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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 ...

Eye Exam

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
Proper evaluation of the eyes in a general practice setting involves vision testing, orbit inspection, and ophthalmoscopic examination. Before beginning the exam, it is crucial to be familiar with the anatomy and physiology of the eye. The upper eyelid should be slightly over the iris, but it shouldn&#39;t cover the pupil when open; the lower lid lies below the iris. The sclera normally appears white or slightly buff in color. The appearance of conjunctiva, a transparent membrane covering the anterior sclera and the inner eyelids, is a sensitive indicator of ocular disorders, such as infections and inflammation. The tear-producing lacrimal gland lies above and lateral to the eyeball. Tears spread down and across the eye to drain medially into two lacrimal puncta before passing into the lacrimal sac and nasolacrimal duct to the nose.
The iris divides the anterior from the posterior chamber. Muscles of the iris control the size of the pupil, and muscles of the ciliary body behind it control the focal length of the lens. The ciliary body also produces aqueous humor, which largely determines intraocular pressure (Figure 1). Cranial nerves II and III control pupillary reaction and lens accommodation; cranial nerve III controls upper lid elevation; cranial nerves III, IV, and VI control eye movement. The six cardinal directions of gaze are controlled by six extraocular muscles (Figure 2) innervated by cranial nerves III, IV, and VI.
Visual testing is an essential part of the ophthalmological exam and is also performed as a part of cranial nerve II assessment during the neurological exam. A focused image is projected onto the retina after its light passes through the cornea, pupil, lens, and vitreous body. The projection is upside down and reversed right to left, which means that light entering from the lower temporal field of vision strikes the upper nasal quadrant of the retina. Photosensitive cells of the retina respond by generating electrical impulses, which are relayed to the optic nerve and passed to the visual cortex through the optic tracts. The right and left visual cortices process images entering from the left and right visual fields, respectively.
<img alt="Figure 1" src="/files/ftp_upload/10149/10149fig1.jpg" /> 
Figure 1. Anatomy of the Eye. A diagram showing a sagittal view of the human eye with the structures labeled.
<img alt="Figure 2" src="/files/ftp_upload/10149/10149fig2.jpg" />
Figure 2. Muscles of the Eye. A cartoon showing a frontal view of the human eye and the extraocular muscles (labeled).

Anatomy and Physiology of Eye; Acuity and Vision Testing

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
...

Ophthalmoscopic Examination

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
The simplest ophthalmoscopes consist of an aperture to look through, a diopter indicator, and a disc for selecting lenses. The ophthalmoscope is primarily used to examine the fundus, or the inner wall of the posterior eye, which consists of the choroid, retina, fovea, macula, optic disc, and retinal vessels (Figure 1). The spherical eyeball collects and focuses light on the neurosensory cells of the retina. Light is refracted as it passes sequentially through the cornea, the lens, and the vitreous body.
The first landmark observed during the funduscopic exam is the optic disc, which is where the optic nerve and retinal vessels enter the back of the eye (Figure 2). The disc usually contains a central whitish physiologic cup where the vessels enter; it normally occupies less than half the diameter of the entire disc. Just lateral and slightly inferior is the fovea, a darkened circular area that demarcates the point of central vision. Around this is the macula. A blind spot approximately 15&#176; temporal to the line of gaze results from a lack of photoreceptor cells at the optic disc.
<img alt="Figure 1" src="/files/ftp_upload/10146/10146fig1.jpg" /> 
Figure 1. Anatomy of the eye. A diagram showing a sagittal view of the human eye with the structures labeled.
<img alt="Figure 2" src="/files/ftp_upload/10146/10146fig2.jpg" /> 
Figure 2: Normal retina. A photograph showing an ophthalmoscopic view on the normal retina.

Ophthalmoscopic Functioning and Examination of the Fundus

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
The ...

