CHAPTER4FH

7/30/2019 CHAPTER4FH

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C ha pt er I V

Fl uid Flow Theor y and Practices

L e a r n i n g O b j ec t i v es

R e a d i ng t h i s c h a p te r w o u l d e n a bl e y o u t o u n d e r st a n d :

l Various types of fluids, there flows and friction factors.

l R e l a ti o n w i t h e c o n o mi c v e l o ci t y a n d l i ne s i z i n g .

Contents

4 .1 I nt ro du ct io n

4.2 Schedule Number

4 . 3 T u b i n g a n d O t h e r F l o w C o n d u it s

4.4 Velocity Constraints

4 .5 G ra vi ty Fl ow

4.6 Viscosity

4 . 7 V i s c o s i t y C l a s si f i c a ti o n s

4 .8 T y p es o f F lu id s4.8.1 Newtonian Fluids

4 . 8 . 2 B i n g ha m P l a s t i c F l u i ds

4 . 8 . 3 D il a t a nt F l u i ds

4 . 8 . 4 P s e u d op l a s t ic F l u i ds

4 . 8 . 5 T h i xo t r o p ic F l u i ds

4 . 8 . 6 R h e op e c t ic F l u i ds

4 . 9 R ey n o l d s N u m b er

4.10 Velocity Head

4.11 Friction Factors

4 . 1 2 R o u g hn e s s ( e )4 . 1 3 L a mi n a r F l o w F r ic t i o n

4 . 14 T h e Ru l e of F o ur s f o r P r es s ur e D r op4 . 1 5 Va l v e C o e f f i c i en t C v

4 . 1 6 C o m pr e s s i b le F l u i ds

4 . 17 S t ep s i n L in e S i zi n g

4.18 Newtonian and Non-Newtonian Fluids DP (CGS System)

4 . 1 9 E c o n om i c Ve l o c it y f o r L i n e S i z i ng

4.20 Numericals

Self-assessment

C as e S tu dy

References

4 . 1 I n tr o du c ti o n

O ne o f t he p r oc es s e ng in ee r' s m os t i mp or t a nt t as ks i n t he d e si gn o f a f ac il it y i s t he si zi ng of t he pi pe s a nd du ct s t ha t c on ne ct e qu ip me nt o r p ip es w i tho t he r e q ui p me n t, p i pe s o r b o un d ar y p o i n t s.

S t a n d ar d c o mm e r c i al p i p e s i z e s w e r e o r i g i na l l y d e f i n ed b y t h e Am e r i ca nS t a n d ar d s A s s o c ia t i o n ( A S A ) n o w k n o w n a s t h e A m e r ic a n N a t i on a l S t a n d ar d sI n st i tu t e ( A NS I ). T h es e c om m er c ia l s i ze s a r e kn o wn a s i r o n pi p e si z es ( I PS ) .F o r 1 - th r o ug h 1 2 in c h p i pe , t h e O D i s s o me w ha t a b ov e t h e n o mi n al s i ze ; i . e. , a n8 - in c h p i pe h a s a n O D o f 8 . 62 5 i n ch H o we v er a t d i am e te r s o f 1 4 -i n ch a n d l a rg e r,

t h e O D i s e q ua l t o t h e no m in a l s i z e of t h e p ip e .

The ASA also established several categories of pipe according to the pressures e r v i c e t o w h i c h a p i p e m a y b e s u b j ec t e d . T h es e a r e t e r m e d S c h e du l e s ( S c h ) ,

Fluid Flow Theory and Practices

1/MITSDE


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a nd th ey a r e l is te d a s S ch 1 0, Sc h 2 0, Sc h 3 0, Sc h 4 0, Sc h 6 0, Sc h 8 0, Sc h 1 00 ,

S c h1 2 0, Sc h 1 4 0, an d S c h 1 6 0. Th e O D f o r e a ch n o mi n al s i ze is t h e s a me fo r a l l

s ch ed ul es . A s w ou ld b e ex pe ct ed , th e wa ll t hi ck ne ss f or a g iv en s ch ed ul e

i n cr e as e s w i th t h e n o mi n al s i z e o f t h e p i pe .

