nondimensional number

简明释义

无因次数

英英释义

例句

1.When designing chemical reactors, engineers must consider the Damköhler number, which is a significant 无量纲数 for reaction kinetics.

在设计化学反应器时，工程师必须考虑达姆科勒数，这是反应动力学中的一个重要无量纲数。

2.The Reynolds number is a crucial 无量纲数 used to predict flow patterns in different fluid flow situations.

雷诺数是一个关键的无量纲数，用于预测不同流体流动情况中的流动模式。

3.In heat transfer analysis, the Nusselt number is an important 无量纲数 that signifies the ratio of convective to conductive heat transfer.

在热传递分析中，努塞尔数是一个重要的无量纲数，表示对流与导热的比率。

4.The Froude number helps in understanding the influence of gravity on fluid motion and is classified as a 无量纲数.

弗劳德数有助于理解重力对流体运动的影响，被归类为一种无量纲数。

5.The Strouhal number is often used in fluid dynamics and is a type of 无量纲数 that relates the frequency of vortex shedding to the flow velocity.

斯特劳哈尔数常用于流体动力学，是一种无量纲数，将涡脱落的频率与流速相关联。

作文

In the realm of engineering and physics, the concept of a nondimensional number plays a crucial role in simplifying complex phenomena. A nondimensional number is essentially a mathematical quantity that has no units associated with it, which allows for the comparison of different systems or processes regardless of their physical dimensions. This characteristic makes nondimensional numbers particularly useful in various fields such as fluid dynamics, heat transfer, and structural analysis.To understand the importance of nondimensional numbers, consider fluid dynamics, where the behavior of fluids is often described using equations that involve multiple variables, including velocity, density, and viscosity. By introducing nondimensional numbers like the Reynolds number, engineers can predict flow patterns and transitions between laminar and turbulent flow without needing to delve into the complexities of each individual variable's units. The Reynolds number, defined as the ratio of inertial forces to viscous forces, allows for a simplified analysis of flow behavior across different scales and conditions.Similarly, in heat transfer applications, the Nusselt number serves as a nondimensional number that characterizes the convective heat transfer relative to conductive heat transfer. By utilizing the Nusselt number, engineers can assess the efficiency of heat exchangers and other thermal systems without being bogged down by the specifics of temperature and material properties. This ability to generalize findings through nondimensional numbers fosters a deeper understanding of thermal processes and aids in the design of more efficient systems.The use of nondimensional numbers extends beyond fluid dynamics and heat transfer. In structural analysis, the dimensionless form of equations helps engineers understand the behavior of materials under various loading conditions. For instance, the Strouhal number, which represents the oscillating flow characteristics of structures, is a nondimensional number that enables the comparison of different vibrating systems without the influence of size or scale. This universality is what makes nondimensional numbers so powerful in engineering analyses.Furthermore, nondimensional numbers also facilitate communication among scientists and engineers from different disciplines. When researchers present their findings using nondimensional numbers, they provide a common language that transcends specific units and measurements. This is particularly beneficial in interdisciplinary projects where collaboration between experts in varying fields is necessary. For example, a mechanical engineer and a civil engineer can discuss fluid flow around a bridge structure using the same nondimensional numbers, leading to a more cohesive understanding of the system's behavior.In conclusion, the significance of nondimensional numbers cannot be overstated. They simplify complex systems, facilitate comparisons, and enhance communication across disciplines. As technology advances and the need for multidisciplinary approaches increases, the reliance on nondimensional numbers will likely become even more prevalent. Understanding and utilizing these mathematical tools will empower engineers and scientists to tackle challenges more effectively, paving the way for innovations that benefit society as a whole.

在工程和物理学领域，无量纲数的概念在简化复杂现象中发挥着重要作用。无量纲数本质上是一个没有单位关联的数学量，这使得可以比较不同的系统或过程，而不考虑它们的物理维度。这一特性使得无量纲数在流体动力学、热传递和结构分析等多个领域特别有用。为了理解无量纲数的重要性，可以考虑流体动力学，其中流体的行为通常用涉及多个变量的方程描述，包括速度、密度和粘度。通过引入无量纲数，如雷诺数，工程师可以预测流动模式以及层流与湍流之间的转变，而无需深入探讨每个变量单位的复杂性。雷诺数被定义为惯性力与粘性力的比率，允许在不同的尺度和条件下对流动行为进行简化分析。同样，在热传递应用中，努塞尔数作为一个无量纲数，表征了对流热传递相对于导热传递的特性。通过利用努塞尔数，工程师可以评估热交换器和其他热系统的效率，而不必被温度和材料属性的具体细节所困扰。这种通过无量纲数普遍化发现的能力促进了对热过程的更深入理解，并有助于设计出更高效的系统。无量纲数的使用超越了流体动力学和热传递。在结构分析中，方程的无量纲形式帮助工程师理解材料在各种载荷条件下的行为。例如，斯特劳哈尔数，它代表了结构的振荡流动特性，是一个无量纲数，使得在不受大小或规模影响的情况下比较不同的振动系统成为可能。这种普遍性正是使得无量纲数在工程分析中如此强大的原因。此外，无量纲数还促进了来自不同学科的科学家和工程师之间的沟通。当研究人员使用无量纲数展示他们的发现时，他们提供了一种超越特定单位和测量的共同语言。这在需要跨学科专家合作的跨学科项目中尤为有利。例如，机械工程师和土木工程师可以使用相同的无量纲数讨论桥梁结构周围的流体流动，从而更好地理解系统的行为。总之，无量纲数的重要性不容小觑。它们简化复杂系统，促进比较，并增强跨学科沟通。随着技术的进步和对多学科方法需求的增加，依赖于无量纲数的情况可能会变得更加普遍。理解和利用这些数学工具将赋予工程师和科学家更有效地应对挑战的能力，为创新铺平道路，从而造福整个社会。