Ear Exam

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
This video describes the examination of the ear, beginning with a review of its surface and interior anatomy (Figure 1). The cartilaginous auricle consists of the helix, antihelix, earlobe, and tragus. The mastoid process is positioned just behind the earlobe. The slightly curving auditory canal ends at the tympanic membrane, which transmits sound waves collected by the external ear to the air-filled middle ear. The Eustachian tube connects to the middle ear with the nasopharynx. Vibrations of the tympanic membrane transmit to the three connected ossicles of the middle ear (the malleus, incus, and stapes). The vibrations are transformed into electrical signals in the inner ear, and then carried to the brain by the cochlear nerve. Hearing, therefore, comprises a conductive phase that involves the external and middle ear, and a sensorineural phase that involves the inner ear and cochlear nerve.
The auditory canal and the tympanic membrane are examined with the otoscope, a handheld instrument with a light source, a magnifier, and a disposable cone-shaped speculum. It is important to be familiar with the tympanic membrane landmarks (Figure 2). Only two of the three ossicles - the malleus and incus - can normally be seen; the malleus is near the center, and the uncus is just posterior. A cone of light can be seen emanating downward and anteriorly from the umbo, or point of contact between the membrane and the tip of the malleus. The short process roughly demarcates the boundary between the two regions of the tympanic membrane: the pars flaccida, lying superior and posterior, and the far larger pars tensa, lying anterior and inferior. Normally, the tympanic membrane is pink-gray in color and readily reflects the light of the otoscope.
<img alt="Figure 1" src="/files/ftp_upload/10148/10148fig1.jpg" /> 
Figure 1. Anatomy of the Ear. A schematic drawing of the human ear in frontal section with outer, middle, and inner ear structures labeled.

Anatomy of the Ear, External Ear Exam and Hearing Tests

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
This ...

Nose, Sinuses, Oral Cavity and Pharynx Exam

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
This video provides an overview of sinus, nose, and throat examinations. The demonstration begins with a brief overview of the anatomy of the region. The upper third of the nose is bony, and the bottom two-thirds are cartilaginous. Air entering the nares passes through the nasal vestibules and into the narrow passageway between the nasal septum medially and the bony turbinates laterally. Beneath each curving turbinate is a groove or meatus. The nasolacrimal duct and most of the air-filled paranasal sinuses drain into the inferior and middle meatuses, respectively. Of the three sets of paranasal sinuses, only the maxillary and frontal can be readily examined. A continuous, highly vascular mucosa lines the entire nasal cavity and sinuses.
<img alt="Figure 1" src="/files/ftp_upload/10152/10152fig1.jpg" /> 
Figure 1. Anatomy of the Nose. 
<img alt="Figure 2" src="/files/ftp_upload/10152/10152fig2.jpg" /> 
Figure 2. Location of the Major Sinuses.
Muscular folds of the lips mark the entrance to the oral cavity. The pinkish gingiva, or gums, attach firmly to the teeth and adjacent bone into which the teeth embed. The buccal mucosa lines the inner cheeks, where the Stensen duct drains the parotid glands into small papillae near the upper second molars. Small, red papillae cover the dorsal surface of the tongue along with a whitish coat of varying thickness. The midline lingual frenulum connects the undersurface of the tongue to the floor of the mouth, where the Wharton duct drains the submandibular glands into papillae on either side. Arching over the tongue are the anterior and posterior pillars of the soft palate and midline uvula. If present, the tonsils can be seen protruding bilaterally between the pillars. The bony hard palate rises anteriorly above the soft palate. The pharynx lies posteriorly behind the soft palate and tongue.
<img alt="Figure 3" src="/files/ftp_upload/10152/10152fig3.jpg" /> 
Figure 3. Anatomy of the Oral Cavity.
<img alt="Figure 4" src="/files/ftp_upload/10152/10152fig4.jpg" /> 
Figure 4. Pharyngeal Regions.

