INTRODUCTION

The expe r imen t i s conduc t ed ma in ly t o s t udy t he c r i t e r i on o f

l amina r , t r an s i t i on and t u rbu l en t f l ow . In f l u id mechan i c s , i n t e rna l f l ow i s

de f i ned a s a f l ow fo r wh ich t he f l u id i s con f ined by a su r f ace . The f l ow

may be l amina r o r t u rbu l en t . Osbo rne Reyno lds (23 Augus t 1832 – 21

Feb rua ry 1912 ) was a p rominen t i nnova to r i n t he unde r s t and ing o f f l u id

dynamics and mechan i c s .

Osbo rne Reyno lds Appa ra tu s cons i s t s o f wa t e r r e sou rce fo r t he

sy s t em supp ly , f i x -head wa t e r i npu t t o b ig and sma l l t r anspa ren t p ipe s ,

dye i npu t by i n j ec t i on un i t , and wa t e r ou tpu t un i t t o de t e rmine wa t e r f l ow

r a t e . The l amina r , t r an s i t i on and t u rbu l en t f l ows can be ob t a ined by

va ry ing t he wa t e r f l ow r a t e u s ing t he wa t e r ou t l e t con t ro l va lve . Wa te r

f l ow r a t e and hence t he f l ow ve loc i t y i s measu red by t he vo lume t r i c

measu r ing t ank . The supp ly t ank cons i s t s o f g l a s s beads t o r educe f l ow

d i s t u rbances . F low pa t t e rn s a r e v i sua l i z ed u s ing dye i n j ec t i on t h rough a

need l e va lve . The dye i n j ec t i on r a t e c an be con t ro l l ed and ad ju s t ed t o

improve t he qua l i t y o f f l ow pa t t e rn s .

AIMS / OBJECTIVES

1 . To obse rve t he cha rac t e r i s t i c s o f l amina r , t r an s i t i on and t u rbu l en t

f l ow .

2 . To p rove t ha t t he Reyno lds number i s d imens ion l e s s by u s ing t he fo rmu la ;

ℜ= ρ ν dµ

THEORY

In f l u id mechan i c s , Reyno lds Number (R e ) i s a d imens ion l e s s

number t ha t i s exp re s sed a s t he r a t i o o f i ne r t i a l f o r ce s (pV 2 /L ) t o v i s cous

fo r ce s ( µV/L 2 ) . Thus , t he Reyno lds number c an be s imp l i f i ed a s

fo l l owings ;

R e = (pV 2 /L ) / ( µV/L 2 )

= pVL/ µ

Where p i s t he dens i t y o f t he f l u id , V i s t he mean f l u id ve loc i t y , L i s a

cha rac t e r i s t i c l i nea r d imens ion , and µ i s t he dynamic v i s cos i t y o f t he

f l u id .

When a f l u id f l ows t h rough a p ipe t he i n t e rna l r oughnes s ( e ) o f t he

p ipe wa l l c an c r ea t e l oca l eddy cu r r en t s w i th in t he f l u id add ing a

r e s i s t ance t o f l ow o f t he f l u id . P ipe s w i th smoo th wa l l s such a s g l a s s ,

coppe r , b r a s s and po lye thy l ene have on ly a sma l l e f f ec t on t he f r i c t i ona l

r e s i s t ance . P ipe s w i th l e s s smoo th wa l l s such a s conc re t e , c a s t i r on and

s t e e l w i l l c r ea t e l a rge r eddy cu r r en t s wh ich w i l l some t imes have a

s i gn i f i c an t e f f ec t on t he f r i c t i ona l r e s i s t ance . The ve loc i t y p ro f i l e i n a

p ipe w i l l show tha t t he f l u id a t t he c en t r e o f t he s t r e am wi l l move more

qu i ck ly t han t he f l u id t owards t he edge o f t he s t r e am. The re fo re f r i c t i on

w i l l occu r be tween l aye r s w i th in t he f l u id . F lu id s w i th a h igh v i s cos i t y

w i l l f l ow more s l owly and w i l l gene ra l l y no t suppo r t eddy cu r r en t s and

t he r e fo re t he i n t e rna l r oughnes s o f t he p ipe w i l l have no e f f ec t on t he

f r i c t i ona l r e s i s t ance . Th i s cond i t i on i s known a s l amina r f l ow .

Reyno lds number ba s i ca l l y de t e rmines t he t r ans i t i on o f f l u id f l ow

fo rm l amina r f l ow to t u rbu l en t f l ow . When t he va lue o f Reyno lds number

i s l e s s t han 2300 , l amina r f l ow wi l l occu r and t he r e s i s t ance t o f l ow wi l l

be i ndependen t o f t he p ipe wa l l r oughnes s ( ℮ ) . Meanwhi l e , t u rbu l en t f l ow

occu r s when t he va lue o f Reyno lds number i s exceed ing 4000 .

