滤动之学基础 三、流管、流束与过流断面 1、流管 定义 在流场中取任意封闭曲线C,经过曲线C的每一点作流线, 由这些流线所围成的管称为流管。如图34所示。 dA A d41 图34流管图35流束和总流图36过流断面 由于流线不能相交,所以各个时刻,流体质点只能在流管 内部或沿流管表面流动,而不能穿越流管,故流管仿佛就是一 根真实的管子
26 三、流管、流束与过流断面 定义： L 图 3—4 流管 A1 A2 dA1 dA2 图3—5流束和总流 图 3—6 过 流 断 面 由于流线不能相交，所以各个时刻，流体质点只能在流管 内部或沿流管表面流动，而不能穿越流管，故流管仿佛就是一 根真实的管子。 1、流管 在流场中取任意封闭曲线C，经过曲线C的每一点作流线， 由这些流线所围成的管称为流管。如图3—4所示
BasisofFhid Dynamic 2)Stream flow Definition The summation of all streamlines in stream tube is called stream flow O The stream whose sections is infinitesimal is called elementary flow. As in Figure 3-5 the stream tube whose section is dA,. dA The summation of countless elementary flow is called whole stream (3)Cross section offlow Definition The transects which keep orthogonal with all the streamlines in the streamline tube are called cross section of flow as shown in Figure 3-6 When all the streamlines which consist the streamline tube keep parallel the cross section is a plane or else the Cross section is a curve surface 27
27 (2) Stream flow 1 2 dA ,dA The summation of all streamlines in stream tube is called stream flow. The stream whose sections is infinitesimal is called elementary flow . As in Figure 3-5 the stream tube whose section is . The summation of countless elementary flow is called whole stream. Definition： (3) Cross section of flow When all the streamlines which consist the streamline tube keep parallel the cross section is a plane or else the Cross section is a curve surface. The transects which keep orthogonal with all the streamlines in the streamline tube are called cross section of flow. As shown in Figure 3-6. Definition：
滤动之学基础 2、流束 定义: 流管内所有流线的总和称为流束 断面无穷小的流束称为微小流束,(元流) 如图3-5中断面为d4,dA2的流束。 无数微小流束的总和称为总流 3、过流断面 定义: 与流束中所有流线正交的横断面称为过流断面。如图36所 小 当组成流束的所有流线互相平行时,过流断面是平面;否 则,过流断面是曲面。 28
28 2、 流束 3、 过流断面 当组成流束的所有流线互相平行时，过流断面是平面；否 则，过流断面是曲面。 1 2 dA ,dA 流管内所有流线的总和称为流束。 断面无穷小的流束称为微小流束，（元流） 如图3—5中断面为 的流束。 无数微小流束的总和称为总流。 定义： 与流束中所有流线正交的横断面称为过流断面。如图3—6所 示。 定义：
BasisofFhid Dynamics 4. Discharge and average velocity of section (1). Discharge Definition The fluid quantity through a certain spatial curved surface in unit time is called Discharge Two kinds of expressing methods: The method which is expressed by the fluid volume in unit time is called volumetric flow rate or discharge. That is@(m/s or 1/5) The method which is expressed by the fluid mass in unit time is called mass flow. That is @m(kg/s) The discharge flowing via the random curved surface is Q=[成A=cos元A (3-10) A and the unit vector n in normal orientation of infinitesimal areadq In this formula cos(i, n )is the cosine of inclination of velocity vect 29
29 4.Discharge and average velocity of section (1). Discharge Definition： Two kinds of expressing methods: The method which is expressed by the fluid volume in unit time is called volumetric flow rate or discharge. That is ( ) 3 Q m s or l s . The method which is expressed by the fluid mass in unit time is called mass flow. That is . Qm (kg s) The discharge flowing via the random curved surface is = = ( ) Q u nd u u n d cos , （3—10） The fluid quantity through a certain spatial curved surface in unit time is called Discharge . In this formula is the cosine of inclination of velocity vector and the unit vector in normal orientation of infinitesimal area . (u n) cos , n d
动之学 四、流量与断面平均速度 1、流量 定义: 单位时间内通过某一特定空间曲面的流体量称为流量。 两种表示方法: 以单位时间通过的流体体积表示,称为体积流量(流量), 记为QGm/s或) 以单位时间通过的流体质量表示,称为质量流量,记作 On(kg/s) 流经任意曲面的流量 o=lundA=Lucos(i, n A (3—10) 式中cos(l,n)为速度矢量与微元面积dA法线方向单位 矢量n的夹角余弦
30 四、流量与断面平均速度 1、流量 定义： 两种表示方法： 以单位时间通过的流体体积表示，称为体积流量（流量）， 记为 Q(m 3 s或l s)。 以单位时间通过的流体质量表示，称为质量流量，记作 Qm (kg s) 流经任意曲面的流量 = = ( ) Q u nd u u n d cos , （3—10） 式中 为速度矢量与微元面积 法线方向单位 矢量 的夹角余弦。 (u n) cos , d n 单位时间内通过某一特定空间曲面的流体量称为流量