4 . 2 S c he d ul e N u mb e r

l The relationships between pressure, schedule, corrosion allowance and

wall thickness are expressed by the following equations:

S c h e d ul e n u m b er = 1 0 00 P / S

A n d t = ( P /S x d / 2 ) + C

Where,

P = maximum internal working pressure; psig

S = a l l o w ab l e w o r k i ng s t r e s s a t d e s i g n t e m p er a t u r e, p s i g

t = p i p e t h i c kn e s s , i nd = outside pipe diameter, in

C = c o r r o s i o n a l l o w an c e , i n

l C o r r o s i o n a l l o w an c e s a r e n o t n o r m a l ly us e d i n a s s o c ia t i o n w i t h s t a i nl e s s

s t ee l o r a l lo y p i pi n g s i nc e t h es e m a te r ia l s a r e c ho s en f o r t h ei r r e s is t an c e t o

c o r r o s i o n .

4 .3 T ub in g a nd Ot h er F l ow C o nd u it s

Tubing and other flow conduits are described as under:

Tubing has mechanical characteristics, dif ferent from those of pipe and can

s om et im es b e u se d i n pl ac e o f i t t o g re at a dv an ta ge . It i s e sp ec ia ll y u se fu l f or

r u n s o f 1 - i n ch d i a m et e r a n d l e s s w h e n t h e f l e x ib i l i t y o f t u b i n g c o m p ar e d w i t h t h e

g r e a t er r i g i d it y o f p i p e i s d e s i r ed . T u b i ng i s n o r m a l ly a va i l a bl e in n o mi n a l s i z e s

f r o m 1 / 8 to 1 2 i nc h es d i am e te r a n d is u s ed f o r a p pl i ca t io n s s u ch a s r e a ct o r c o il s

a n d h e at i n g c oi l s i n s m a ll v e s s el s o r l a r g e s to r a g e ta n k s .

A ver y important use for tubes is in heat exchangers. In this case, the OD of the

t ub e i s th e s am e as i ts n omi na l s iz e. T he wal l t hi ck ne ss es a re set b y t he

s ta nd ar ds o f t he T ub ul ar E xc ha ng er M an uf ac tu re rs A ss oc ia ti on ( TE MA ) i n

B i r m i n g ha m w i r e g a u g e u n i t s , a s c a l e o r i gi n a l l y d e ve l o p ed f o r w i r e d i a m e te r sa n d a ls o u s ed f o r s h e e t m e t a l t h i c k ne s s .

4 . 4 Ve l o c it y C o n st r a in t s

The following are the various factors for velocity constraints:

The existence of velocity constraints on fluids flowing in pipes must always bek e p t i n m in d .

E a ch t y pe of f l ow ha s i t s o w n p e cu l ia r a n d d i st i nc t v e lo c it y l i mi t s b e yo n d

which it should not be designed.

S in gl e p ha se l iq u id s s uc h a s w at er, h yd r oc ar bo ns , s o lu ti on s a nd o th er s c anc a u s e w a t e r h a m m er o r e r o s i o n o f t h e p ip i n g if v e l o ci t i e s a r e s u f f i c i en t l y gr e a t .

Fluid Handling


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Wa t e r h a m me r i s t h e t e r m g iv e n t o t he f o r c e s

c es c an b e

d e s t r u c t i ve e n o u g h t o d a m a ge p i p i n g o r s u p p o r t s .

