理想液體:既無粘性又不可壓縮的液體 恒定流動(穩(wěn)定流動、定常流動):流動液體中的任一點p,u和ρ流不會隨時間而變化流動. 流線—某一瞬時液流中各處質點運動狀態(tài)的一 條條曲線 流束—通過某截面上所有各點作出的流線集合構成流束 有與流線正交的截面(垂直于液體流動方向的截面) 流量—單位時間內(nèi)流過某通流截面液體體積qdq=v/t=udA 整個過流段流量:q=∫AudA 平均流速—通流截面上各點均勻分布假想流速 q=vA=∫AudA v=q/A液壓缸的運動速度取決于進入液壓缸的流量,并且隨著流量的變化而變化。
連續(xù)性原理-當理想液體在管道中恒定流動時,根據(jù)質量守恒定律,管道中的液體既不能增加也不能減少因此,在單位時間內(nèi)流入液體的質量應與流出液體的質量相等 結論:當液體在管道中流動時,流過各段的流量相等,因此流量與流過段成反比。
能量守恒定律:當理想液體在管道中穩(wěn)定流動時,根據(jù)能量守恒定律,同一管道任何一段的總能量應相等 或者:外力對物體的作用應等于物體機械能的變化 理想液體伯努利方程 1外力對液體所做的功 W=p1A1v1dt-p2A2v2dt=(p1-p2)?V2機械能的變化量位能的變化量:?Ep=mg?h=ρg?V(z2-z1) 動能的變化量:?Ek=m?v2/2=ρ?V(v22-v21)/2 根據(jù)能量守恒定律,有:W=?Ep+?Ek (p1-p2)?V=ρg?V(z2-z1)+ρ?V(v22-v21)/2 整理后得單位重量理想液體伯努利方程為:p1+ρgZ1+ρv12/2=p2+ρgZ2+ρv22/2 或p/ρg+Z+v2/2g=C(c為常數(shù))理想液體伯努利方程的物理意義:在封閉管道中恒定流動的理想液體有壓力能、位能和動能三種形式。
在流動過程中,三種能量可以相互轉化,但三種能量之和恒定在每個過流截面上 實際液體伯努利方程 ∵實際液體具有粘性 ∴液體流動時會產(chǎn)生內(nèi)摩擦力,從而損耗能量 故應考慮能量損失hw,并考慮動能修正系數(shù) ,則實際液體伯努利方程為: p1/ρg+Z1+α1v12/2g=p2/ρg+Z2+α2v22/2g+hw層流α=2 紊流α=1 p1-p2=△p=ρghw應用伯努利方程時必須注意的問題 (1)斷面1、2需順流向選?。ǚ駝thw為負 值),且應選在緩變的過流斷面上。
(2)斷面中心在基準面以上時,z取正值;反之取負值通常選取特殊位置的水 平面作為基準面動量定理:作用在物體上的外力等于物體單位時 間內(nèi)動量的變化量即∑F=d(mv)/dt X向動量方程:∑Fx=ρq(β2v2x-β1v1x) X向穩(wěn)態(tài)液動力:F'x=-∑Fx=ρq(β1v1x-β2v2x) 結論:作用于滑閥閥芯的穩(wěn)態(tài)液動力總是試圖關閉閥口。
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