a test of paired-associate learning, which measures explicit or declarative memory, and mirror-drawing, a test of implicit skill learning.2

Testing Short- and Long-term Memories in Patients with Brain Injuries

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Anterograde amnesia is the loss of the ability to form ...

Physiological Correlates of Emotion Recognition

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
The autonomic nervous system (ANS) controls the activity of the body's internal organs and regulates changes in their activity depending on the current environment. The vagus nerve, which innervates many of the internal organs, is an important part of the system. When our brain senses danger, vagal tone is inhibited, leading to a set of changes in the body designed to make us more prepared to fight or flee; for example, our heart rate increases, our pupils dilate, and we breath more quickly. Conversely, when the vagal system is activated, these physiological responses are inhibited, leading to a calmer state. The vagus nerve, then, acts as a kind of "brake" on our arousal. One interesting consequence of this calmer state is that it tends to promote social interaction-when we are not tensed and afraid of our immediate environment we are instead receptive to interacting with others. Poor functioning of this regulatory mechanism, therefore, may be associated with difficulties in social behavior.
One index of autonomic regulation is heart rate variability (HRV). HRV is a measure of how much the gap between one beat and the next varies over time. High HRV means there are continual fluctuations in the heart rate over time, a reflection of successful autonomic regulation. Low HRV means there is consistency of the heart rate over time, a condition associated with poor autonomic regulation. 
In this study we will test the hypothesis that increased HRV is associated with more accurate categorization of emotional stimuli.1,2 Following a study by Park et al., we will measure HRV and test its association on a task that measures skill at perceiving facial emotions.3

Correlating Heart Rate Variability with Emotion Recognition

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
The autonomic nervous system (ANS) controls the ...

Event-related Potentials and the Oddball Task

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Given the overwhelming amount of information captured by the sensory organs, it is crucial that the brain is able to prioritize the processing of certain stimuli, to spend less effort on what might not be currently important and to attend to what is. One heuristic the brain uses is to ignore stimuli that are frequent or constant in favor of stimuli that are unexpected or unique. Therefore, rare events tend to be more salient and capture our attention. Furthermore, stimuli that are relevant to our current behavioral goals are prioritized over those that are irrelevant. 
The neurophysiological correlates of attention have been experimentally examined through the use of the oddball paradigm. Originally introduced in 1975, the oddball task presents the participant with a sequence of repetitive audio or visual stimuli, infrequently interrupted by an unexpected stimulus.1 This interruption by a target stimulus has been shown to elicit specific electrical events that are recordable at the scalp known as event-related potentials (ERPs). An ERP is the measured brain response resulting from a specific sensory, cognitive, or motor event. ERPs are measured using electroencephalography (EEG), a noninvasive means of evaluating brain function in patients with disease and normally functioning individuals. A specific ERP component found across the parietal region of the scalp, known as the P300, is enhanced in response to oddball events. The P300 is a positive-going deflection in the EEG signal that occurs about between 250 and 500 ms after stimulus onset. In general, early potentials reflect sensory-motor processing while later potentials like the P300 reflect cognitive processing. 
In this video, we show how to administer the oddball task using EEG. The video will cover the setup and administration of EEG, and analysis of ERPs related to both control and target stimuli in the oddball task. In this task, participants are set up with the EEG electrodes, then brain activity is recorded while they view control stimuli, interspersed with target stimuli. The procedure is similar to that of Habibi et al.2 Each time a target stimulus is presented, the participant presses a button. When the ERPs are averaged across the control and target stimuli, the neural correlates of each event can be compared in a selected time window.

Measuring Event-related Potentials Using EEG in Oddball Task

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Given the overwhelming amount of information captured ...