A rough thumb rule, based on engineering experience, for use with water in

m e ta l li c p i pe s w h i ch a r e o f 3 i n ch e s d i am e te r a n d gr e a te r a n d ar e i n c on t in u ou s

s e r v i c e i s t h a t t h e v e l o ci t y i n fe e t p e r s e c o n d s h o u l d n o t e x c e ed ab o u t 4 p lu s o n e -h a l f o f t h e n o mi n a l d i a m et e r i n i n c he s . i . e. 4 + d /2 . T h u s, t h e ve l o c it y i n a 3 i n c h e

p i p e s h o u l d no r m a l l y b e k e pt b e l o w 5 1 / 2 ft / s , an d t h e ve l o c it y i n a 1 6 - i nc h l i n e

c o u l d b e a s g r e a t a s 1 2 f t / s , i n t h e a b s e nc e o f o t h e r c o n s tr a i n t s. I n no c a s e s h o u l d

a pumped liquid velocity be allowed to exceed 14 to 17 ft/s. Below 3 inch

d i a m et e r, v e l o c i ti e s o f 5 f t / s a r e a c c e pt a b l e f o r l i q u i ds .

4 . 5 G r av i ty F l ow

B e si d es i n d uc e d f l ow s b y me a ns o f p u mp s , co m pr e s so r s, o r v a cu u m d e vi c es ,t h er e c a n be g r av i ty f l ow, o r f l ow c a us e d so l el y b y di f f e r en c es i n e le v at i on o r

s t a t ic p r e s s u r e b e t w ee n t w o po i n t s i n t h e sy s t e m. I n t he s e c as e s , t he t o t alp r es s ur e or f ri ct io n lo ss c an no t b e gr e at er t ha n th e st at ic h ea d or

f ri ct io n lo ss a t a r ea so na bl e v al ue f or t he r eq ui re d fl ow. A p ro pe rl y si ze dd ia me te r a ls o p rev en ts a h ig h e nt ran ce lo ss or b ui ld -u p o f l iq ui d d ue t oconstriction above the inlet to the piping system.

4 . 6 V i s c o si t y

An important physical proper ty of a fluid that influences the type of flow pattern,

which will be developed in a conduit and, thus, the friction loss, is the fluid's

viscosity.

Figure 4.1 Viscosity

E x p e ri m e n ta l r e s u l ts s h o w t h a t f o r a l l N e w t on i a n f l u i d s, t h e s l o p e o f t h e ve l o c i ty d i s t r ib u t i o n l i n e , i. e . u / d, c o r r e l a t es w e l l w i t h a n d i s p r o p o r t i o n al t o t h e sh e a r

r a t e o r s t r e s s , i .e .

The propor tionality factor between the two elements is termed as the dynamic

o r a b s o l ut e v i s c o s i t y m s u ch t h at

s e t u p , s h o ul d t h e ve l o c it y o f t h e

f l ow i ng m e d ia b e c h an g ed s u d d en l y. A t h i gh e r v e lo c it i es , t h e f o r

pressured i f f e r e n t i al . A p i p e o f s u f f i c i e n t ly l a r g e d ia m e t er m u s t b e c h o s en t o m a i nt a i n t he

A

F


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Area A

Area AForce F

d

u = 0


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=

M o s t a b s o l ut e v is c o s i ti e s a r e c om m o n ly r e f er r e d t o i n t e r m s o f c e n t ip o i s e s ( c p ) ,

o r o n e h u n d r e dt h o f p o i s e ( P ) , t h e m e t ri c u n i t f o r v i s c o si t y.

F r e q u en t l y, m e a su r e m e nt s o f v i s c os i t y a r e m a d e w he n t h e fl u i d i s f l o w i ng . T h er e s u l t s o o b t a i ne d i s t e r m e d t h e k in e m at i c v i s c o si t y z .