Fo r l a rge v i s cous fo r ce , whe reby R e v a lue i s l e s s t han 2300 , v i s cous

e f f ec t s a r e g r ea t enough t o damp any d i s t u rbance i n t he f l ow and t he f l ow

r ema ins l amina r . The f l ow i s c a l l ed l amina r because t he f l ow t akes p l ace

i n l aye r s . Any combina t i on o f l ow ve loc i t y , sma l l d i ame te r , o r h igh

k inema t i c v i s cos i t y wh ich r e su l t s i n R e v a lue o f l e s s t han 2300 w i l l

p roduce l amina r f l ow . As Re i nc r ea se s , t he v i s cous damping o f f l ow

d i s t u rbances o r pe r t u rba t i ons dec rea se s r e l a t i ve t o t he i ne r t i a l e f f ec t s .

Because o f a l a ck o f v i s cous damping , d i s t u rbances a r e amp l i f i ed un t i l t he

en t i r e f l ow b reaks down in to i n i r r egu l a r mo t ion . The re i s s t i l l a de f i n i t e

f l ow d i r ec t i on , bu t t he r e i s an i r r egu l a r mo t ion supe r imposed on t he

ave rage mo t ion . Thus , f o r t u rbu l en t f l ow in a p ipe , t he f l u id i s f l owing i n

t he downs t r eam d i r ec t i on , bu t f l u id pa r t i c l e s have an i r r egu l a r mo t ion i n

add i t i on t o t he ave rage mo t ion . The t u rbu l en t f l uc tua t i ons a r e i nhe ren t l y

uns t eady and t h r ee d imens iona l . As a r e su l t , p a r t i c l e s wh ich pa s s t hough a

g iven po in t i n t he f l ow do no t f o l l ow the s ame pa th i n t u rbu l en t f l ow even

t hough t hey a l l a r e f l owing gene ra l l y downs t r eam. F lows w i th 2000 < Re

< 4000 a r e c a l l ed t r ans i t i ona l . The f l ow can be uns t ab l e and t he f l ow

swi t ch back and fo r t h be tween t u rbu l en t and l amina r cond i t i ons .

APPARATUS

* A r e - en t r an t be l l mou thed g l a s s expe r imen t a l t ube o f 16 mm bo re and

app rox ima te ly 790 mm long moun ted ho r i zon t a l l y i n a 103 mm bo re

Pe r spex t ube .

* Dye i n j ec to r w i th need l e va lve con t ro l .

* Ro tome te r f l ow me te r .

* Wa te r supp ly f rom a t ank w i th c l e a r t e s t s ec t i on t ube and “be l l mou th”

en t r ance .

EXPERIMENTAL PROCEDURES

Thi s expe r imen t demons t r a t e s v i sua l l y l amina r (o r s t r e aml ine ) f l ow and

i t s t r ans i t i on t o t u rbu l en t f l ow a t a pa r t i cu l a r ve loc i t y .

1 . F i r s t l y , t he appa ra tu s i s s e t up and i n se r t t he r ed dye i n to t he dye

r e se rvo i r w i th a s t e ady f l ow o f wa t e r .

2 . The dye i s a l l owed t o f l ow f rom the nozz l e a t t he en t r ance o f t he

channe l un t i l a co lo r ed s t r e am i s v i s i b l e a l ong t he pa s sage . The

ve loc i t y o f wa t e r f l ow shou ld be i nc r ea sed i f t he dye accumula t e s

a round t he nozz l e .

3 . Ad jus t t he wa t e r f l ow un t i l a l amina r f l ow pa t t e rn wh ich i s a

s t r a i gh t t h in l i ne o r s t r e aml ine o f dye i s ab l e t o be s een a long t he

who le pa s sage .

4 . Co l l e c t t he vo lume o f wa t e r t ha t f l ows fo r 10 s econds t hen measu re

t he amoun t o f wa t e r i n t he vo lume t r i c measu r ing t ank . Repea t t h i s

s t ep 3 t imes t o ge t t he ave rage and more accu ra t e vo lume o f wa t e r .

The vo lume f l ow r a t e i s c a l cu l a t ed f rom the vo lume and a known

t ime .

5 . The wa t e r f l ow r a t e i s i nc r ea sed by open ing t he p ipe ve s se l and t he

f l ow pa t t e rn o f t he f l u id i s obse rved . Repea t s t ep 2 -4 fo r t r ans i t i on

and t u rbu l en t f l ow .

6 . C lean a l l t he appa ra tu s a f t e r t he expe r imen t i s done .