Thyroid Exam

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
The thyroid gland is located in the neck anterior trachea between the cricoid cartilage (above) and the suprasternal notch (below) (Figure 1). It consists of a right and left lobe connected by an isthmus. The isthmus covers the second, third, and fourth tracheal rings, and the lobes curve posteriorly around the sides of the trachea and esophagus. The normal gland, weighing 10 - 25 g, is usually invisible on inspection and often difficult to palpate. A goiter is an enlarged thyroid from any cause. In addition to assessing its size, it is important to palpate the thyroid for its shape, mobility, consistency, and tenderness. A normal thyroid is soft, smooth, symmetrical, and non-tender, and it slides upward slightly when swallowing. Symmetrical enlargement of a soft, smooth thyroid suggests endemic hypothyroidism due to iodine deficiency or one of two prevalent autoimmune disorders: Graves&#39; disease or Hashimoto&#39;s thyroiditis. Thyroid nodules are common and usually incidental; however, 10% of thyroid nodules turn out to be malignant. They may be single or multiple, and are most often firm and non-tender. A tender, symmetrical goiter typically indicates thyroiditis.
<img alt="Figure 1" src="/files/ftp_upload/10098/10098fig1.jpg" /> 
Figure 1. Anatomy of the thyroid gland. Illustration of the location and anatomy of the thyroid gland with respect to the neck structures.
Thyroid disease rarely manifests as a palpable goiter in isolation. Thyroid hormones serve to maintain homeostasis primarily by stimulating cellular metabolism throughout the body. Thus, hypo and hyperthyroidism are associated with a range of symptoms and physical findings (Table 1). It is important to note that goiters may be euthyroid (normal thyroid hormone levels), hyperthyroid, or hypothyroid. Headaches or visual disturbances may suggest a secondary thyroid disorder due to a pituitary adenoma
<img alt="Table 1" src="/files/ftp_upload/10098/10098table1.jpg" />
Table 1. Symptoms and physical findings for hypo- and hyper-thyroidism.&#160;

Thyroid Anatomy, Physiology and Palpation Examination

Lymph Node Exam

Source: Richard Glickman-Simon, MD, Assistant Professor, Department of Public Health and Community Medicine, Tufts University School of Medicine, MA
The lymphatic system has two main functions: to return extracellular fluid back to the venous circulation and to expose antigenic substances to the immune system. As the collected fluid passes through lymphatic channels on its way back to the systemic circulation, it encounters multiple nodes consisting of highly concentrated clusters of lymphocytes. Most lymph channels and nodes reside deep within the body and, therefore, are not accessible to physical exam (Figure 1). Only nodes near the surface can be inspected or palpated. Lymph nodes are normally invisible, and smaller nodes are also non-palpable. However, larger nodes (&#62;1 cm) in the neck, axillae, and inguinal areas are often detectable as soft, smooth, movable, non-tender, bean-shaped masses imbedded in subcutaneous tissue.
Lymphadenopathy usually indicates an infection or, less commonly, a cancer in the area of lymph drainage. Nodes may become enlarged, fixed, firm, and/or tender depending on the pathology present. For example, a soft, tender lymph node palpable near the angle of the mandible may indicate an infected tonsil, whereas a firm, enlarged, non-tender lymph node palpable in the axilla of a female patient may be a sign of breast cancer.
Regional lymph nodes draining the area of a localized infection typically remain invisible but may become enlarged and tender on palpation. An infected wound or cellulitis may also result in lymphangitis or lymphadenitis, a condition in which the infection spreads along the chain of lymph channels and nodes. This may be accompanied by the appearance of red streaks and systemic symptoms such as fever, chills, and malaise. In rare cases, the intensity of the inflammatory reaction may cause the nodes to adhere to the surrounding soft tissue, fixing them in place.
Many metastatic cancers spread to regional lymph nodes first. Unlike infections, malignant cells invading lymph nodes may cause them to feel irregular and firm (even rock hard) but remain non-tender. If the cancer invades the outer capsules, nodes may become fixed to the surrounding soft tissue or matted together. Lymphoma, a primary cancer intrinsic to the lymphatic system, may be present anywhere in the body as single or multiple enlarged lymph nodes, which may become big enough to see on inspection, and are generally hard and non-tender on palpation. In addition to lymphoma, diffuse lymphadenopathy may be an indication of generalized infectious or inflammatory disorders such as HIV, mononucleosis, or sarcoidosis.
<img alt="Figure 1" src="/files/ftp_upload/10061/10061fig1.jpg" /> 
Figure 1. The Lymphatic System.