I n t h e m e t ri c s y s t em , k i n e ma t i c v i s c os i t y i s m e a s ur e d i n s q u a r e c e n ti m e tr e s p e r

s e c o n d, o r s t o k e s ( S t ) . I t i s o b t a i ne d b y d i v i d in g t he a b so l u t e v i s c o si t y in p o is e s

b y t h e s p ec i f i c g r a v i ty s o f t h e f l u id . S i m i la r l y, c e n t ip o i s e s d i v i de d b y t h e s pe c i f i c

g r a v it y i s c a l l ed c e n t i s t o k es ( c S t ).

z ( cS t) = ( cp ) / s

4.7

l All gases and the great majority of liquids are known as true, simple, or

N e w t o ni a n f l u i d s . T h e c r i t er i o n f o r t h i s c l a s s if i c a ti o n i s t h a t t h e v i s c o si t y o f

t h e f lu i d b e a p o in t f u nc t io n o f i t s t e mp e ra t ur e a n d p re s su r e o n ly a n d t ha t i t

n ot b e a f f ec te d b y t he ty pe or a mp li tu de of m ot io n t o w hi ch i t m ay be

s u b j e ct e d o r b y t i m e .

Thus, for a Newtonian liquid, when temperature and pressure remain

constant,

l The viscosity or ratio of shear stress to shear rate is a constant for all

s h e a r r a t es ,

l There is no shear rate only when there is no shear stress, and

l The viscosity does not change with time.

l N o n - Ne w t o n ia n l i q u i ds o b v i o us l y d e v ia t e f r o m N ew t o n i an o n e s i n t h a t t h e y

d o n o t f o l l o w on e o r m o r e o f t h e s e cr i t e ri a .

4 . 8 T y p e s of F l u i d s

Fluid can be divided into the following categories

4 . 8 .1 N e w to n i an F l u i ds

F i g u r e 4 . 2 N e w t o ni a n f l u i d s ( a )

P l as t ic s u bs t an c es h a ve de f in i te yi e ld st r en g th a n d d o n o t f l ow un t il a c e r t ai n

d e g r e e o f s h e a r s t r e s s h a s b e e n a p p l i ed . E x am p l e : O i l p a i n ts

Viscosity Classifications

A

F

d

Fluid Handling

F/A

u/d F/Au/d


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4 . 8 .2 B i n g ha m Pl a s t ic F l u i ds

F i g u r e 4 .3 B i n g h a m p l as t i c f l u i d s ( b )

4 . 8. 3 D i la t an t F l ui d s

D i la t an t f l u id s e x hi b it a n i n cr e as e o f v i sc o si t y w it h a n i n cr e as i ng r a t e o f s t r es s .E x a m pl e : C o n c e n t ra t e d s u s p e n s io n s o f t i t a ni u m d i o x i d e p a r t i c l e s i n w a t e r.

F i g u r e 4 .4 D i l a t an t f l u i d s ( c )

4 . 8 .4 P s e ud o p l as t i c F l u i d s

The viscosity of a Pseudoplastic material decreases with the increase in shear

stress.

E xa mp le : M an y s ol ut io ns o f h ig h m ol ec ul ar w ei gh t i nd us tr ia l p ol ym er s i n

o r g a n ic s o l v en t s b e l o n g t o t h i s c l a s si f i c a ti o n .

F i g u r e 4 . 5 P s e u d op l a s ti c f l u i d s ( d )

4 . 8 .5 T h i x ot r o p ic F l u i d s

Thixotropy is the proper ty, exhibited by certain gels and emulsions, ofb e c o mi n g m or e l i q ui d w h e n s t i r r e d o r s h a k en i . e . th e s t r u c t u r e o f t h e f l ui dc h a n ge s w i t h t i m e . E x a m pl e : Ma n y d r i l l in g m ud s , g r ea s e s a n d in k s f a l l i n t o t h i scategory.

F/A

u/d F/Au/d

F/A

u/d u/d

F/A

F/A

u/d u/d

F/A


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F i g u r e 4 . 6 T h i x o tr o p i c f l u i d s ( e )

4 . 8. 6 R h eo p ec t ic F l ui d s

The viscosity of rheopectic fluids is also a function of time and the manner inwhich the shear stress was applied. Their viscosities remain constant at a

g i ve n in s ta n t o f t i me b u t a r e d e pe n de n t o n ti m e. Ex a mp l e: Ge l at i ns .