Language: The N400 in Semantic Incongruity

Source: Laboratories of Sarah I. Gimbel and Jonas T. Kaplan&#8212; University of Southern California
Understanding language is one of the most complex cognitive tasks that humans are capable of. Given the incredible amount of possible choices when combining individual words to form meaning in sentences, it is crucial that the brain is able to identify when words form coherent combinations and when an anomaly appears that undermines meaning. Extensive research has shown that certain scalp-recorded electrical events are sensitive to deviations in this kind of expectation. Importantly, these electrical signatures of incongruity are specific to unexpected meanings, and are therefore different from the brain's general responses to other kinds of anomalies. 
The neurophysiological correlates of semantic incongruity have been experimentally examined through the use of paradigms that present semantically congruent and incongruent ends to sentences. Originally introduced in 1980, the semantic incongruity task presents the participant with a series of sentences that end with either a congruent or incongruent word. To test that the response is from semantic incongruity and not more generally due to surprise, some sentences included words presented in a different size.1 The semantically incongruent end to a sentence has been shown to elicit specific electrical events that are recordable at the scalp known as event-related potentials (ERPs). An ERP is the measured brain response resulting from a specific sensory, cognitive, or motor event. ERPs are measured using electroencephalography (EEG), a noninvasive means of evaluating brain function in patients with disease and normally functioning individuals. A specific ERP component found across the scalp, known as the N400, shows greater amplitude in response to semantically incongruent events. The N400 is a negative-going deflection in the EEG signal that occurs about between 250 and 400 ms after stimulus onset. In general, early potentials reflect sensory-motor processing, while later potentials like the N400 reflect cognitive processing. 
In this video, we show how to administer a semantic incongruity task using EEG. The video will cover the setup and administration of EEG, and analysis of ERPs related to both control and target stimuli in the semantic incongruity. In this task, participants are set up with the EEG electrodes, then brain activity is recorded while they view control sentences and semantically incongruent sentences. The EEG procedure is similar to that of Habibi et al.,1 and the task is modeled after Kutas and Hillyard.2 When the ERPs are averaged across the congruous and incongruous sentences, the neural correlates of each event can be compared in a selected time window.

Studying Language Processing: the N400 in Semantic Incongruity

Source: Laboratories of Sarah I. Gimbel and Jonas T. Kaplan&#8212; University of Southern California
Understanding language is one of the most complex ...

Learning and Memory: The Remember-Know Task

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Our experience of memory is varied and complex. Sometimes we remember events in vivid detail, while other times we may only have a vague sense of familiarity. Memory researchers have made a distinction between memories that are recollected versus those that are familiar. A recollected item is one that is not only remembered, but carries with it details of the time at which it was learned or encoded. Like a recollected item, a familiar item is also remembered, but is void of any details about the circumstances surrounding its encoding. Many studies of recollection and familiarity have focused on the medial temporal lobe (MTL), specifically the hippocampus, since its involvement in memory encoding, consolidation, and retrieval is well-known and well-studied.1-3
This video shows how to administer the Remember-Know task4 to compare brain activation in these two types of memory retrieval. In this context, remember is another term for recollection, while know refers to memories that are familiar but not explicitly recollected. In this version of the Remember-Know task, participants are exposed to a series of color images, and asked to remember what they see. Inside an fMRI scanner, they will be exposed to both images that were studied and to novel images, and they will make a "remember," "know," or "new" judgment about each image, indicating what kind of memory they have for that item. Following the scan, whole brain and hippocampal activity will be examined to determine differential activity related to recollection and familiarity. This study is based on a study performed by Gimbel and Brewer.5

The Remember-Know Task: Memory Recall and Brain Activation

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Our experience of memory is varied and complex. ...

Measuring Grey Matter Differences with Voxel-based Morphometry: The Musical Brain

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Experience shapes the brain. It is well understood that our brains are different as a result of learning. While many experience-related changes manifest themselves at the microscopic level, for example by neurochemical adjustments in the behavior of individual neurons, we may also examine anatomical changes to the structure of the brain at a macroscopic level. One famous example of this kind of change comes from the case of the London taxi drivers, who along with learning the complex routes of the city show larger volume in the hippocampus, a brain structure known to play a role in navigational memory.1
Many traditional methods of examining brain anatomy require painstaking tracing of anatomical regions of interest in order to measure their size. However, using modern neuroimaging techniques, we can now compare the anatomy of the brains across groups of people using automated algorithms. While these techniques do not avail themselves of the sophisticated knowledge that human neuroanatomists may bring to the task, they are quick, and sensitive to very small differences in anatomy. In a structural magnetic resonance image of the brain, the intensity of each volumetric pixel, or voxel, relates to the density of the gray matter in that region. For example, in a T1-weighted MRI scan, very bright voxels are found in locations where there are white matter fiber bundles, while darker voxels correspond to grey matter, where the cell bodies of neurons reside. The technique of quantifying and comparing brain structure on a voxel-by-voxel basis is called voxel-based morphometry, or VBM.2 In VBM, we first register all of the brains to a common space, smoothing over any gross differences in anatomy. We then compare the intensity values of the voxels to identify localized, small scale differences in gray matter density.
In this experiment, we will demonstrate the VBM technique by comparing the brains of musicians with those of non-musicians. Musicians engage in intense motoric, visual, and acoustic training. There is evidence from multiple sources that that the brains of people who have gone through musical training are functionally and structural different from those who haven't. Here, we follow Gaser and Shlaug3 and Bermudez et al.4 in using VBM to identify these structural differences in the brains of musicians.