Lymph Nodes: Head &amp; Neck, Axillae, Upper &amp; Lower Extremities

Abdominal Exam I: Inspection and Auscultation

Source: Alexander Goldfarb, MD, Assistant Professor of Medicine, Beth Israel Deaconess Medical Center, MA
Gastrointestinal disease accounts for millions of office visits and hospital admissions annually. Physical examination of the abdomen is a crucial tool in diagnosing diseases of the gastrointestinal tract; in addition, it can help identify pathological processes in cardiovascular, urinary, and other systems. As physical examination in general, the examination of the abdominal region is important for establishing physician-patient contact, for reaching the preliminary diagnosis and selecting subsequent laboratory and imaging tests, and determining the urgency of care.
As with the other parts of a physical examination, visual inspection and auscultation of the abdomen are done in a systematic fashion so that no potential findings are missed. Special attention should be paid to potential problems already identified by the patient&#39;s history. Here we assume that the patient has already been identified, and has had history taken, symptoms discussed, and areas of potential concern identified. In this video we will not review the patient&#39;s history; instead, we will go directly to the physical examination.
Before we get to the examination, let&#39;s briefly review surface landmarks of the abdominal region, abdominal anatomy, and topography. Here is a list of useful landmarks: costal margins, xiphoid process, rectus abdominal muscle, linea alba, umbilicus, iliac crest, inguinal ligament, and symphysis pubis. The abdominal exam covers the area down from the xiphoid and costal margins superiorly to the symphysis pubis inferiorly.
For diagnostic and descriptive purposes, the abdomen is subdivided into four quadrants: right upper quadrant (often designated as RUQ), left upper quadrant (LUQ), right lower quadrant (RLQ), and left lower quadrant (LLQ) (Figure 1). The more detailed topography of the abdomen divides it into 9 regions: right and left hypochondriac, right and left lumbar, right and left iliac, and also epigastric, umbilical, and hypogastric regions in the middle (Figure 2).
Remember which organs typically project into each abdominal region (Figure 3). It is essential to know the region&#39;s anatomy and topography well to adequately document and interpret a patient&#39;s complaints and symptoms, as well as physical findings during the examination.
<img alt="Figure 1" src="/files/ftp_upload/10088/10088fig1.jpg" /> 
Figure 1. Four abdominal quadrants. The abdomen can be divided into four regions by two imaginary lines intersecting at the umbilicus: right upper quadrant (often designated as RUQ), left upper quadrant (LUQ), right lower quadrant (RLQ), and left lower quadrant (LLQ) are shown.
<img alt="Figure 2" src="/files/ftp_upload/10088/10088fig2.jpg" /> 
Figure 2. Nine abdominal regions. Midclavicular lines and subcostal and intertubercular planes separate the abdomen into nine regions: epigastric region, right hypochondriac region, left hypochondriac region, umbilical region, right lumbar region, left lumbar region, hypogastric region, right inguinal region, and left inguinal region. Terms for epigastric, umbilical, and hypogastric and suprapubic regions are the most commonly used in clinical practice.
<img alt="Figure 3" src="/files/ftp_upload/10088/10088fig3.jpg" /> 
Figure 3. Location of different organs in the four abdominal regions. Organs in the abdominal cavity and their location with respect to four abdominal quadrants.

Abdominal Exam I: Anatomy, Topography and Auscultation

Source: Alexander Goldfarb, MD, Assistant Professor of Medicine, Beth Israel Deaconess Medical Center, MA
Gastrointestinal disease accounts for millions ...

Abdominal Exam II: Percussion

Source: Alexander Goldfarb, MD, Assistant Professor of Medicine, Beth Israel Deaconess Medical Center, MA
Medical percussion is based on the difference in pitch between the sounds elicited by tapping on the body wall. The auditory response to tapping depends on the ease with which the body wall vibrates, and is influenced by underlying organs, strength of the stroke, and the state of the body wall. There are three main medical percussion sounds: resonance (heard over lungs), tympany (heard over the air-filled bowel loops), and dullness (heard over fluid or solid organs). The contrast between dullness vs. tympany or resonance allows for determination of the size and margins of organs and masses, as well as identification of fluid accumulation and areas of consolidation. Percussion remains an intricate part of the physical diagnosis since it was first introduced more than 200 years ago, and is especially useful in examination of the lungs and abdomen.
As a part of an abdominal examination, percussion follows visual inspection and auscultation. The examiner should first percuss over each of the nine abdominal regions (epigastric region, right hypochondriac region, left hypochondriac region, umbilical region, right lumbar region, left lumbar region, hypogastric region, right inguinal region, and left inguinal region). Tenderness elicited by percussion is abnormal, and peritoneal inflammation should be suspected. As the air-filled bowel loops are positioned in the closest proximity to the abdominal wall, the percussion over most parts of the abdominal cavity elicits a predominantly tympanic sound. The presence of large areas of dullness should prompt evaluation for organomegaly, intra-abdominal masses, or fluid.
In addition to assessing the amount and distribution of abdominal gas, an abdominal exam should include an estimation of liver and spleen size by percussion. As the liver and spleen are covered by the rib cage, the examiner should percuss over the lower anterior chest as well. Normally, one expects to hear dull sound on percussion of the right anterior chest over the liver, and tympanic sound on percussion of left anterior chest over the gastric air bubble and the splenic flexure of the colon (Figure 1).
<img alt="Figure 1" src="/files/ftp_upload/10090/10090fig1.jpg" />
Figure 1. Normal percussion notes over abdominal region. With the exception of an area of dullness over the liver in the right lower anterior chest, tympany is the predominant sound heard over the region.

