What is it about?
When liquids or gases move through pipes, they experience resistance, or friction, which slows them down. Scientists have long used a well-known mathematical rule to describe this friction, but there are still unanswered questions—especially about the exact values of certain key numbers in the equation. Different studies give different results, showing that more research is needed. The most common way to predict this friction is based on a well-established pattern of how fluid moves near a pipe’s walls. However, in special cases this traditional method doesn’t work well. In such cases, more advanced models are needed to better understand what’s happening. One big challenge is figuring out how swirling structures near the pipe walls affect friction. These small vortices help transfer momentum between the fast-moving center of the flow and the slower-moving regions near the walls. Some scientists have developed different equations to describe this process, but none fully capture the complexity of turbulence near walls. Recent research has tried to improve these models by dividing the flow into different regions and studying how turbulence behaves in each one. Some models split the flow into two regions, while others suggest there’s actually a third layer, which acts as a bridge between the inner and outer parts of the flow. In this study, we propose a new friction equation that works across all conditions by introducing improved ways to describe how turbulence dissipates near the wall. Our new model accounts for this middle layer and better explains how energy is transferred through the flow. When tested against real-world data, our approach showed strong accuracy, making it a promising step toward a more complete understanding of turbulent flow resistance.
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Why is it important?
The results are important because they provide a more accurate and unified equation for calculating turbulent pipe flow friction and the power required for pumping. This has several key implications: 1. Improved Efficiency in Engineering Applications – Accurately predicting friction allows engineers to design more efficient piping systems, reducing energy losses and optimizing pump performance. This is crucial in industries such as oil and gas, water distribution, and chemical processing. 2. Better Understanding of Turbulence – The study refines how we model turbulence near pipe walls by incorporating a more detailed three-layer structure. This improves our fundamental knowledge of fluid dynamics and could lead to advancements in other areas, such as aerodynamics and environmental fluid flows. 3. Bridging Theoretical Gaps – Previous models either relied on multiple equations for different flow conditions or failed to capture certain turbulent behaviors. The new model offers a unified approach that works across a broad range of Reynolds numbers, making it more widely applicable and reliable. 4. Experimental Validation – The new friction equation has been tested against real-world data, showing strong agreement with experimental results. This validation gives confidence that the model can be practically applied to real engineering problems. In summary, the results contribute both to fundamental science—by refining turbulence modeling—and to practical engineering—by improving energy efficiency and reliability in flow systems.
Perspectives
In this work, we focused on developing a new friction equation to more accurately calculate turbulent pipe flow friction and the power required for pumping. The motivation behind this research comes from a long-standing challenge in fluid dynamics: while the classical logarithmic friction models are widely used, they still leave uncertainties regarding their fundamental constants and struggle to account for certain flow conditions. Our goal was to create a unified equation that not only improves accuracy but is also easier to use in practical applications. One of the key advantages of the equation we developed is its simplicity. Unlike some existing models that require iterative methods to determine the friction factor, our formulation is an explicit equation. This means it can be directly calculated without the need for complex numerical procedures, making it more efficient and practical for real-world applications. Beyond its immediate applications, this work is also a necessary step toward a more complete friction equation that accounts for rough wall effects. In real systems, pipes are rarely perfectly smooth, and roughness plays a crucial role in determining friction and energy loss. By first addressing the fundamental structure of turbulent friction in smooth-walled flows, this research lays the groundwork for future extensions that will incorporate surface roughness in a rigorous way. Overall, we see this work as both a refinement of existing turbulence models and a stepping stone toward a more comprehensive understanding of wall-bounded turbulent flows. It bridges gaps in current models, enhances usability, and paves the way for further developments in friction modeling—an essential factor in optimizing energy efficiency across various engineering applications.
Daniel Cruz
federal university of rio de janeiro
Read the Original
This page is a summary of: On the turbulent friction and the near wall structure of pipe flows, Physics of Fluids, February 2025, American Institute of Physics,
DOI: 10.1063/5.0249159.
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