深度研究北京市2020年普通高考物理第14题

根据伯努利原理对北京市2020年普通高考物理第14题进行深度剖析,利用伯努利方程详细分析由于空气动力学原理造成篮球下落轨迹偏离竖直方向的本质原因.并试图从该试题的命题视角窥视高考改革的导向或高考试题的命题走向.     

"伯努利方程"教学中应注意的几个问题

现在的新教材把"伯努利方程"增加为选学内容,我认为还是很有必要的.因为伯努利方程不仅能解释很多物理现象,而且它也体现了能量这一概念在解决复杂问题时的重要性,还有伯努利方程在物理学发展史上也有较高的地位,就是从伯努利方程开始建立起了完整的流体动力学体系,而后又使麦克斯韦在研究电磁场时有了可参照的体系,建立起了麦克斯韦方程组;另有拉格朗日、达朗伯等人正是沿着伯努利的方法创立了《分析力学》.但因为是选学内容,许多教师和学生并没有加以足够的重视,可能会忽视下面几个问题.     

“车窗悖论”的成因及澄清

在行驶的车里,以车为参照物,外面的空气流速更大,但以地面为参照物,车内的空气流速更大,根据中学所学的伯努利原理,“究竟是车内还是车外压强更大”成了一个悖论.通过查阅相关资料发现,不能用伯努利原理比较车内外的气压大小,而应当用仿真模拟.根据模拟的结果,气流是双向的,不仅有从车外到车内的气流,也有车内到车外的气流.     

理想流体稳定流动的热力学解释

通过引入热力学焓，给出伯努利方程的正确解释，证明了理想流体的稳定流动具有等焓过程。     

用循环流体验证伯努利方程

用循环流体验证伯努利方程徐仲坤（长沙工程兵学院４１００７２）一、引言对理想流体伯努利方程作定性验证，以及对文特利体积流量公式作定量验证，通常选用水和空气作流动介质．不言而喻，用水实验时，要求具备恒压稳流的水源；用空气实验时，要动用气泵、储气箱等大型设...     

可压缩流体的伯努利方程

引入适用于可压缩流体的伯努利方程,讨论了储液器内的峰值气压.     

一例关于伯努利方程知识点的教学案例

伯努利方程是"工程流体力学""液压与气压传动""土木工程结构抗风设计""连续介质力学"等课程的核心基础,而这些课程又是机械类、土木工程类等专业的专业基础课."大学物理"作为理工科专业的公共基础课,应该全部或部分讲授伯努利方程这一重要的知识点.文章通过对工程上有关伯努利方程应用的实例进行合理抽象,为大学物理课程中所讲解的"伯努利方程"知识点营造工程教育情境.通过这种教学设计,能够实现在加深学生对基础知识掌握程度的同时,增强学生工程背景阅历和工程实践意识.     

流体流动状态与伯努利方程

本文用欧拉公式和伽利略变换讨论了流体的流动状态与参照系的关系，由于伯努利方程只适用于理想流体在其中作定常流的惯性系，从而说明在诸如马格努斯效应等流体动力学问题中选择合适惯性系的重要性。     

伯努利方程实验仪

介绍了一种新型伯努利方程实验仪， 该仪器能实现水的自动循环和液面高度任意调节， 且安装测量方便， 实验误差小．     

“三位一体”模式下力学课程思政教学设计与实践

近年来,课程思政是高等教育改革的重点,课程思政教学是在知识传授和能力培养中融入正确的价值观、人生观,它推动了课堂教学改革,实现了立德树人.主要从5个方面分析讨论了思政元素的教学设计,并以伯努利方程为例进行教学实践,从引出课程、知识讲解及应用、课堂教学总结3方面出发,对课程教学进行精心设计,“润物细无声”中助力学生形成正确的世界观、人生观、价值观.     

Computational Simulations of Vocal Fold Vibration: Bernoulli Versus Navier–Stokes

The use of the mechanical energy (ME) equation for fluid flow, an extension of the Bernoulli equation, to predict the aerodynamic loading on a two-dimensional finite element vocal fold model is examined. Three steady, one-dimensional ME flow models, incorporating different methods of flow separation point prediction, were compared. For two models, determination of the flow separation point was based on fixed ratios of the glottal area at separation to the minimum glottal area; for the third model, the separation point determination was based on fluid mechanics boundary layer theory. Results of flow rate, separation point, and intraglottal pressure distribution were compared with those of an unsteady, two-dimensional, finite element Navier-Stokes model. Cases were considered with a rigid glottal profile as well as with a vibrating vocal fold. For small glottal widths, the three ME flow models yielded good predictions of flow rate and intraglottal pressure distribution, but poor predictions of separation location. For larger orifice widths, the ME models were poor predictors of flow rate and intraglottal pressure, but they satisfactorily predicted separation location. For the vibrating vocal fold case, all models resulted in similar predictions of mean intraglottal pressure, maximum orifice area, and vibration frequency, but vastly different predictions of separation location and maximum flow rate.     

流体力学中的总流伯努利方程

文章从宏观上分析流体的平衡和运动规律,着重阐述流体力学中理想流体和压强的概念以及静止流体内压强的分布规律.文章介绍了流体的定常运动及流线、流量和总流的概念,给出了连续性方程,并在此基础上推导了理想流体定常运动的总流伯努利方程.结合工程实际问题,文章还介绍了实际流体的定常流动的总流伯努利方程.     