Abdominal Exam II: Percussion Sounds, Dullness and Tympany

Source: Alexander Goldfarb, MD, Assistant Professor of Medicine, Beth Israel Deaconess Medical Center, MA
Medical percussion is based on the difference in ...

Abdominal Exam III: Palpation

Source: Alexander Goldfarb, MD, Assistant Professor of Medicine, Beth Israel Deaconess Medical Center, MA
Abdominal palpation, if performed correctly, allows for examination of the large and relatively superficial organs; for a skilled examiner, it allows for assessment of the smaller and deeper structures as well. The amount of information that can be obtained by palpation of the abdominal area also depends on the anatomical characteristics of the patient. For example, obesity might make palpation of internal organs difficult and require that additional maneuvers be performed. Abdominal palpation provides valuable information regarding localization of the problem and its severity, as abdominal palpation identifies the areas of tenderness as well as presence of organomegaly and tumors. The specific focus of palpation is driven by the information collected during history taking and other elements of the abdominal exam. Palpation helps to integrate this information and develop the strategy for subsequent diagnostic steps.

Abdominal Exam III: Light and Deep Palpation

Source: Alexander Goldfarb, MD, Assistant Professor of Medicine, Beth Israel Deaconess Medical Center, MA
Abdominal palpation, if performed correctly, ...

Abdominal Exam IV: Acute Abdominal Pain Assessment

Source: Joseph Donroe, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Abdominal pain is a frequent presenting concern in both the emergency department and the office setting. Acute abdominal pain is defined as pain lasting less than seven days, while an acute abdomen refers to the abrupt onset of severe abdominal pain with features suggesting a surgically intervenable process. The differential diagnosis of acute abdominal pain is broad; thus, clinicians must have a systematic method of examination guided by a careful history, remembering that pathology outside of the abdomen can also cause abdominal pain, including pulmonary, cardiac, rectal, and genital disorders.
Terminology for describing the location of abdominal tenderness includes the right and left upper and lower quadrants, and the epigastric, umbilical, and hypogastric regions (Figures 1, 2). Thorough examination requires an organized approach involving inspection, auscultation, percussion, and palpation, with each maneuver performed purposefully and with a clear mental representation of the anatomy. Rather than palpating randomly across the abdomen, begin palpating remotely from the site of tenderness, moving systematically toward the tender region, and thinking about what lies below the fingers at each position. A helpful technique is to imagine a clock face with the xiphoid process at 12:00 and the pubic symphysis at 6:00 (Figure 3). When palpating at 8:00, there is skin, muscle, cecum, appendix, and ureters. Performing the exam in this fashion assists in clinical reasoning and minimizes the chance of missing pathology.
<img alt="Figure 1" src="/files/ftp_upload/10120/10120fig1.jpg" /> 
Figure 1. Four abdominal quadrants. Abdomen can be divided into four regions by two imaginary lines intersecting at umbilicus. Right upper quadrant (often designated as RUQ), left upper quadrant (LUQ), right lower quadrant (RLQ), and left lower quadrant (LLQ) are shown.
<img alt="Figure 2" src="/files/ftp_upload/10120/10120fig2.jpg" /> 
Figure 2. Nine abdominal regions. Midclavicular lines and subcostal and intertubercular planes separate abdomen into nine regions: epigastric region, right hypochondriac region, left hypochondriac region, umbilical region, right lumbar region, left lumbar region, hypogastric region, right inguinal region, and left inguinal region.
<img alt="Figure 3" src="/files/ftp_upload/10120/10120fig3.jpg" /> 
Figure 3. Visualizing a clock face over the abdomen for thinking about the underlying anatomy while performing the exam.