Figure 4.7 Rheopectic fluids

4 . 9 R e y no l d s N u m b er

I t e xp r es s es t he r a ti o o f i ne r t ia f or c es o f a m ov in g f lu id t o i t s v is co us f or ce s a ndwas developed in the late 1800's by Osborne Reynolds, an English scientist, whowas one of the earlier investigators into the nature of fluid flow.

Re = Du

R e : D i me n si o nl e ss n u mb e r ( R ey n ol d 's N u mb e r) , D = ID o f p i pe , f t ,u = mean linear velocity, ft/h, r = fluid density , lb/ft3, m = absolute

viscosity, lbm / (ft-h).

L a mi n ar r e gi o n: Re < 2 1 00 ( I nd e pe n de n t o f / D ), = R o ug h ne s s o f p i pe , D= I D o f p ip e, / D = D im en si on le ss .

C r i t i ca l r e g i o n: R e 2 1 0 0 4 0 0 0 ( I n d ep e n d e nt o f / D )

Transient + Turbulent: Re + 4000 (Depends on /D)

4 . 1 0 Ve l o c it y H e a d

A significant concept in all situations involving fluid flow is that of velocity

head.

F/A

u/d u/d

F/A

q22

q22

q11 q11

q =tim e=time

F/A

u/d u/d

F/A

q22q22q11 q11

q =tim e=time q00 q00

q22

q11

q00

F luid H andling


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h = u 2 / 2 g ,h = v e l oc i ty h e ad , f t f l ui d ,u = mean linear velocity, ft/sg = dimensional constant, 32.17 (lbm/lbf)(ft/s2)

4 . 11 F r ic t io n F a ct o rs

The friction that is developed in a section of a conduit is a function of many

variables, some of which are interrelated. They are:

l M e a n l i n ea r v e l o ci t y a n d d e n s it y o r t h e i r p r o d u ct , m a s s v e l o ci t y.

l P i p e d i a m et e r o r h y d r a ul i c r a d i us

l Viscosity l

l R o u g h ne s s o f c o n d u it

l L e ng t h o f p i pe

F = f ( L/ D) ( u 2/ 2g )

F = f r ic t io n l o s s, ft f l u id , f = Mo o dy fr i ct i on fa c to r, L = Eq u iv a le n t l e ng t h o f

c on d ui t, f t, D= Eq ui va le nt d ia me te r o f c on du it ( ft ), u = v el oc it y ( ft /s ), g =

dimensional constant, 32.17 (lbm / lbf) (ft/s2).

4 . 1 2 R o u g hn e s s ( )

R ou gh ne ss i s a m ea su re o f t he h ei gh t o f r eg ul ar p ro tr u si on s o r u ne ve nn es s,which extend from the sur face of the conduit to disturb fluid flow. Thesep r o t r u s i o n s c a n r a ng e f r o m 0. 0 0 1 to 0 . 0 1 f t ( 0 . 3 05 t o 3 . 05 m m ) f o r c o n c r et e p i p e,0 .0 00 5 f t ( 0. 15 m m) f or g al va ni se d - i r on p ip e, a nd 0. 00 01 5 f t ( 0. 05 m m) f or

c o mm e rc i al s t ee l p i pe . T h e l e as t r o u gh n es s i s g i ve n a s 0 . 00 0 00 5 f t ( 1 .5 n m m ) f or s m o o th b r a s s , l e ad , g l a s s , o r s o m e l i n ed p i p e .

4 . 13 L a mi n ar F l ow F r ic t io n

f = 6 4 / R e

Transition and turbulent flow friction factors

C r i t i ca l r e g i o n : 2 - 4 t i m es o f L a m i na r f l o w f r i c ti o n f a c t or

Transition and turbulent:

1/4Transition: f = 0.316 / (Re)

4 5( fo r 1 0 < Re < 1 0 )

0. 237f = 0 . 00 3 2 + ( 0 .2 2 1/ R e ) f o r a l l R e

R o u g h t u r b u le n t :

0. 51/f = 2 log (r / ) + 1.740

2= ( u f ) / 8 , = s h ea r s t r es s a t b o un d ar y.