Natural vibrations and stability of shells of revolution interacting with an internal fluid flow

A finite-element algorithm is proposed to investigate the dynamic behavior of elastic shells of revolution containing a quiescent or a flowing inviscid fluid in the framework of linear theory. The fluid behavior is described using the perturbed velocity potential. The shell behavior is treated in the framework of the classical shell theory and variational principle of virtual displacements incorporating a linearized Bernoulli equation for calculation of hydrodynamic pressure acting on the shell. The problem reduces to evaluation and analysis of the eigenvalues in the connected system of equations obtained by coupling the equations for velocity perturbations with the equations for shell displacements. For cylindrical shells, the results of numerical simulations are compared with recently published experimental, analytical and numerical data. The paper also reports the results of studying the dynamic behavior of shells under various boundary conditions for the perturbed velocity potential. The investigation made for conical shells has shown that under certain conditions an increase in the cone angle can change a divergent type of instability to a flutter type.     

Bernoulli excitation and detection of gas bubbles.

A simple method is proposed for detecting and sizing bubbles in pipeline fluid flow. This is based on changing the pressure of the fluid, which in turn excites volume oscillations in the bubble. If the change in pressure is of sufficient brevity and magnitude, the transient distortion results in excitation of the bubble into radiative oscillation at its natural frequency. In a moving fluid, the Bernoulli equation predicts that such a pressure change can be achieved through a suitable gradient in the flow velocity. In the experiments described here, this is achieved by altering the cross-sectional area of the pipe in which the fluid is flowing. We demonstrate the efficacy of this excitation method and, by detecting the radiated sound using a nearby hydrophone, determine the size of individual bubbles from their characteristic oscillation frequency.     

Radial profiles of velocity and pressure for condensation-induced hurricanes

The Bernoulli integral in the form of an algebraic equation is obtained for the hurricane air flow as the sum of the kinetic energy of wind and the condensational potential energy. With an account for the eye rotation energy and the decrease of angular momentum towards the hurricane center it is shown that the theoretical profiles of pressure and velocity agree well with observations for intense hurricanes. The previous order of magnitude estimates obtained in pole approximation are confirmed.     

Simple approach to approximate predictions of the vapor–liquid equilibrium curve near the critical point and its application to Lennard-Jones fluids

We propose a simple analytical form of the vapor–liquid equilibrium curve near the critical point for Lennard-Jones fluids. Coexistence densities curves and vapor pressure have been determined using the Van der Waals and Dieterici equation of state. In described method the Bernoulli differential equations, critical exponent theory and some type of Maxwell?s criterion have been used. Presented approach has not yet been used to determine analytical form of phase curves as done in this Letter. Lennard-Jones fluids have been considered for analysis. Comparison with experimental data is done. The accuracy of the method is described.     

On some connections between the Gompertz function and special numbers

In the present paper we show that the Gompertz function, the Fisher–Tippett and the Gumbel probability distributions are related to both Stirling numbers of the second kind and Bernoulli numbers. Especially we prove for the Gumbel probability density function an analog of the Grosset–Veselov formula which connects 1-soliton solution of the KdV equation with Bernoulli numbers.     

The thermal effect on vibration and instability of carbon nanotubes conveying fluid

Based on the theory of thermal elasticity mechanics, an elastic Bernoulli–Euler beam model is developed for vibration and instability analysis of fluid-conveying single-walled carbon nanotubes (SWNTs) considering the thermal effect. Results are demonstrated for the dependence of natural frequencies on the flow velocity as well as temperature change. The influence of temperature change on the critical flow velocity at which buckling instability occurs is investigated. It is concluded that the effect of temperature change on the instability of SWNTs conveying fluid is significant.     

Comparison of modeling of the rotating tapered axially functionally graded Timoshenko and Euler–Bernoulli microbeams

The target of this paper is to present an exhaustive study on the small scale effect on vibrational behavior of a rotary tapered axially functionally graded (AFG) microbeam on the basis of Timoshenko and Euler–Bernoulli beam and modified couple stress theories. The variation of the material properties and cross section along the longitudinal direction of the microbeam are taken into consideration as a linear function. Hamilton's principle is used to derive the equations for cantilever and propped cantilever boundary conditions and the generalized differential quadrature method (GDQM) is employed to solve the equations. By parametric study, the effects of small-scale parameter, rates of cross section change of the microbeam and angular velocity on the fundamental and second frequencies of the microbeam are studied. Also, comparison between the frequencies of Timoshenko and Euler–Bernoulli microbeams are presented. The results can be used in many applications such as micro-robots and biomedical microsystems.     

The nano scale vibration of protein microtubules based on modified strain gradient theory

This paper investigates the free vibration of protein microtubules (MTs) embedded in the cytoplasm by using linear and nonlinear Euler–Bernoulli beam model based on modified strain gradient theory. The protein microtubule is modeled as a simply support or clamped–clamped beam. Beside, the elastic medium surrounding of MTs is modeled with Pasternak foundation. Vibration equations are obtained by using Hamilton principle and these equations are solved according to boundary conditions. Finally the dependency of vibration frequencies on environmental conditions, MTs size, changes of temperature and material length scale parameters (size effects) is studied. By comparing the findings, it could be said that the MTs' frequency is greatly increased in the presence of cytoplasm and it is very dependent to material length scale parameters.