CHAPTER 6FLOWS IN PIPE6.1 IntroductionFlowinclosed conduits is veryimportant part of studyof fluid mechanics asexamples are very common. Water for domestic use is districted to all parts of thehouse in pipe, sewers and drain pipes carry waste water away.Crude oil is pumpedfrom oil well to refinery in pipes. Natural gas is brought to the consumer throughpipes.Heated or cold air in distributed to all parts of a house in circular or rectangularducts. All these examples show that water, oil or gas is usually transported throughpipes. he purpose of this chapter is to describe laminar and turbulent flowphenomena, to determine the effect of viscosity and also examine various flow lossesthat ta!ing place in the piping systems.6.2 Laminar and Turbulnc Flo!""npipeflowthreeflowregimes exist whicharelaminar andturbulent. At lowvelocities the layers of fluid move smoothly over one and another and this is !nownas#laminarflow$. However,asthevelocityisincreasedsmalldisturbancescauseeddies which #mix up$ the layer of fluid and produce a different pattern of flow !nownas #turbulent$.he nature of flow determines the pressure loss and hence the powerre%uired to pump the fluid along the pipe.&sborne 'eynolds is the first person to investigate the behavior of flow in pipes andproduced a rational method of predicting the nature of flow. 'eynolds showed thatthe flows behavior depends on inertia and viscous forced in the fluid.He introduced anon(dimensionalparametercalled'eynoldsnumberwhichgivesratioofinertiatoviscous forces and this number can identify the conditions under which flow changesfrom laminar to turbulent.)ividing theinertiaforces bytheviscous force,weobtain 'eynoldsnumber. hisnumber is used to identify the flow developed"nertia force*mass + changes of velocity , time-.-*mass flow rate + changes of velocity*density + velocity + area + changes of velocity */ + u + A + u*/ + u0 + A */ u0 )01iscous force *shear stress + area* areadydu *0DDu *2 u )herefore, 'eynolds number 3 "nertia force , 1iscous force uDuDD u= =0 0'e 45.-6hetermto writecalled !inematicsviscosity 7anditisoften convenienttowritee%uation 8.- as uD= 'e45.06he important discovery made by 'eynolds was that for a normal flow in a pipe thetransitionbetweenlaminarandturbulent flowalwaysoccursat approximatelythesame value of 'e irrespective of fluid and the si9e of pipe.his helps to predict theflow conditions in pipes of any si9e carrying the fluid.6.# R$nold" E%&rimnt"'eynoldsapparatusisshownschematicallyinFigure5.-a.Atransparent tubeisattached to a constant(head water tan!. he opposite end of the tube has a valve to-.0control flow rate.)ye in in:ected into water tube at inlet and resulting flow pattern inobserved.For low velocities of flow something similar to that represented in Figure5.-bisobserved.hedyepatternisregularandformsasinglelineli!ethread.here is no mixing in any part of the tube.he flow show that particles of fluid flowin parallel lines.his is called laminar flow.As the flow rate of water is increased beyond a certain point the dye is dispersed.hedye mixes with water as shown in Figure 5.-c.his is called turbulent flow."t has been found that when the flow in laminar the 'e ; 00= 45.-.66.* Friction Lo""" "naturbulent flowmixingta!esplacebetweenlayersofthefluidandasaresultdistribution of velocity in more uniform than in laminar flow.Cet us consider a cross(section of the pipe as shown in Figure 5.>.-.GFigure 5.> urbulent flow distributionsForacontrolvolumefrompoints A andB.heshearstressisactingonthewallsurface depends on the average velocity, thusE f Vo00- = 45.->6Where00-V 3 dynamics pressure and f 3 friction factor. heLoand00-V havedimensions but f is a dimensionless.'esultant force due to shear stress 3 shear stress + area-.H3 Lo+0Dal

al f V 00-0 =45.-86'esultant force due to pressure drop 3 pressure changes + area 3 @A D a045.-56K%uations 5.-8 and 5.-5 will giveEal V f a P 00-0 0= afl VP0= 45.-G6he relationship between pressure drop and head losses is given byEfgh P = 45.-H6From e%uation 5.-G and 5.-H will produceEgDflVhf00= 45.-J6where )3 0a.he comparison of e%uation 5.-. and 5.-J, the friction factor of laminar flow isE'e5>= f 45.08m and diameter of -8