Chapter 8 INTERNAL FLOW

1 Fluid Mechanics: Fundamentals and Applications, 2nd EditionYunus A. Cengel, John M. CimbalaYunus A. Cengel, John M. CimbalaMcGraw-Hill, 2010 Chapter8 Chapter 8 INTERNAL FLOWL ecture slides byLecture slides byHASAN HACI EVK Copyright The McGraw-Hill Companies, Inc. Permission required for reproduction or flows through pipesthrough pipes, elbows, tees,valves, etc., as in this oil refinery, are foundin nearly2foundin nearly every Have a deeper understanding of laminar and turbulent flow in pipes and the analysis of fully developed flow Calculate the major and minor losses associated with pipeflow in piping networks and determinewith pipeflow in piping networks and determine the pumping power requirements Understand various velocityand flow rateUnderstand various velocityand flow rate measurement techniques and learn theiradvantages and disadvantages38 1 INTRODUCTION Liquid or gas flow through pipesor ductsis commonly used in heating andcooling applications and fluid distribution networks.

2 The fluid in such applications is usually forced to flow by a fan or pumpthh fltithrough a flow section. We pay particular attention to friction, which is directly related to the pressuredropand head lossduring flow through pipes and ducts. The pressure drop is then used to determine the pumping power pipes can withstand largepressure differences4 Circular pipes can withstand largepressure differences between the inside and the outside without undergoing any significant distortion, but noncircular pipes solutions are obtained only for a few simple cases such as fully developed laminar flow in a circular pipe. Therefore, we must rely on experimental results and empirical relations for most fluid flow problems rather than closed-form analytical value of the average velocity Vavgat gyavg some streamwise cross-section isdetermined from the requirement that the conservation of mass principle be satisfiedThe average velocity for incompressibleflow in a circular pipe of radius RAverage velocity Vavgis defined as the average speed through a cross sectionFor fully developed5cross fully developed laminar pipe flow.

3 Vavgis half of the maximum 2 LAMINAR AND TURBULENT FLOWSL aminar flow is encountered when highly viscous fluids such as oils flow in small pipes or narrowpassagesTURBULENT FLOWSL aminar:Smooth streamlines and highly in small pipes or :Velocity fluctuations and highly disorderedmotiondisorderedmotion. Transition:The flow fluctuates between laminar and turbulent flows encountered in practice are and The behavior of colored fluid injected into the flow in laminar6turbulent flow regimes of candle in laminar and turbulentflows in a NumberThe transition from laminar to turbulent At large Reynolds numbers, the inertial forces, which are proportional to the fluid density and the square of the fluidflow depends on the geometry,surfaceroughness, flow velocity, surface temperature, and type of density and the square of the fluid velocity, are large relative to the viscous forces.

4 And thus the viscous forces cannot prevent the random and rapid The flow regime depends mainly on the ratio of inertial forcesto viscous forces(Reynolds number).fluctuations of the fluid (turbulent).At small or moderate Reynolds numbers, the viscous forces are large enough to suppress these fluctuationsCritical Reynolds number, Recr:Th Rldbt hi h thenough to suppress these fluctuations and to keep the fluid in line (laminar).The Reynolds number at which the flow becomes turbulent. The value of the critical Reynolds number is different for differentThe Reynolds number can be number is different for different geometries and flow as the ratio of inertial forces to viscous forces acting on a fluid flow through noncircular pipes, the Reynolds number is based on thehydraulicis based on the hydraulic diameterFor flow in a circular pipe:The hydraulic diameter D4A/idfi dhtht8Dh=4Ac/p isdefined such that it reduces to ordinary diameter for circular the transitional flow region of 2300 Re 10,000, the flow switches between laminar and turbulent seemingly 3 THE ENTRANCE REGIONV elocity boundary layer.

5 The region of the flow in which the effects of the viscous shearing forces caused by fluid viscosity are layer region:The viscous effects and the velocity changes are significant. Irrotational (core) flow region:The frictional effects are negligible and theIrrotational (core) flow region:The frictional effects are negligible and the velocity remains essentially constant in the radial development of the velocity boundary layer in a pipe. The developed average velocity profile is parabolic in laminar flow, but somewhat flatter or fuller in turbulent entrance region:The region from the pipe inlet to the point at which the boundary layer merges at the entry length Lh:The length of this region.