Source: Joseph Donroe, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Abdominal pain is a frequent presenting concern in ...

Male Rectal Exam

Source: Joseph Donroe, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
While its usefulness in cancer screening is debated, the male rectal examination remains an important part of the physical exam. The exam is indicated in selected patients with lower urinary tract symptoms, urinary and/or fecal incontinence or retention, back pain, anorectal symptoms, abdominal complaints, trauma patients, unexplained anemia, weight loss, or bone pain. There are no absolute contraindications to the rectal exam; however, relative contraindications include patient unwillingness to undergo the exam, severe rectal pain, recent anorectal surgery or trauma, and neutropenia.
When performing the rectal exam, the examiner should conceptualize the relevant anatomy. The external anal sphincter is the most distal part of the anal canal, which extends three to four centimeters before transitioning into the rectum. The prostate gland lies anterior to the rectum, just beyond the anal canal. The posterior surface of the prostate, including its apex, base, lateral lobes, and median sulcus, can be palpated through the rectal wall (Figure 1). The normal consistency of the prostate is similar to the thenar eminence when the hand is in a tight fist. The thumb knuckle is representative of what a hard nodule may feel like. The normal size of the prostate increases with age and is approximately 4.0 cm by 3.5 cm, or 20-30 g, in a young man.
The steps of the male rectal exam, including preparation, positioning, neurologic assessment, external inspection and palpation, examination of the prostate and rectum, and evaluation of the stool, are detailed in this video.
<img alt="Figure 1" src="/files/ftp_upload/10102/10102fig1.jpg" /> 
Figure 1. Male rectal anatomy (left) and regions of prostate gland posterior surface (right).

Male Rectal Anatomy and Exam Procedure

Source: Joseph Donroe, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
While its usefulness in cancer screening is debated, ...

Comprehensive Breast Exam

Source: 
Alexandra Duncan, GTA, Praxis Clinical, New Haven, CT 
Tiffany Cook, GTA, Praxis Clinical, New Haven, CT 
Jaideep S. Talwalkar, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Breast exams are a key part of an annual gynecological exam and are important for all patients, no matter their sex or gender expression. One out of every 8 women will be diagnosed with breast cancer; male breast cancer, though less common, has a lifetime incidence of 1 in 1000.
Breast exams can feel invasive to patients, so it is important to do everything possible to make the patients feel comfortable and empowered, rather than vulnerable. Examiners should be aware of what they are communicating, both verbally and non-verbally, and give their patients control wherever possible (for instance, always allowing them to remove their own gowns). Examiners may choose to utilize chaperones for the patients&#39; (as well as their own) comfort. Some institutions require the use of chaperones.
While it is always important to avoid overly clinical language, certain colloquial words can cross the line from caring to overly intimate in this exam. It is helpful to avoid the words &#34;touch&#34; and &#34;feel&#34; in this exam, as this language can feel sexualized. Instead, use words like &#34;assess,&#34; &#34;check,&#34; or &#34;examine.&#34;
Additionally, the best practice dictates avoiding assumptions about patients&#39; gender, as patients with female anatomy may identify as another gender (e.g., transgender, genderqueer, etc.). This video depicts the approach to patients whose history has revealed no specific complaints or risk factors related to breast health.
In order to avoid missing potential findings, the breast exam should be performed in a systematic approach and consist of three main components: visual inspection of the breast tissue, palpation of the lymph nodes, and palpation of breast tissue.
The breast tissue extends from directly under the clavicle to around the fifth rib (or bra line). Laterally, it extends from the midaxillary line to the sternal border. The breast is viewed in four quadrants; the upper outer quadrant has the most tissue and is the location of many lymph nodes, and the tail of Spence (or axillary tail) extends to the edge of the axilla, where it attaches to the chest wall (Figure 1).
<img alt="Figure 1" src="/files/ftp_upload/10118/10118fig1.jpg" /> 
Figure 1. Breast anatomical landmarks.

