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1、1,CHAPTER 5Incompressible Flow in Pipes and Channels,2,content,5.1 SHEAR STRESS AND SKIN FRICTION IN PIPES 5.2 LAMINAR FLOW IN PIPES AND CHANNELS 5.3 TURBULENT FLOW IN PIPES AND CHANNELS 5.4 FRICTION FROM CHANGES IN VELOCITY OR DIRECTION5.5 DESIGN OF PIPE SYSTEM*,3,5.1 SHEAR STRESS AND SKIN FRICTION
2、 IN PIPES,1. Shear-stress distribution 2. Relation between skin friction and wall shear 3. The friction factor 4. Relations between skin friction parameters 5. Flow in noncircular channels,4,1. Shear-stress distribution,Consider the steady flow of fluid of constant density in fully developed flow th
3、rough a horizontal pipe.,5,Apply momentum equation (4.42) between two faces of the disk.,(4.42),(5.1),rearranging,6,Subtracting Eq. (5.1) from Eq. (5.2) gives,(5.2),(5.3),also,(5.1),7,A straight line with slop,8,2. Relation between skin friction and wall shear,Writing Bernoulli equation over a defin
4、ite length L of the complete stream.,9,Eq. (5.2),(5.2),become,(5.5),10,(5.5),f,11,3. The friction factor,-Fanning friction factory,(5.6),-Blasius or Darcy friction factor,12,4. Relations between skin friction parameters,The relation of common quantities used to measure skin friction in pipes.,Pressu
5、re drop caused by friction loss阻力降, Pa,(5.7),13,5. Flow in noncircular channels,equivalent diameter,hydraulic radius,14,Flow between parallel plates, when the distance between them b is much smaller than the width of the plates,A annulus between two concentric pipes,(5.15),A square duct with a width
6、 of side b,15,5.2 LAMINAR FLOW IN PIPES AND CHANNELS,1. Laminar flow of newtonian fluids 2. Hagen-Poiseuille equation 3. Laminar flow of non-newtonian liquids4. Laminar flow in an annulus,16,1. Laminar flow of newtonian fluids,Newtonian fluid is flowing in a circular channel in laminar flow.,17,Velo
7、city distribution,Newtons law,(5.13),Eliminating by,Therefore,(5.14),18,Integration of Eq. (5.14) with the boundary condition u = 0, r=rw gives,(5.15),When r=0,(5.16),19,The ratio of the local velocity to the maximum velocity,(5.17),In laminar flow the velocity distribution with respect to the radiu
8、s is a parabola.,20,21,Average velocity,(5.18),22,(5.19),The average velocity is precisely one-half the maximum velocity.,23,Kinetic energy correction factor,Momentum correction factor,24,2. Hagen-Poiseuille equation,to eliminate,(5.7),Using,In Eq. 5.7,25,(5.20),- Hagen-Poiseuille equation,Compare w
9、ith,(5.22),Therefore,In laminar flow, friction factor is only influenced by Re.,26, 3. Laminar flow of non-newtonian liquids,27,4. Laminar flow in an annulus,Velocity distribution for the laminar flow of a newtonian fluid through an annular space,where = radius of outer wall of annulus = ratio = rad
10、ius of inner wall of annulus,(5.28),28,For annular flow the Reynolds number is,(5.29),(5.30),29,30,5.3 TURBULENT FLOW IN PIPES AND CHANNELS,1. Velocity distribution for turbulent flow 2. Universal velocity distribution equations 3. Limitations of universal velocity distribution laws 4. Flow quantiti
11、es for turbulent flow in smooth round pipes,31,5. Relations between maximum velocity and average velocity 6. Effect of roughness 7. The friction factor chart 8. Reynolds numbers and friction factor for non-newtonian fluids 9. Drag reduction in turbulent flow10. Nonisothermal flow 11. Turbulent flow
12、in noncircular channels,32,1. Velocity distribution for turbulent flow,Flow in turbulent through a closed channel,33,Viscous stresses 粘性应力,Viscous stress + Turbulent stress,Turbulent stress or Reynold stress湍流应力or 雷诺应力,viscous sublayer:buffer layer : turbulent core:,34,viscous sublayer:buffer layer
13、: turbulent core:,Velocity gradient large middle small,35,36,It is customary to express the velocity distribution in turbulent flow in terms of dimensionless parameters,(5.31),Friction velocity摩擦速度，m/s,Friction distance,摩擦距离，m.,37,(5.32),velocity quotient, dimensionless 无量纲速度,(5.33),dimensionless di
14、stance, 无量纲距离,y = distance from wall of tube,(5.34),38,2. Universal velocity distribution equations通用速度分布方程,39,viscous sublayer,(5.35),(5.36),for the viscous sublayer:,40,buffer layer : an empirical equation,(5.37),for the buffer zone:,41,turbulent core :,(5.38),for the turbulent core:,42,43,3. Limi
15、tations of universal velocity distribution laws,44,4. Flow quantities for turbulent flow in smooth round pipes,45,Average velocity,(5.46),(5.47),46,The Reynolds number-friction factor law for smooth tubes,von Karman equation,(5.50),47,The kinetic energy and momentum correction factors,(5.51),(5.52),
16、48,For a Reynolds number of 104, the friction factor for a smooth tube is 0.0079, is 1.084, and is 1.031.,For example:,For Re = 106 the values are f= 0.0029, =1.032, and = 1.011.,For turbulent flow the error is usually very small ifandare assumed to be unity,49,5. Relations between maximum velocity
17、and average velocity,Experimentally measured values of as a function of the Reynolds number are shown in Fig. 5.8,50,51,6. Effect of roughness,52,k and is called the roughness parameter粗糙度 .,k/D is defined as relative roughness相对粗糙度.,53,Smooth pipe光滑管Rough pipe粗糙管,hydraulically smooth pipe: hydrauli
18、cally rough pipe:,Drawn copper and brass pipeOld, foul, and corroded pipe,54,Fig. 5.10 give the roughness parameter of several material of new pipe. (p112),55,The effect of roughness on the friction factor,Roughness has no appreciable effect on the friction factor for laminar flow unless k is too la
19、rge.,56,From dimensional analysis.,f is a function of both Re and the relative roughness k/D,57,7. The friction factor chart,From dimensional analysisf is a function of both Re and the relative roughness k/D Friction factor chart is a log-log plot of f versus Re.,58,59,二、管内湍流的摩擦系数,60,61,62,Laminar f
20、lowBuffer TurbulenceComplete turbulence （完全湍流区,阻力平方区）,63,Laminar flow,64,Turbulent flow: for hydraulically smooth pipe,Coburn equation,Blasius equation,This applies over Re from about 50,000 to 1 x 106.,Applicable over Re from 3,000 to 3 x 106,65,Complete turbulent flow:,Turbulent flow: for rough pipe,66, 8. Reynolds numbers and friction factor for non-newtonian fluids,for pseudoplastic fluids and laminar flow,(5.56),
