[전체1등 & A+] 인천대 기계공학실험(2) 파이프 유동실험 1 (급확대관) 레포트

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1. Laminar & Turbulent Flow

Laminar flow refers to a flow in which a layer moves in a traveling direction because fluid particles are attached to each other and thus do not diffuse well. Turbulence refers to a disorderly and unsteady-State flow, as opposed to laminar flow, has low diffusion, high momentum convection, and changes rapidly over time.
2. Reynolds number

The Reynolds number is the ratio of force due to inertia to force due to viscosity, indicating the relative dynamics of these two types of forces under a given flow condition. Reynolds number is one of the most important dimensionless numbers in hydrodynamics, and this Reynolds number can be used to determine whether the fluid flow is laminar or turbulent. In general, laminar flow is defined as when the Reynolds number is lower than 2100 and when the Reynolds number is higher than 4000.
3. Continuity Equation

The continuous equation is a mathematical representation of the law of mass conservation. The continuous equation of an incompressible fluid in a steady state is derived from the law of mass conservation. The law of mass conservation has no change in mass over time. The equation is Q=A*V. (Q=Flow rate, A= Area of pipe, V=Velocity of fluid)
4. Flow characteristics in pipe

For most pipe flows, the pipe cross section perpendicular to the direction in which the fluid flows is a circle. This is to prevent the pipe from being damaged when a force is applied through the pressure difference between the inlet and outlet of the pipe. Circular cross sections allow the force to be evenly distributed. The Bernoulli Equation is . The Head Loss is the sum of Major Loss and Minor Loss. In this experiment, there is not a height difference of the pipe and the velocity is constant because the cross-sectional area does not change. Therefore, we can simplify the above equation. → So, major loss means a pressure difference. In this case, the inside of the pipe should be completely filled with fluid. In laminar flow, the farther away from the center of the pipe, the speed decreases proportionally. The reason for the speed decrease is that the viscous force on the pipe wall acts. In the case of turbulent flow, the viscosity effect is small due to the mixing of fluid particles due to eddy, so the velocity distribution is constant.
5. Major Loss & Friction Factor in Laminar Flow

In laminar flow, the pressure difference may be caused by the flow rate, the length of the pipe, the diameter of the pipe, and the viscosity of the fluid. There are three reference dimensions, and the repetitive variables are set to to obtain dimensionless parameters. In a circular pipe, C is 32. So, , and divided a dynamic pressurein both term.Then, . We can know that the friction factor of laminar flow is 64/Re. As Re number increases, the friction factor tends to decreases.
6. Major Loss & Friction Factor in Turbulent Flow

Although cross-sectional roughness was not affected in laminar flow, it should be considered in turbulent flow. With reference to PI theory, in turbulent flow, the pressure difference considers additional cross-sectional roughness and fluid density of the pipe in addition to flow velocity, pipe length, pipe diameter, and fluid viscosity. There are three reference dimensions and four dimensionless parameters.Simplify through the theory and experiment Pull forward., we can write . So, the friction factor is determined by relative roughness and Reynolds number.
7. Moody Chart

In order to determine the friction factor through the relationship between the relative roughness and the Reynolds number, the moddy chart is the graph by organizing the friction factor data of various pipes. Moody's team used the available data to show that fluid flow in rough pipes could be described by four dimensionless quantities: Reynolds number, pressure loss coefficient, diameter ratio of the pipe and the relative roughness of the pipe. They then produced a single plot which showed that all of these collapsed onto a series of lines, now known as the Moody chart. This dimensionless chart is used to work out pressure drop, and flow rate through pipes. Head loss can be calculated using the Darcy–Weisbach equation in which the Darcy friction factor appears. The chart plots Darcy–Weisbach friction factor against Reynolds number Re for a variety of relative roughnesses, the ratio of the mean height of roughness of the pipe to the pipe diameter or .
8. Experimental Results

The experiment was conducted for pipes with diameters of 6 mm, 11 mm, and 17 mm, respectively. In Case 1, the Reynolds number is in the laminar flow range, and the ideal friction factor is 64/Re. The experimental friction factor was calculated using Darcy's friction factor equation, and the error rate was up to 11%. In Case 2, the laminar flow friction factor equation (64/Re) cannot be used because the Reynolds number falls within the turbulent range. The ideal friction factor was obtained using the Blasius equation, and the error rates were found to be up to 11 percent, indicating a smooth pipe. Case 3 is also assumed to be a smooth pipe, but the error rate obtained using the Blasius equation was very large at 144% to 192%, indicating a rough pipe. The roughness was estimated using the Colebrook equation. Case 4 shows that the pipe is smooth with an error of up to 20% when using the Blasius equation.
9. Conclusion

In a smooth pipe, the error rate is up to 0~20%. The reasons for the error include the pipe not being perfectly smooth, the assumption of friction neglect and steady state, and the impurities in the water used in the experiment. When calculating roughness, the Colebrook equation was used, which involves an approximate solution through numerical analysis, leading to errors. The Haaland Equation could provide a more accurate solution. The experiment also revealed a phenomenon where roughness decreases in Cases 2 and 4 and increases in Case 3, despite the same trend in Reynolds number increase. This suggests that the friction factor affects roughness, which can be observed in the Moody Chart.