Breast Tissue Anatomy; Tissue and Lymph Node Examination

Source:
Alexandra Duncan, GTA, Praxis Clinical, New Haven, CT
Tiffany Cook, GTA, Praxis Clinical, New Haven, CT
Jaideep S. Talwalkar, MD, Internal ...

Pelvic Exam I: Assessment of the External Genitalia

Source: 
Alexandra Duncan, GTA, Praxis Clinical, New Haven, CT 
Tiffany Cook, GTA, Praxis Clinical, New Haven, CT 
<a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
The pelvic exam can feel invasive to patients, so it is important to do everything possible to make patients feel comfortable and empowered, rather than vulnerable. Clinicians should be aware of how they are communicating, both verbally and nonverbally, and should give their patients control whenever possible. There are many ways to do this, from how the exam table is positioned to how the patient is engaged throughout the exam. As many as 1 in 5 patients may have experienced sexual trauma; therefore, it is important to avoid triggering those patients, but it&#39;s not always possible to know who they are. The exam in this video demonstrates neutral language and techniques that can be employed with all patients to create the best experience possible.
It&#39;s important to keep the patient covered wherever possible and to minimize extraneous contact. A clinician should be careful to tuck fingers that aren&#39;t being used to examine the patient to avoid accidental contact with the clitoris or anus.
Before performing the pelvic examination, examiners should find out how knowledgeable the patients are about the exam and their own bodies, and establish the expectation that the patients can communicate questions or concerns throughout the exam. While it is always important to avoid extremely clinical language, certain colloquial words can cross the line from caring to overly intimate during this exam. It is helpful to avoid the words &#34;touch&#34; and &#34;feel,&#34; which can feel sexualized in this context; instead, the words &#34;assess,&#34; &#34;check,&#34; &#34;inspect,&#34; or &#34;examine&#34; should be used. The words &#34;bed&#34; and &#34;sheet&#34; should be avoided, and &#34;table&#34; and &#34;drape&#34; should be used instead. Also, a clinician should use the word &#34;footrests&#34; rather than &#34;stirrups&#34; to avoid connoting horses. It&#39;s a good idea to avoid telling patients to &#34;relax,&#34; because it&#39;s a hard order for a patient to follow when anxious. Asking patients to &#34;soften&#34; or &#34;release&#34; specific muscles can be more useful, and having a patient do a Kegel exercise or Valsalva maneuver can serve as a specific relaxation technique.
Best practice dictates avoiding assumptions about patients&#39; gender, as patients with female anatomy may identify as another gender (e.g., transgender or genderqueer). This video depicts the approach to a patient whose history has revealed no specific complaints or risk factors related to gynecological health.
The pelvic exam consists of three parts: the visual and manual exam of the external genitalia, a speculum exam, and a bimanual exam. This video covers the introduction to the pelvic exam and the external genitalia exam. To avoid missing potential findings, the external pelvic exam should be performed in a systematic approach consisting of two main components: a visual inspection of the vulva (Figure 1), and internal palpation and assessment of glands and tone.
<img alt="Figure 1" src="/files/ftp_upload/10144/10144fig1.jpg" /> 
Figure 1. Diagram of the vulva. A diagram showing external genitals with the structures labelled.

