工程流体力学4章.pptx

§4-1 系统和控制体1.系统:在研究流体运动时,为了确定研究的对象,规划出研究的范围,常取出需要研究的部分,即一团流体质点的微团,在运动过程中,它始终包含着这些流体质点。2.控制体:流场中某个确定的空间区域。控制体内流体可随时变化，流进流出。yIIIxIIIz控制体控制体, 系统Vin0V0θ0θini§4-2 雷诺输运定理一.雷诺输运方程系统§4-2 雷诺输运定理§4-2 雷诺输运定理§4-3 流体流动的连续性方程一.连续性方程要应用质量守恒,系统的物理量B就成为质量m, 单位质量的物理量雷诺输运方程成为因质量守恒§4-3 流体流动的连续性方程二.不可压缩流体的连续性方程对定常流动,有再对不可压缩流体，密度不随时间而变，则有V2dA2V1dA1§4-3 流体流动的连续性方程对任意有限截面的流管，有§4-3 流体流动的连续性方程§4-4 理想流体的能量方程上节根据质量守恒推出了连续性方程，现根据能量守恒来推导能量方程。由热力学第一定律，得应用雷诺输运方程，单位质量的能量§4-4 理想流体的能量方程 上式表示单位时间输入系统的热量与环境对系统所作的功等于控制体内的能量对时间的变化率与通过控制体表面的能量流率之和。 重力场中，单位质量的能量可表示为§4-4 理想流体的能量方程为单位时间作用在控制面上的表面应力所做的功对理想流体，切向应力=0，法向应力为§4-4 理想流体的能量方程在定常且绝热的情况下，有§4-5 伯努利方程一.伯努利方程理想流体,绝热定常流动,侧面流入截面A1,流出截面A2, 有§4-5 伯努利方程根据连续性方程有对于不可压缩理想流体与绝热边界，内能和密度皆为常数§4-5 伯努利方程即§4-5 伯努利方程Daniel Bernoulli (1700-82)Mathematician born in Groningen in theNetherlands. A good friend of Euler. Made efforts to popularise the law of fluid motion, while tackling various novel problems in fluid statics and dynamics. Originated the Latin word hydrodynamica, meaning fluid dynamics.§4-5 伯努利方程The law of conservation of energy in that the sum of the kinetic energy, energy due to pressure and potential energy (i.e. the total energy) is always constant. This is Bernoullis equation.Condition:1. Perfect fluid;2.Non compressible;3.Mass force is gravity;4. Steady state;5.One dimension§4-5 伯努利方程Exchange between pressure head and velocity head§4-5 伯努利方程Hydraulic grade line and energy lineh2 and h3 are the losses of head between section 1 and either of the respective sections.§4-5 伯努利方程二.应用1.小孔出流若皆暴露于大气压下,则§4-5 伯努利方程2.皮托(Pitot)管直角弯曲管一端朝上,一端向来流,朝向来流处成为驻点,速度为0,该点的压强称为总压强,其值高于周围的静压。§4-5 伯努利方程However, with an actual Pitot tube, since some loss occurs due to its shape and the fluid viscosity, the equation is modified as follows:§4-5 伯努利方程3.汾丘里(Venturi)管Assuming that the pipe line is horizontal,§4-5 伯努利方程However, since there is some loss of energy between sections, in actual cases, the above equation is amended as follows:§4-5 伯努利方程例 求水位从H1降到H2所需时间,小孔面积为a,桶截面积为AC is calle