FTFS Chap14 P001 - Chapter 14 Flow in Pipes Chapter 14 FLOW...

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Chapter 14 Flow in Pipes Chapter 14 FLOW IN PIPES Laminar and Turbulent Flow 14-1C Liquids are usually transported in circular pipes because pipes with a circular cross-section can withstand large pressure differences between the inside and the outside without undergoing any significant distortion. 14-2C 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 : ν D m V = Re ( b ) For flow in a rectangular duct of cross-section a × b : 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. 14-3C Reynolds number is inversely proportional to kinematic viscosity, which is much larger for water than for air (at 25 ° C, ν air = 1.562 × 10 -5 m 2 /s and ν water = μ∕ρ = 0.891 × 10 -3 /997 = 8.9 × 10 -5 m 2 /s). Therefore, noting that Re = V D / ν , the Reynolds number will be higher for motion in air for the same diameter and speed. 14-4C Reynolds number for flow in a circular tube of diameter D is expressed as υ D m V = Re where ρ μ ρπ π = = = = and 4 ) 4 / ( 2 2 D m D m A m c V Substituting, D m D D m D m 4 ) / ( 4 Re 2 = = = V 14-5C Engine oil requires a larger pump because of its much larger density. 14-6C The generally accepted value of the Reynolds number above which the flow in a smooth pipe is turbulent is 4000. 14-7C Reynolds number is inversely proportional to kinematic viscosity, which is much larger for water than for air (at 25 ° C, ν air = 1.562 × 10 -5 m 2 /s and ν water = μ∕ρ = 0.891 × 10 -3 /997 = 8.9 × 10 -5 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. 14-8C For flow through non-circular 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 cross-sectional 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 = = = 4 / 4 4 2 . 14-1 D b m, V m
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Chapter 14 Flow in Pipes 14-9C 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 . The entry length is much longer in laminar flow than it is in turbulent flow. But at very low Reynolds numbers, L h is very small ( L h = 1.2 D at Re = 20). 14-10C The wall shear stress τ w is highest at the tube inlet where the thickness of the boundary layer is zero, and decreases gradually to the fully developed value. The same is true for turbulent flow.
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This homework help was uploaded on 04/18/2008 for the course EML 3007 taught by Professor Chung during the Spring '08 term at University of Florida.

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FTFS Chap14 P001 - Chapter 14 Flow in Pipes Chapter 14 FLOW...

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