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Experience shapes the brain. It is well understood ...

Decoding Auditory Imagery with Multivoxel Pattern Analysis

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Imagine the sound of a bell ringing. What is happening in the brain when we conjure up a sound like this in the "mind's ear?" There is growing evidence that the brain uses the same mechanisms for imagination that it uses for perception.1 For example, when imagining visual images, the visual cortex becomes activated, and when imagining sounds, the auditory cortex is engaged. However, to what extent are these activations of sensory cortices specific to the content of our imaginations? 
One technique that can help to answer this question is multivoxel pattern analysis (MPVA), in which functional brain images are analyzed using machine-learning techniques.2-3 In an MPVA experiment, we train a machine-learning algorithm to distinguish among the various patterns of activity evoked by different stimuli. For example, we might ask if imagining the sound of a bell produces different patterns of activity in auditory cortex compared with imagining the sound of a chainsaw, or the sound of a violin. If our classifier learns to tell apart the brain activity patterns produced by these three stimuli, then we can conclude that the auditory cortex is activated in a distinct way by each stimulus. One way to think of this kind of experiment is that instead of asking a question simply about the activity of a brain region, we ask a question about the information content of that region. 
In this experiment, based on Meyer et al., 2010,4 we will cue participants to imagine several sounds by presenting them with silent videos that are likely to evoke auditory imagery. Since we are interested in measuring the subtle patterns evoked by imagination in auditory cortex, it is preferable if the stimuli are presented in complete silence, without interference from the loud noises made by the fMRI scanner. To achieve this, we will use a special kind of functional MRI sequence known as sparse temporal sampling. In this approach, a single fMRI volume is acquired 4-5 s after each stimulus, timed to capture the peak of the hemodynamic response.

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Imagine the sound of a bell ringing. What is happening ...

Visual Attention: fMRI Investigation of Object-based Attentional Control

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212; University of Southern California
The human visual system is incredibly sophisticated and capable of processing large amounts of information very quickly. However, the brain's capacity to process information is not an unlimited resource. Attention, the ability to selectively process information that is relevant to current goals and to ignore information that is not, is therefore an essential part of visual perception. Some aspects of attention are automatic, while others are subject to voluntary, conscious control. In this experiment we explore the mechanisms of voluntary, or "top-down" attentional control on visual processing. 
This experiment leverages the orderly organization of visual cortex to examine how top-down attention can selectively modulate the processing of visual stimuli. Certain regions of the visual cortex appear to be specialized for processing specific visual items. Specifically, work by Kanwisher et al.1 has identified an area in the fusiform gyrus of the inferior temporal lobe that is significantly more active when subjects view faces compared to when they observe other common objects. This area has come to be known as the Fusiform Face Area (FFA). Another brain region, known as the Parahippocampal Place Area (PPA), responds strongly to houses and places, but not to faces.2 Given that we know how these regions respond to specific types of stimuli, their activity can be further explored to identify a key component of vision-visual attention. 
This video shows how to use fMRI to localize the FFA and PPA in the brain, and then examines how object-based attentional control modulates activity in these areas. The use of a functional localizer to restrict subsequent hypothesis testing is a powerful technique in functional imaging. Participants will undergo functional MRI while being presented with an overlaid image of a face and a house. Even though both a face and a house are presented in each stimulus, we predict that patterns of activity in their FFA and PPA will change based on which item is being attended to.3

fMRI Investigation of Object-based Visual Attentional Control

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212; University of Southern California
The human visual system is incredibly sophisticated ...

