理想液体:既无粘性又不可压缩的液体 恒定流动(稳定流动、定常流动):流动液体中的任一点p,u和ρ流不会随时间而变化流动. 流线—某一瞬时液流中各处质点运动状态的一 条条曲线 流束—通过某截面上所有各点作出的流线集合构成流束 有与流线正交的截面(垂直于液体流动方向的截面) 流量—单位时间内流过某通流截面液体体积qdq=v/t=udA 整个过流段流量:q=∫AudA 平均流速—通流截面上各点均匀分布假想流速 q=vA=∫AudA v=q/A液压缸的运动速度取决于进入液压缸的流量,并且随着流量的变化而变化。
连续性原理-当理想液体在管道中恒定流动时,根据质量守恒定律,管道中的液体既不能增加也不能减少因此,在单位时间内流入液体的质量应与流出液体的质量相等 结论:当液体在管道中流动时,流过各段的流量相等,因此流量与流过段成反比。
能量守恒定律:当理想液体在管道中稳定流动时,根据能量守恒定律,同一管道任何一段的总能量应相等 或者:外力对物体的作用应等于物体机械能的变化 理想液体伯努利方程 1外力对液体所做的功 W=p1A1v1dt-p2A2v2dt=(p1-p2)?V2机械能的变化量位能的变化量:?Ep=mg?h=ρg?V(z2-z1) 动能的变化量:?Ek=m?v2/2=ρ?V(v22-v21)/2 根据能量守恒定律,有:W=?Ep+?Ek (p1-p2)?V=ρg?V(z2-z1)+ρ?V(v22-v21)/2 整理后得单位重量理想液体伯努利方程为:p1+ρgZ1+ρv12/2=p2+ρgZ2+ρv22/2 或p/ρg+Z+v2/2g=C(c为常数)理想液体伯努利方程的物理意义:在封闭管道中恒定流动的理想液体有压力能、位能和动能三种形式。
在流动过程中,三种能量可以相互转化,但三种能量之和恒定在每个过流截面上 实际液体伯努利方程 ∵实际液体具有粘性 ∴液体流动时会产生内摩擦力,从而损耗能量 故应考虑能量损失hw,并考虑动能修正系数 ,则实际液体伯努利方程为: p1/ρg+Z1+α1v12/2g=p2/ρg+Z2+α2v22/2g+hw层流α=2 紊流α=1 p1-p2=△p=ρghw应用伯努利方程时必须注意的问题 (1)断面1、2需顺流向选取(否则hw为负 值),且应选在缓变的过流断面上。
(2)断面中心在基准面以上时,z取正值;反之取负值通常选取特殊位置的水 平面作为基准面动量定理:作用在物体上的外力等于物体单位时 间内动量的变化量即∑F=d(mv)/dt X向动量方程:∑Fx=ρq(β2v2x-β1v1x) X向稳态液动力:F'x=-∑Fx=ρq(β1v1x-β2v2x) 结论:作用于滑阀阀芯的稳态液动力总是试图关闭阀口。
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