管空流动 三、管中层流、紊流的水头损失规律 在所实验的管段上,因为水平直管路中流体作稳定流时, 根据能量方程可以写出其沿程水头损失就等于两断面间的压力 水头差,即 P1=p2 y 改变速度逐次测量层流、紊流两种情况下的与对应的h 值,实验结果如图52所示。 lg h lg k lgU 图5—2层流、紊流的水头损失规律 16
16 三、管中层流、紊流的水头损失规律 p1 p2 hf − = 改变速度逐次测量层流、紊流两种情况下的 与对应的 值,实验结果如图5—2所示。 f h 0 45 lg hf lg1 lg k 2 lg k c lg c lgC C 图5—2层流、紊流的水头损失规律 在所实验的管段上,因为水平直管路中流体作稳定流时, 根据能量方程可以写出其沿程水头损失就等于两断面间的压力 水头差,即
Dang in Pipe The result shows No matter how on laminar flow state or on turbulent flow state the experimental points all concentrate on the straight lines with different slope. The equation is g h,=lg k+mIgu In the formula le k-intercept of a straight line m -slope of a straight line, and m=tge( is a angle of a straight line and a horizontal line) Many experiments prove On laminar flow 8=45, m=1 namely lgh =lgk+lgD or h,=ku(5-1) The on-way head loss is in direct ratio with average velocity of fd On turbulent flow:0>45 m=1.75--2 namely 1gh,=Igk,+mlg or h, =kUm(5-2) The on-way head loss is in direct ratio with the 1. 75th to 2th 17 power of the average velocity of flow
17 The result shows : lg hf = lg k + mlg In the formula lg k —intercept of a straight line. m —slope of a straight line ,and ( is a angle of a straight line and a horizontal line). m = tg Many experiments prove: The on-way head loss is in direct ratio with average velocity of flow . On turbulent flow : 0 2 > 45 , 1 1 0 1 = 45 ,m =1 namely lg h f = lg k + lg or hf = k (5—1) m namely or m f f h k m h k 2 2 =1.75—2 lg = lg + lg = (5—2) The on-way head loss is in direct ratio with the 1.75th to 2th power of the average velocity of flow. No matter how on laminar flow state or on turbulent flow state the experimental points all concentrate on the straight lines with different slope. The equation is On laminar flow:
管空流动 结果表明: 无论是层流状态还是紊流状态,实验点都分别集中在不同 斜率的直线上,方程式为 式中 gh=lg k+migu lgk—直线的截距; m一直线的斜率,且m=2g6(6为直线与水平线 的交角)。 大量实验证明: 层流时 =45,m=1gh=gk+gU减或h=kD (5—1) 沿程水头损失与平均流速成正比。 紊流时: 2>45),m=1752即gb=gk2+mgU或h=k(5-2) 沿程水头损失与平均流速的1.752次方成正比
18 结果表明: lg hf = lg k + mlg 式中 lg k —直线的截距; m —直线的斜率,且 ( 为直线与水平线 的交角)。 m = tg 大量实验证明: 1 1 0 1 45 ,m 1 lg h lg k lg h k = = 即 f = + 或 f = (5—1) 沿程水头损失与平均流速成正比。 紊流时: m f f m h k2 m h k2 0 2 > 45 , =1.75—2即lg = lg + lg 或 = (5—2) 沿程水头损失与平均流速的1.75—2次方成正比。 无论是层流状态还是紊流状态,实验点都分别集中在不同 斜率的直线上,方程式为 层流时:
Flo Dang in Pipe $5-3 Laminar Flow in Round Pipe d As Reynolds number is less, it is to say that when the velocity and diameter are less and viscosity is bigger the laminar flow appears On engineering laminar flows often exist. Such as on oil transport, chemical conduit, underground seep and even light industry, construction, physiology Methods to analyze the laminar flow motion Found the steady differential equation of laminar flow based on the balance relation of micro units, as shown in Figure 5-3, choose a cylinder the radius as rand the length is the cylinder is in a balance state in the constant flow SN bzrzzzzzzlzzzz R O y P1 Figure 5-3 the laminar flow in round pipe 19
19 §5-3 Laminar Flow in Round Pipe As Reynolds number is less,it is to say that when the velocity and diameter are less and viscosity is bigger the laminar flow appears. On engineering laminar flows often exist . Such as on oil transport , chemical conduit, underground seep and even light industry , construction , physiology etc. v d Found the steady differential equation of laminar flow based on the balance relation of micro units , as shown in Figure 5—3,choose a cylinder , the radius is r and the length is , the cylinder is in a balance state in the constant flow . l x y z o 1 p R 1 p p2 2 p l r Figure 5—3 the laminar flow in round pipe 1. Methods to analyze the laminar flow motion
着空 §5-3管流中的层流 雷诺数~较小,也就是速度,直径较小而粘度较大时 出现层流。工程上层流情况很多。如石油输运,化工管道, 地下水渗流甚至轻工、建筑、生理等许多领域都有 、分析层流运动的方法 从微元体的受力平衡关系出发建立层流的常微分方程。 如图5-3所示,取半径为r,长度为的一个圆柱体,在定常 流动中这个圆柱体处于平衡状态 pi p R →D O p2 y 图5—3圆管层流 20
20 §5-3 管流中的层流 雷诺数 较小,也就是速度,直径较小而粘度较大时 出现层流。工程上层流情况很多。如石油输运,化工管道, 地下水渗流甚至轻工、建筑、生理等许多领域都有。 v d 从微元体的受力平衡关系出发建立层流的常微分方程。 如图5—3所示,取半径为 r ,长度为 的一个圆柱体,在定常 流动中这个圆柱体处于平衡状态。 l x y z o 1 p R p1 p2 2 p l r 图 5—3 圆 管 层 流 一、分析层流运动的方法