Using Diffusion Tensor Imaging in Traumatic Brain Injury

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Traditional brain imaging techniques using MRI are very good at visualizing the gross structures of the brain. A structural brain image made with MRI provides high contrast of the borders between gray and white matter, and information about the size and shape of brain structures. However, these images do not detail the underlying structure and integrity of white matter networks in the brain, which consist of axon bundles that interconnect local and distant brain regions.
Diffusion MRI uses pulse sequences that are sensitive to the diffusion of water molecules. By measuring the direction of diffusion, it is possible to make inferences about the structure of white matter networks in the brain. Water molecules within an axon are constrained in their movements by the cell membrane; instead of randomly moving in every direction with equal probability (isotropic movement), they are more likely to move in certain directions, in parallel with the axon (anisotropic movement; Figure 1). Therefore, measures of diffusion anisotropy are thought to reflect properties of the white matter such as fiber density, axon thickness, and degree of myelination. One common measure is fractional anisotropy (FA). FA values range from 0, which represents completely isotropic movement, to 1, reflecting maximum anisotropy.
<img alt="Figure 1" src="/files/ftp_upload/10276/10276fig1.jpg" /> 
Figure 1: Diffusion anisotropy. When the direction of diffusion is unconstrained and random, movement is measured in all directions equally. This is isotropic diffusion (A). When water molecules are contained within the axon of a neuron, diffusion is anisotropic, tending to occur more frequently along the direction of the axon (B). <a href="http://www.jove.com/files/ftp_upload/10276/10276fig1large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>
In this experiment we will use diffusion tensor imaging (DTI) to measure white matter integrity in traumatic brain injury (TBI). TBI occurs when an external force injures the brain, such as a blow to the head or a sudden movement like the kind that might occur in a car accident. This type of brain injury from mechanical forces is associated with diffuse axonal injury-damage to white matter throughout the brain. Because it is an injury affecting white matter integrity, standard neuroimaging techniques may not reveal the damage. However, measures of diffusion are especially sensitive to these anatomical changes. Following a study by Kraus et al.1, we compare a group of healthy controls to a group of people with TBI and use diffusion imaging to measure the effect of TBI on cerebral white matter. Furthermore, we will test the relationship between white matter integrity and cognitive function using an attention task.2 This study uses a region of interest (ROI) approach focusing on three white matter tracts: the splenium of the corpus callosum, the anterior corona radiata, and the superior longitudinal fasciculus (Figure 2).
<img alt="Figure 2" src="/files/ftp_upload/10276/10276fig2.jpg" /> 
Figure 2: Regions of interest. The three ROIs, defined from the ICBM DTI-81 atlas, are shown here in horizontal slices through the brain. In green is the splenium of the corpus callosum. The splenium is the most posterior part of the corpus callosum. In blue is the anterior corona radiata. The superior longitudinal fasciculus is shown in red. <a href="http://www.jove.com/files/ftp_upload/10276/10276fig2large.jpg" target="_blank">Please click here to view a larger version of this figure.</a>

Diffusion Tensor Imaging in Traumatic Brain Injury

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Traditional brain imaging techniques using MRI are ...

Using TMS to Measure Motor Excitability During Action Observation

Source: Laboratories of Jonas T. Kaplan and Sarah I. Gimbel&#8212;University of Southern California
Transcranial Magnetic Stimulation (TMS) is a non-invasive brain stimulation technique that involves passing current through an insulated coil placed against the scalp. A brief magnetic field is created by current in the coil, and because of the physical process of induction, this leads to a current in the nearby neural tissue. Depending on the duration, frequency, and magnitude of these magnetic pulses, the underlying neural circuitry can be affected in many different ways. Here, we demonstrate the technique of single-pulse TMS, in which one brief magnetic pulse is used to stimulate the neocortex.
One observable effect of TMS is that it can produce muscle twitches when applied over the motor cortex. Due to the somatotopic organization of the motor cortex, different muscles can be targeted depending on the precise placement of the coil. The electrical signals that cause these muscle twitches, called motor evoked potentials, or MEPs, can be recorded and quantified by electrodes placed on the skin over the targeted muscle. The amplitude of MEPs can be interpreted to reflect the underlying excitability of the motor cortex; for example, when the motor cortex is activated, observed MEPs are larger. 
In this experiment, based on a study originally performed by Fadiga and colleagues1 and since replicated by many others,2 we use single-pulse TMS to test the excitability of motor cortex during action observation. It is known that motor cortex can be activated not only when we move, but when we watch others perform movements. A common interpretation of this phenomenon is that it reflects a simulation process that may play a role in the understanding of others' actions. Here we will record MEPs evoked by TMS over the primary motor cortex while subjects observe the movements of others compared with control stimuli.

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