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1. Laminar & Turbulent Flow

Laminar and turbulent flow are two fundamental types of fluid flow that have significant implications in various engineering applications. Laminar flow is characterized by smooth, parallel streamlines, where fluid particles move in an orderly and predictable manner. In contrast, turbulent flow is marked by chaotic, irregular, and unpredictable fluid motion, with eddies and vortices forming within the flow. Understanding the differences between these two flow regimes is crucial for accurately modeling and predicting fluid behavior, as well as for designing efficient systems and components. The transition from laminar to turbulent flow is governed by the Reynolds number, which represents the ratio of inertial to viscous forces within the fluid. Accurately determining the critical Reynolds number at which this transition occurs is essential for many engineering applications, such as the design of pipelines, aerodynamic systems, and heat exchangers. Overall, the study of laminar and turbulent flow is a fundamental aspect of fluid mechanics, with far-reaching implications in various industries and disciplines.
2. Reynolds number

The Reynolds number is a dimensionless quantity that plays a crucial role in the study of fluid mechanics and the understanding of fluid flow behavior. It represents the ratio of inertial forces to viscous forces within a fluid system, and its value determines whether the flow will be laminar or turbulent. At low Reynolds numbers, viscous forces dominate, and the flow is typically laminar, characterized by smooth, predictable streamlines. As the Reynolds number increases, the inertial forces become more significant, leading to the onset of turbulence, where the flow becomes chaotic and unpredictable. The critical Reynolds number, at which the transition from laminar to turbulent flow occurs, is an important parameter that varies depending on the specific fluid system and its geometry. Accurately determining the Reynolds number and understanding its implications is essential for a wide range of engineering applications, such as the design of pipelines, aerodynamic systems, and heat exchangers, where the flow characteristics can significantly impact the performance and efficiency of the system. The study of the Reynolds number and its relationship to fluid flow behavior is a fundamental aspect of fluid mechanics, with far-reaching implications across various industries and disciplines.
3. Continuity Equation

The continuity equation is a fundamental principle in fluid mechanics that describes the conservation of mass in a fluid flow system. It states that the rate of mass flow into a control volume must be equal to the rate of mass flow out of the control volume, assuming no accumulation or depletion of mass within the control volume. This principle is essential for understanding and analyzing fluid flow behavior, as it allows for the prediction of flow rates, velocities, and pressure changes within a system. The continuity equation is particularly important in the study of pipe flow, where it can be used to determine the relationship between the cross-sectional area and the flow velocity, as well as in the analysis of compressible and incompressible fluid flows. Understanding and applying the continuity equation is crucial for the design and optimization of various engineering systems, such as hydraulic and pneumatic systems, heat exchangers, and fluid transport networks. The continuity equation is a fundamental tool in the field of fluid mechanics, providing a powerful framework for the analysis and prediction of fluid flow behavior in a wide range of applications.
4. Flow characteristics in pipe

The study of flow characteristics in pipes is a critical aspect of fluid mechanics, with significant implications for the design and optimization of various engineering systems. Pipe flow can exhibit both laminar and turbulent flow regimes, depending on the Reynolds number and other factors, such as the pipe's geometry and surface roughness. Understanding the differences between these flow regimes is essential, as they have distinct characteristics that impact the pressure drop, flow rate, and overall system performance. In laminar pipe flow, the fluid particles move in smooth, parallel streamlines, resulting in a parabolic velocity profile and relatively low pressure drop. In contrast, turbulent pipe flow is characterized by the presence of eddies and vortices, leading to a more uniform velocity profile and higher pressure drop. The transition between these flow regimes is governed by the critical Reynolds number, which can be influenced by factors such as pipe roughness and flow disturbances. Accurately predicting and modeling the flow characteristics in pipes is crucial for the design of efficient fluid transport systems, heat exchangers, and other engineering applications where pipe flow plays a significant role. The study of flow in pipes is a fundamental aspect of fluid mechanics, providing valuable insights and tools for engineers to optimize system performance and ensure the reliable operation of various engineering systems.
5. Major Loss & Friction Factor in Laminar Flow

The study of major losses and friction factors in laminar pipe flow is a crucial aspect of fluid mechanics, with significant implications for the design and optimization of various engineering systems. In laminar flow, the dominant mechanism for energy dissipation is the viscous shear stress between the fluid and the pipe wall, which results in a pressure drop along the length of the pipe. The Darcy-Weisbach equation, which relates the pressure drop to the flow rate, pipe diameter, and a dimensionless friction factor, is a fundamental tool for analyzing and predicting the behavior of laminar pipe flow. The friction factor in laminar flow is inversely proportional to the Reynolds number, and it can be accurately determined using the Hagen-Poiseuille equation. Understanding the relationship between the friction factor, Reynolds number, and other system parameters is essential for the design of efficient fluid transport systems, such as pipelines, hydraulic systems, and heat exchangers. Accurately modeling the major losses and friction factors in laminar pipe flow allows engineers to optimize system performance, minimize energy consumption, and ensure the reliable operation of various engineering applications. The study of major losses and friction factors in laminar flow is a fundamental aspect of fluid mechanics, providing valuable insights and tools for engineers to improve the design and performance of a wide range of engineering systems.
6. Major Loss & Friction Factor in Turbulent Flow

