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Unformatted text preview: Chapter 14 Flow in Pipes 141 Chapter 14 FLOW IN PIPES Laminar and Turbulent Flow 141C Liquids are usually transported in circular pipes because pipes with a circular crosssection can withstand large pressure differences between the inside and the outside without undergoing any significant distortion. 142C Reynolds number is the ratio of the inertial forces to viscous forces, and it serves as a criteria for determining the flow regime. At large Reynolds numbers, for example, the flow is turbulent since the inertia forces are large relative to the viscous forces, and thus the viscous forces cannot prevent the random and rapid fluctuations of the fluid. It is defined as follows: ( a ) For flow in a circular tube of inner diameter D : n D m V = Re ( b ) For flow in a rectangular duct of crosssection a b : n h m D V = Re where D A p ab a b ab a b h c = = + = + 4 4 2 2 ( ) ( ) is the hydraulic diameter. 143C Reynolds number is inversely proportional to kinematic viscosity, which is much larger for water than for air (at 25 C, air = 1.562 105 m 2 /s and water = = 0.891 103 /997 = 8.9 105 m 2 /s). Therefore, noting that Re = V D / , the Reynolds number will be higher for motion in air for the same diameter and speed. 144C Reynolds number for flow in a circular tube of diameter D is expressed as u D m V = Re where r m u rp p r r = = = = and 4 ) 4 / ( 2 2 D m D m A m c & & & V Substituting, m p r m rp u D m D D m D m & & 4 ) / ( 4 Re 2 = = = V 145C Engine oil requires a larger pump because of its much larger density. 146C The generally accepted value of the Reynolds number above which the flow in a smooth pipe is turbulent is 4000. 147C Reynolds number is inversely proportional to kinematic viscosity, which is much larger for water than for air (at 25 C, air = 1.562 105 m 2 /s and water = = 0.891 103 /997 = 8.9 105 m 2 /s). Therefore, for the same diameter and speed, the Reynolds number will be higher for air flow, and thus the flow is more likely to be turbulent for air. 148C For flow through noncircular tubes, the Reynolds number and the friction factor are based on the hydraulic diameter D h defined as p A D c h 4 = where A c is the crosssectional area of the tube and p is its perimeter. The hydraulic diameter is defined such that it reduces to ordinary diameter D for circular tubes since D D D p A D c h = = = p p 4 / 4 4 2 . D a b m, V m Chapter 14 Flow in Pipes 142 149C The region from the tube inlet to the point at which the boundary layer merges at the centerline is called the hydrodynamic entrance region , and the length of this region is called hydrodynamic entry length ....
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This note was uploaded on 04/07/2008 for the course ENGR 2220 taught by Professor Maples during the Fall '07 term at Auburn University.
 Fall '07
 Maples
 Dynamics

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