= ( 1 r / r 0 ), t = sh e ar s t r es s a t d i st a nc e r f r o m b o un d ar y

0


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0

0 0


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4 . 14 T h e R u le o f F o ur s f o r P r es s ur e D r op

When the piping engineer is required to estimate pressure drop on the spot

without the use of a calculating aid, the following rules of four can be used.

T he p r e ss u r e d r o p o f f o ur h u nd r e d g a ll o ns p e r m i nu t e o f w a te r i n a 4 - in c h c l ea n

s t ee l p i pe i s a l mo s t 4 p s i p e r 1 0 0 f t

2 5

P = 4 [ (g al /m in ) / 40 0 ] ( 4 /d ) ( s / 1. 0) , s : sp ec if ic g ra vi ty 2 2 2 2 2

Relationship between r o u g h ne s s a n d f a n ni n g f r i c t io n f a c t or

0. 18

f 2/ f 1 = ( / )1 2

Friction loss in fittings and piping components2

P = K ( u / 2g ), K va lu e f or v ar io us t yp es o f f it ti ng s c an be o bt ai ne d f r om

f i g u r e 1 . 2 .2

= f . ( L/ D ) . u / 2g ,

L = E q u i va l en t l e ng t h o f f i tt i ng .

4 . 15 Va l ve C oe f f i c i en t C V

0The term C represents the flow of 60 F water in gallons per minute that will pass v

t hr o ug h t he v al ve a t a d if f e re nt ia l p r es s ur e ac ro s s t he v al ve o f 1 p si . I t f ol lo ws

t h a t t h e w a t e r f l o w r a t e f o r a n y o t h e r p r e s s u r e d i f f e r e n t i a l i s

0. 5G al /m in = C ( P ) v

a n d th e p r es s u r e d r o p fo r a n y o t h e r f l o w ra t e i s

2P = [ ( g a l / mi n ) / C ] v

0where gal/min = flow rate of 60 F water

P = P r e s s ur e d r o p a c r o ss v a l v e, p s i

0. 5C = v a lv e c o ef f i c i en t , (g a l/ m in ) / ( p s i) v

4 . 1 6 C o m pr e s s ib l e F l u i d s

l The great and obvious dif ference between an incompressible fluid and ac o mp r e ss i b le f l ui d i s t h e e f f e ct o f a c h an g e i n p r e ss u r e o n t h e s p ec i fi c

volume or density of the fluid.

l D en si ty of a c om pr es si bl e f lu id va ri es a lm os t p ro po r ti on at el y w it h t hesystem pressure.

G e n e ra l i s o t h er m a l e q u a ti o n f o r c o m p r es s i b l e f l u i d s :

2w =

w = mass flow rate kg/sec

2

1

22

2

2

1

1

1

2

)(

PPn

aLf

gAPP

P m

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F or e ng in ee ri ng c al cu la ti on s , 2 ln P / P i s g en er al ly mu ch l es s t ha n f L / d1 2 m

S in ce w = Q x2 2 2 5

(P P ) = (P ) x 16 x Q f L / (g x x d )1 2 1 1 m

U n w i n f o r m u l a f o r s t e a m f l o w :2 5

D P in p si / 10 0 ft = 0 .0 1 30 7 x ( w v / d ) x ( 1+ 3 .6 / d)w = steam flow in lb/min

v = specific volume in cub ft /lb

d = p i pe d i a i n i n c he s

Relationship between fanning friction factor and moody friction factor

f = 4f m f

f = M o od y f r ic t io n f ac t or, f = F a nn i n g fr i ct i on f a ct o r m f

4 . 17 S t ep s i n L i ne S i zi n g

l Assume pipe ID say d

l Ascertain density and viscosity as well as nature of fluid (Newtonian / Non-newtonian)

l Determine Re

l Find f or f .m f

l Use Darcy equation, determine DP

l I f D P c a l cu l a t ed i s n o t w i t h i n + /- 5 % o f s p e c i fi e d D P, a s s u m e n e w p ip e I D .

l R e p e at t h e p r o c e d ur e t i l l t h e r e q u i r e d c o n ve r g e n ce i s a c h i ev e d .

l When convergence is achieved, select standard pipe ID nearest to andhigher than the calculated pipe ID.