Pelvic Exam I: External Genitalia Anatomy and Exam Procedure

Pelvic Exam II: Speculum Exam

Source: 
Alexandra Duncan, GTA, Praxis Clinical, New Haven, CT
Tiffany Cook, GTA, Praxis Clinical, New Haven, CT
Jaideep S. Talwalkar, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
Providing comfortable speculum placement is an important skill for providers to develop, since the speculum is a necessary tool in many gynecological procedures. Patients and providers are often anxious about the speculum exam, but it is entirely possible to place a speculum without patient discomfort. It&#39;s important for the clinician to be aware of the role language plays in creating a comfortable environment; for instance, a provider should refer to the speculum &#34;bills&#34; rather than &#34;blades&#34; to avoid upsetting the patient.
There are two types of speculums: metal and plastic (Figure 1). This demonstration utilizes plastic, as plastic speculums are most commonly used in clinics for routine testing. When using a metal speculum, it&#39;s recommended to use a Graves speculum if the patient has given birth vaginally, and a Pederson speculum if the patient has not. Pederson and Graves speculums are different shapes, and both come in many different sizes (medium is used most often). Prior to placing a metal speculum, it is helpful to perform a digital cervical exam to assess for the appropriate speculum size. The depth and direction of the cervix is estimated by placing one finger into the vagina. If the patient&#39;s cervix can be located while the patient is seated, it is likely that the patient has a shallow vagina, and therefore should be most comfortable with a short metal speculum.
<img alt="Figure 1" src="/files/ftp_upload/10141/10141fig1.jpg" /> 
Figure 1. A photograph of commercially available speculums in different sizes. 
Plastic speculums are all shaped like Pederson metal speculums and come in different sizes. To assess the appropriate size for a plastic speculum, the examiner places two fingers in the patient&#39;s vagina, palm down, and tries to separate the fingers: if there is no space between the fingers, a small plastic speculum should be used; if there is space between the fingers, a medium one should be used. The exam should never be performed with a large speculum (as it is significantly longer) without first determining the length of the vaginal canal.
The speculum is used to perform the Papanicolaou test as part of cervical cancer screening examinations. Cervical cancer was once the leading cause of cancer deaths for women in the United States, but in recent decades the number of cases and deaths has declined significantly1. This change is credited to the discovery made by Georgios Papanicolaou in 1928 that cervical cancer could be diagnosed by vaginal and cervical smears. The Pap test, as it is now called, detects abnormal cells in the cervix, both cancerous and pre-cancerous. Current guidelines for recommended screening intervals can be found through the U.S. Preventive Services Task Force (USPSTF) website2.
The test can be performed using either 1) a conventional glass slide and fixative with a spatula and endocervical brush (the traditional &#34;Pap smear&#34;) or 2) the more commonly utilized liquid-based cytology with a cervical broom or a spatula and endocervical brush (Figure 2). No matter what tools are used, the samples are collected from just inside the external os and the squamocolumnar junction, or transition zone around the os (Figure 3). This video demonstrates the spatula and endocervical brush with liquid-based cytology, as the liquid preparation is a more effective technique for the detection of cervical lesions, and the spatula and endocervical brush improve specimen collection.
<img alt="Figure 2" src="/files/ftp_upload/10141/10141fig2.jpg" /> 
Figure 2. Pap smear tools. Shown in sequence are: a liquid cytology canister, cervical broom, spatula, and endocervical brush.
<img alt="Figure 3" src="/files/ftp_upload/10141/10141fig3.jpg" /> 
Figure 3. Diagram of the cervix withrelevant structures labeled.

Pelvic Exam II: Speculum Exam and Pap Smear Test

Source: 
Alexandra Duncan, GTA, Praxis Clinical, New Haven, CT
Tiffany Cook, GTA, Praxis Clinical, New Haven, CT
Jaideep S. Talwalkar, MD, Internal ...

Pelvic Exam III:  Bimanual and Rectovaginal Exam

Source:
Alexandra Duncan, GTA, Praxis Clinical, New Haven, CT
Tiffany Cook, GTA, Praxis Clinical, New Haven, CT
<a href="https://www.jove.com/author/Jaideep+S._Talwalkar">Jaideep S. Talwalkar</a>, MD, Internal Medicine and Pediatrics, Yale School of Medicine, New Haven, CT
A bimanual exam is a thorough check of a patient&#39;s cervix, uterus, and ovaries. It can tell an experienced provider a great deal, as it may lead to the discovery of abnormalities, such as cysts, fibroids, or malignancies. However, it&#39;s useful even in the absence of such findings, as it allows the practitioner to establish an understanding of the patient&#39;s anatomy for future reference.
Performing the bimanual exam before the speculum exam can help relax patients, mentally and physically, before what is often perceived as the &#34;most invasive&#34; part of the exam. A practitioner already familiar with the patient&#39;s anatomy can insert a speculum more smoothly and comfortably. However, lubrication used during the bimanual exam may interfere with processing certain samples obtained during the speculum exam. Providers must be familiar with local laboratory processing requirements before committing to a specific order of examination.
This demonstration begins immediately after the end of the speculum exam; therefore, it assumes the patient has provided a history and is in the modified lithotomy position.
A rectovaginal exam is not always necessary, but it may be performed to fully assess a retroverted uterus and ovaries (this may be the only way to accomplish full assessment depending on uterine position) or to assess the rectum.

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