The study of major losses and friction factors in turbulent pipe flow is a critical aspect of fluid mechanics, with significant implications for the design and optimization of various engineering systems. In turbulent flow, the dominant mechanism for energy dissipation is the formation of eddies and vortices, which result in a more complex and unpredictable pressure drop along the length of the pipe. The Darcy-Weisbach equation, which relates the pressure drop to the flow rate, pipe diameter, and a dimensionless friction factor, is a fundamental tool for analyzing and predicting the behavior of turbulent pipe flow. However, the friction factor in turbulent flow is not as straightforward to determine as in laminar flow, as it depends on factors such as the pipe's surface roughness and the Reynolds number. The Moody chart, which provides a graphical representation of the friction factor as a function of the Reynolds number and relative roughness, is a widely used tool for estimating the friction factor in turbulent pipe flow. Understanding the relationship between the friction factor, Reynolds number, and other system parameters is essential for the design of efficient fluid transport systems, such as pipelines, HVAC systems, and industrial processes. Accurately modeling the major losses and friction factors in turbulent pipe flow allows engineers to optimize system performance, minimize energy consumption, and ensure the reliable operation of various engineering applications. The study of major losses and friction factors in turbulent flow is a fundamental aspect of fluid mechanics, providing valuable insights and tools for engineers to improve the design and performance of a wide range of engineering systems.
7. Moody Chart

The Moody chart is a fundamental tool in the field of fluid mechanics, providing a graphical representation of the relationship between the friction factor, Reynolds number, and relative roughness for pipe flow. This chart is widely used by engineers and researchers to determine the appropriate friction factor for a given pipe flow scenario, which is essential for accurately predicting pressure drops, flow rates, and other important parameters in various engineering applications. The Moody chart is particularly useful in the analysis of turbulent pipe flow, where the friction factor is influenced by both the Reynolds number and the relative roughness of the pipe surface. By using the Moody chart, engineers can quickly and easily estimate the friction factor for a specific pipe system, allowing them to optimize the design and performance of fluid transport systems, such as pipelines, HVAC systems, and industrial processes. The Moody chart is a powerful tool that simplifies the complex relationships between fluid flow parameters, making it an indispensable resource for engineers and researchers working in the field of fluid mechanics. Its widespread use and continued relevance in the industry and academia underscores the importance of understanding and applying this fundamental tool in the study and analysis of fluid flow phenomena.
8. Experimental Results

Experimental results play a crucial role in the field of fluid mechanics, providing valuable insights and validation for theoretical models and numerical simulations. Through carefully designed experiments, researchers and engineers can observe and measure the behavior of fluid flow under various conditions, allowing them to better understand the underlying principles and phenomena. Experimental data can be used to verify the accuracy of analytical solutions and computational fluid dynamics (CFD) models, ensuring that the predictions made by these tools are reliable and representative of real-world scenarios. Additionally, experimental results can uncover unexpected or complex flow behaviors that may not be captured by theoretical models, leading to the development of new theories and the refinement of existing ones. The collection and analysis of experimental data are essential for advancing the understanding of fluid mechanics and for informing the design and optimization of a wide range of engineering systems, from pipelines and turbomachinery to aerodynamic structures and biomedical devices. By combining theoretical, computational, and experimental approaches, researchers and engineers can gain a more comprehensive and accurate understanding of fluid flow phenomena, ultimately leading to more efficient, reliable, and innovative engineering solutions.
9. Conclusion

In conclusion, the study of fluid mechanics, particularly the topics of laminar and turbulent flow, Reynolds number, continuity equation, pipe flow characteristics, major losses and friction factors, and the Moody chart, is a fundamental and essential aspect of engineering and scientific research. These concepts provide a deep understanding of the behavior and properties of fluids, which is crucial for the design, optimization, and analysis of a wide range of engineering systems and applications. The ability to accurately predict and model fluid flow is essential for the development of efficient and reliable technologies, from pipelines and HVAC systems to aerodynamic structures and biomedical devices. By combining theoretical, computational, and experimental approaches, researchers and engineers can gain a comprehensive understanding of fluid mechanics, leading to innovative solutions that address the complex challenges faced in various industries. The continued advancement and application of fluid mechanics principles are crucial for the progress of science and technology, as they enable the development of more efficient, sustainable, and reliable systems that can meet the growing demands of our modern world. As such, the study of fluid mechanics remains a vibrant and dynamic field, with ongoing research and discoveries that continue to push the boundaries of our understanding and push the limits of what is possible in engineering and beyond.