4 .1 8 N ew to ni an a nd N on -N ew to ni an F lu id s D P ( CG S S y s te m)

I n de p en d en t o f / D c a se .

N ew to ni an P = Q ( 8 L / 3 .1 4 R 4)

Q = c m 3 /s ( F l o w r a t e )

= p o i s e ( v i s c os i t y )

L = cm ( Le n gt h o f p i pe )

R = c m (R a di u s o f p i pe )

P = d y n es / c m 2

N o n - N e w t on i a n P = ( 2 L / R ) [ { ( 3 n +1 ) / 4 n }. ( 4 Q / 3. 1 4 R 3 ] n

n = F l o w b eh a v i o ur i n d e x

4 . 19 E c on o mi c Ve l oc i ty f o r L i ne S i zi n g

E co no mi c v el oc it y i s t he ve lo ci ty at w hi ch c ap it al c os t a nd op er at in g c os t o f p i p i n g s y s t e m f o r t e n u r e o f 1 0 y e a r s i s t h e l o w e s t.

2


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10/11

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0 N4 .2 u mer ic al s

a r o dy r i o1 ) C al cu l t e th e p e ss ur e d r p i n n e/ cm 2 f o a f lu id w ith s hea r v s c s it y o f i o i f l10 po s e fl wing thr ough a p pe o dia 5 cm and length 10 m with a f ow

t 2 o sra e of 0 lit/sec for foll wing ca es:l Newtonian fluidl e a iPs udopl stic fluid w th n = 0.9l =Di la tan t f lu id w it h n 1 .1

s b o s e p l a Discu s a u t p res ur dr op r ofi e for a ll t hes e 3 c ses.

o :Soluti n

c sP ro e ss p ar am et er i n C .G .S . u ni ts :

t ,0F lo w r at e: 2 0 l i / s = 20 0 0 c m3 /s

1 s y= 0 poi e = 10 d ne.s /cm2

0 1 1L = 1 m = 0 x 100 cm = 000 cm

cR = 5 m/2 = 2.5 cm4

l P = ( 3N ew ton ian Q 8 L / . 14 R )

4 6 20 1 x .0 n= 2 x 103x8x 0x1000 / ( 3.14 (2.5) ) = 13 4 x 10 dy e/cm

nl n t 2 ]N on - e w o ni an P = ( L / R) [ { (3 n+ 1) /4 n} . ( 4Q /3. 14 R 3

3 90.

1 [ 2 / ( 0 x( ]= (2 x1000x 0/2.5) {( .7 +1) 4x0.9}. 4x2000 )/3.14 2.5)

6e 2= 6. 38 x 1 0 d yn /c m

3

l P = 0 ) + . x / 2 1(2 x 10 0x10/2.5 [ {( 3x1.1 1)/4x1 1}.(4 20000) 3.14x( .5) ] .1

6 26= 26 . 3 x 10 d yn e/ cm

PD i s c u ss i o n : P < < PudoP se Newt Dilatant

e i m a e2 A pipe of 25 cm diamet r car ries a r ( = 1.22 kg/ 3) at n av rage

8 . T e s ovelocity of m/s he quivalent and grain roughness f the pipe is 0.50

m c t t f u t o y m . C al ula e he riction factor f by ass ming he fl w to be full r ough

u l . h r sturb ent What i s t e sh ea s tr e s a t th e b oundar y?

