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