dimensionless number

简明释义

无因次数

英英释义

例句

1.The Froude number is a dimensionless number 无量纲数 used in hydrodynamics to compare inertial and gravitational forces.

弗劳德数是水动力学中一个无量纲数 dimensionless number，用于比较惯性力和重力。

2.The Prandtl number is another important dimensionless number 无量纲数 that characterizes the relative thickness of the thermal boundary layer.

普朗特数是另一个重要的无量纲数 dimensionless number，表征热边界层的相对厚度。

3.When analyzing chemical reactions, the Damköhler number is a dimensionless number 无量纲数 that compares reaction rates to transport rates.

在分析化学反应时，达姆克勒数是一个无量纲数 dimensionless number，比较反应速率与传输速率。

4.In heat transfer, the Nusselt number is a dimensionless number 无量纲数 that represents the ratio of convective to conductive heat transfer.

在热传递中，努塞尔数是一个无量纲数 dimensionless number，表示对流与导热的比率。

5.The Reynolds number is a crucial dimensionless number 无量纲数 used in fluid mechanics to predict flow patterns.

雷诺数是流体力学中一个重要的无量纲数 dimensionless number，用于预测流动模式。

作文

In the field of science and engineering, understanding the concept of a dimensionless number is crucial for analyzing various physical phenomena. A dimensionless number is a quantity without any physical units, which means it is a pure number that provides a relationship between different physical properties. This characteristic allows scientists and engineers to compare systems and processes that may have different scales or units, making it an essential tool in both theoretical and applied research.For instance, consider the Reynolds number, which is a well-known dimensionless number used in fluid mechanics. The Reynolds number is defined as the ratio of inertial forces to viscous forces and is calculated using the formula: Re = (ρvL)/μ, where ρ is the fluid density, v is the velocity, L is a characteristic length, and μ is the dynamic viscosity. The significance of this dimensionless number lies in its ability to predict flow patterns in different fluid flow situations. When the Reynolds number is low, the flow tends to be laminar, whereas high values indicate turbulent flow. By using this dimensionless number, engineers can design systems such as pipelines and airfoils more effectively, ensuring optimal performance under varying conditions.Another important example is the Nusselt number, which is a dimensionless number used in heat transfer calculations. It represents the ratio of convective to conductive heat transfer across a boundary. The Nusselt number helps engineers understand how effectively heat is being transferred in a given system, whether it be in HVAC applications or in the design of heat exchangers. By utilizing dimensionless numbers like the Nusselt number, engineers can scale their designs and ensure efficiency regardless of the size of the system they are working on.The beauty of dimensionless numbers is that they allow for the simplification of complex equations and models. In dimensional analysis, engineers can reduce the number of variables in a problem by identifying key dimensionless numbers that govern the behavior of the system. This process not only aids in understanding but also enhances the ability to make predictions about system behavior without the need for extensive experimental data.Furthermore, dimensionless numbers play a vital role in similarity analysis, which is often used in experimental fluid dynamics. By creating models that maintain the same dimensionless numbers as the real-world systems they represent, researchers can accurately simulate and study the behavior of those systems at a smaller scale. This approach saves time and resources while providing valuable insights into the dynamics of complex systems.In conclusion, the concept of a dimensionless number is fundamental in the fields of science and engineering. These pure numbers enable comparisons across different systems, simplify complex relationships, and enhance our understanding of physical phenomena. As we continue to advance in technology and research, the importance of dimensionless numbers will only grow, serving as a bridge between theory and practical application. By mastering the use of dimensionless numbers, engineers and scientists can develop more efficient systems and solutions that meet the challenges of our ever-changing world.

在科学和工程领域，理解无量纲数的概念对于分析各种物理现象至关重要。无量纲数是没有任何物理单位的量，这意味着它是一个纯数字，提供了不同物理属性之间的关系。这一特性使得科学家和工程师能够比较可能具有不同规模或单位的系统和过程，从而成为理论研究和应用研究中的重要工具。例如，考虑雷诺数，这是流体力学中一个著名的无量纲数。雷诺数被定义为惯性力与粘性力的比率，其计算公式为：Re = (ρvL)/μ，其中ρ是流体密度，v是速度，L是特征长度，μ是动态粘度。这个无量纲数的重要性在于它能够预测不同流体流动情况下的流动模式。当雷诺数较低时，流动倾向于层流，而高值则表明湍流。通过使用这个无量纲数，工程师可以更有效地设计管道和机翼等系统，确保在不同条件下的最佳性能。另一个重要例子是努塞尔数，这是用于热传递计算的无量纲数。它表示边界上对流与导热的比率。努塞尔数帮助工程师理解在给定系统中热量传递的有效性，无论是在暖通空调应用中还是在热交换器设计中。通过利用像努塞尔数这样的无量纲数，工程师可以缩放他们的设计，并确保无论系统的大小如何都能保持效率。无量纲数的美妙之处在于它们允许简化复杂的方程和模型。在维度分析中，工程师可以通过识别控制系统行为的关键无量纲数来减少问题中的变量数量。这个过程不仅有助于理解，还增强了在没有大量实验数据的情况下对系统行为做出预测的能力。此外，无量纲数在相似性分析中发挥着至关重要的作用，这通常用于实验流体动力学。通过创建与其所代表的真实系统保持相同无量纲数的模型，研究人员可以准确模拟和研究这些系统在较小规模下的行为。这种方法节省了时间和资源，同时提供了对复杂系统动态的宝贵见解。总之，无量纲数的概念在科学和工程领域是基础性的。这些纯数字使得不同系统之间的比较成为可能，简化复杂关系，并增强我们对物理现象的理解。随着我们在技术和研究方面的不断进步，无量纲数的重要性只会增加，作为理论与实际应用之间的桥梁。通过掌握无量纲数的使用，工程师和科学家可以开发出更高效的系统和解决方案，以应对我们不断变化的世界的挑战。