Solution:

n 5 =Give Dia = 2 cm 0.25 m

kgDens ity ( ) = 1.22 /m3

V = 8 m/s

= 0 . 5 0 m m = 0 . 0 0 05 m

To calculate f and

0. 511/(f) = 2 log (r / ) + .740

. 1r = 0 25/2 = 0. 25 m0 0. 5

21 /( f) = 2 l og (0 .1 5 /0 .0 00 5) + 1. 74

8 == 6.535 8 , f 0.0234

0

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2 2= u f / 8 = 1 .2 2 x 8 x 0 .0 234 / 8 = 0 .2 284 P

.5 m/s. If the

f r ic t io n f a ct o r f = 0 . 02 8 , ( a ) d e te r m in e t h e r o ug h n es s h e ig h t b y a s su m in g

f ul ly r ou g h t ur bu le nt f lo w to e xi st , (b ) F in d th e sh ea r s tr e ss a t t he w al l,

a n d ( c) F i nd t h e s h ea r s t r es s a t a r a di a l d i s ta n ce o f 5 c m f r o m th e a x is .

Solution:

G i v e n d i a = 3 0 c m = 0. 3 m , v = 3 . 5 m / s , f = 0 . 02 8 , r = 1 5 5 = 1 0 c m = 0. 1 m , D e n s i ty

( ) = 1 00 0 K g/ m3

For

1 / ( f ) 0. 5 = 2 l o g ( r 0 / ) + 1 . 7 40. 5

1 / (0 . 02 8 ) = 2 l o g ( 0 .1 5 )- 2 l o g + 1 .7 4

2 log = - 5.8839

-3= 1. 14 29 x 10 m = 1. 14 mm .

= v 2 f / 8 = 1 0 0 0 x ( 3 . 5 ) 2 x 0 . 0 2 8/ 8 = 4 2 . 8 75 P a .

= ( 1 r / r 0) = 4 2. 87 5 ( 1 -0 .1 /0 .1 5) = 1 4. 29 P a.

Self-assessment

a . F il l i n t he b la nk s1 ) Oi l p a in t s a r e t he e x am p le o f -- - -- - -- - -- - -- .

2 ) L ' m e an s - - - - -- - - -- - - - -- - - -- - - - -.

3 ) D e ns i t y o f a c o m p re s s i b l e f l u i d v a r i es a l m o st p r o p o r t i o n al l y wi t h - -- - - - -- - - -- - .

4 ) v ' s t an d s f o r - - -- - -- - -- - .

b. State whether tr ue or f alse

1 )O il p ai nt i s a d il at an t f lu id .

2 ) M a n y d r i ll i n g m u ds , g r e a s es a n d i n k s b e l o n g t o be p s e u d o pl a s t ic

category.

3 )4 fm = f f

f m = M o o d y f r ic t i o n f ac t o r, f f = F a n n i ng f r i c t i on f a c t o r

C as e S tu dy

1 . A 5 0 cm d ia me te r p ip el in e c ar r i es w at er a t a v el oc it y of 3 .5 m /s . If t he f ri ct io n

f a c t or f = 0 . 02 5 , ( a) d e t e r m in e t h e r o u g h n es s h e i g h t b y a s su m i n g f u l l y r o u g h

t u r b u le n t f l o w t o ex i s t , ( b ) F i n d t h e s h e a r s t r e s s a t t h e w a l l , a n d ( c ) F i n d t h e

s h ea r s t r es s a t a r a di a l d i s ta n ce o f 8 c m f r o m th e a xi s .

References

th1 . H . W. K i n g an d E . F. B r a te r, H a nd b oo k o f H y dr a ul i cs , 6 e d ., M c Gr a w H il l

Book Comnay, New York, 1976.

2 . A .H . S h ap ir o , T he D yn am ic s a nd T h e r mo dy na mi cs o f C om pr e ss ib le F l u id

Flow, Vol. I, The Ronald Press Company, New York, 1953.

a.

3) A 30 cm diameter pipeline car ries w ater at a velocity of 3

0

0

0


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CHAPTER4FH

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Transcript of CHAPTER4FH