6 Hydrodynamically developing flow:Flow in the entrance region. This is the region where the velocity profile fully developed region:The region beyond the entrance region in which the velocity profile is fully developed and remains developed:When both the velocity profile the normalized temperature ypyppprofile remain fully developedIn the fully developed flow region of a pipe, the velocity profile does not change downstream and thus the10downstream, and thus the wall shear stress remains constant as pressure drop is higher in the entrance regions of a pipe, and the effect of the entrance region is always toincrease the averagefriction factor for the entire variation of wall shear stress in the flow direction for flow in a pipefrom the entrance region into the fully developed LengthsThe hydrodynamic entry length is usually taken to be the distance from the pipe entrance to where the wall shear stress (and thus the friction factor)

7 Reaches within about 2 percent of the fully developed entry length for The pipes used in practice are usually several times the length of the entrance region, yglaminar flowhydrodynamic entry length forggand thus the flow through the pipes is often assumed to be fully developed for the entire length of the pipeentry length for turbulent flowhydrodynamic entry lthftbltfllength of the pipe. This simplistic approach gives reasonable results for long pipes but sometimes poorlength for turbulent flow, an approximationpipes but sometimes poor results for short ones since it underpredicts the wall shear stress and thus the friction 4 LAMINAR FLOW IN PIPESWe consider steady, laminar, incompressible flow of a fluid with constanty,,pproperties in the fully developed region of a straight circular fully developed laminar flow, each fluid particle moves at a constant axialvelocity along a streamline and the velocity profile u(r) remains unchanged inthe flow direction.

8 There is no motion in the radial direction, and thus thevelocity component in the direction normal to the pipe axis is everywhere is no acceleration since the flow is steady and fully diagram of a ring-shapeddifferential fluid element of radius r,13thickness dr, and length dx orientedcoaxially with a horizontal pipe in fully developed laminar yconditionsAverage velocityVelocityMaximim velocity ttliVelocity profile14 Free-body diagram of a fluid disk element of radius R and length dx in fully developed laminar flow in a horizontal centerlinePressure Drop and Head LossA pressure drop due to viscouseffects represents an irreversible pressureA pressure drop due to viscouseffects represents an irreversible pressure loss, and it is called pressure loss loss for all types offully developedCircular pipe, types offully developed INTERNAL flowsdynamic pressureDarcy friction laminarHead lpressurefactorlossIn laminar flow.

9 The friction factor is a function of the Reynolds number only and is independent of the roughness of the pipesurface15only and is independent of the roughness of the head loss represents the additional height that the fluid needs to beraised by a pump in order to overcome the frictional losses in the pipePoiseuille s lawFor a specified flow rate, the pressure drop and thus the required pumping power is proportional to the length of the pipe and the viscosity of the fluid, but it is inversely proportional to the fourth power of the diameterof of the diameterof relation for pressure loss (andhead loss) is one of the most generalrelations in fluid mechanics, and it isvalid for laminar or turbulent flows16valid for laminar or turbulent flows,circular or noncircular pipes, andpipes with smooth or rough pumping power requirement for a laminar flow piping system can be reduced by a factor of 16 by doubling the pipe pressure drop P equals the pressure loss PLin the case of a horizontal pipe, but this is not the case for inclined pipes or pipes with variable cross-sectional area.

10 This can be demonstrated by writing the energy equation for steady, incompressible one-dimensional flow in terms of heads as17 Effect of Gravity on Velocity and Flow Rate in Laminar FlowFree-body diagram of a ring-shapeddifferential fluid element of radius r,thickness dr, and length dx oriented18coaxially with an inclined pipe in fullydeveloped laminar Flow in Noncircular PipesThe friction factor f relations are given in Table 8 1 for fully dldli fliNoncircular Pipesdeveloped laminar flow in pipes of various cross sections. The Reynolds number for flow in these pipes u be o oese p pesis based on the hydraulic diameter Dh=4Ac/p, where Acis the cross-sectional area of thepipeandpis its wettedthe pipe and p is its wetted perimeter202122232425268 5 TURBULENT FLOW IN PIPESMost flows encountered in engineering practice are turbulent, and thus it isimportant to understand how turbulence affects wall shear stress.