RESULTS

SAMPLE CALCULATIONS

Time (s) Volume( × 10-5 m3)

Flow Rate( × 10-5 m3/s)

Velocity, V (m/s)

Reynolds No.

Type of Flow

1 3 8.40 2.80 0.1393 2228.8 laminar

2 3 8.00 2.67 0.1328 2124.8 laminar

3 3 9.60 3.20 0.1592 2547.2 transition

4 3 9.40 3.13 0.1557 2491.2 transition

5 3 13.0 4.33 0.2153 3444.8 transition

6 3 12.4 4.13 0.2054 3286.4 transition

7 3 18.0 6.00 0.2984 4774.4 turbulent

8 3 17.2 5.73 0.2850 4560.0 turbulent

9 3 16.8 5.60 0.2785 4456.0 turbulent

Data Given:

Times = 3 sec

Density of water, ρ = 1000 kg/m³

Viscosity, μ = 10.00 x 10-4 Ns/m²

Diameter of tube, d = 16 x 10 ³ mˉ

Length, l = 0.103 m

Area of cross passage, a = πd²/4

= π (16 x 10ˉ0³) / 4

= 2.0106 x 10ˉ4 m²

From experiment:

Laminar Flow:

Volume flow rate = volume/ time

= 8.4 x 10-5 m3 / 3s

= 2.8 x 10-5 m3/s

Velocity, v = (m / ρa) = volume flow rate / area

= 2.8 x 10-5 m3/s ÷ 2.0106x 10-4 m2

= 0.1393 m/s

Reynolds number, Re = ρvd / μ

= (1000 kgm-3 x 0.1393 m/s x 16 x 10-3 m) ÷ 10.00 x 10-4Ns/m2

= 2228.8

* For laminar flow Re should be less than 2300.

Transition Flow:

Volume flow rate = volume/ time

= 9.6 x 10-5 m3 ÷ 3s

= 3.2 x 10-5 m3/s

Velocity, v = (m / ρa) = volume flow rate / x area

= 3.2 x 10-5 m3/s ÷ 2.0106 x 10-4m

= 0.1592 m/s

Reynolds number, Re = ρvd / μ

= (1000 kgm-3 x 0.1592 m/s x 16x 10-3m) ÷ 10.00 ˉ4 Ns/m²

= 2547.2

*For transition flow Re should be in between 2300 and 4000

Turbulent Flow:

Volume flow rate = volume/ time

= 16.8 x 10-5 m3 ÷ 10s

= 5.60 x 10-5 m3/s

Velocity, v = (m / ρa) = volume flow rate / area

= 5.60 x 10-5 m3/s ÷ 2.0106 x 10-4m2

= 0.2785 m/s

Reynolds number, Re = ρvd / μ

= (1000kgm-3x 0.2785 m/s x 0.016m) ÷ 10.00 x 10 4ˉ Ns/m²

= 4456.0

*For turbulent flow Re should be more than 4000

DISCUSSION

I t i s nece s sa ry t o know the d i f f e r ences be tween l amina r , t u rbu l en t

and t r ans i t i on f l ow be fo re one i s abou t t o conduc t t h i s expe r imen t . As fo r

l amina r f l ow , i t i s de f i ned a s a h igh ly o rde red f l u id mo t ion w i th smoo th

s t r e aml ine s . Tu rbu l en t f l ow i s much d i f f e r en t w i th l amina r , a s i t i s a

h igh ly d i so rde red f l u id mo t ion cha rac t e r i z ed by ve loc i t y and f l uc tua t i ons

and edd i e s , whe rea s t r ans i t i on f l ow i s known a s a f l ow tha t con t a in s bo th

l amina r and t u rbu l en t r eg ions .

Based on Reyno lds appa ra tu s expe r imen t , l amina r f l ow i s ob t a ined

when a s i ng l e o rde red l i ne i s s een a f t e r a t h in f i l amen t o f dye i s i n j e c t ed

i n to t he t r anspa ren t g l a s s t ube . The re i s no t much d i spe r s i on o f dye can be

obse rved t h roughou t t he f l owing f l u id . Neve r the l e s s , t he c a se i s no t t he

s ame wi th t u rbu l en t f l ow , a s t he r e i s obv ious d i spe r s i on o f dye a long t he

g l a s s t ube , whe reby t he l i ne s o f dye b r eaks i n to myr i ad en t ang l ed t h r eads

o f dye .

Th roughou t t he expe r imen t , we obse rved t ha t t he r ed dye l i ne s t a r t s

f l owing i n a s t r a i gh t o rde red l i ne t h rough t he g l a s s t ube , and a s t he

ve loc i t y i nc r ea se s a f t e r some t ime , t he o rde red s t r e aml ine s i s s een t o

beg in t o d i spe r se a t abou t t he m idd l e o f t he s t r e aml ine s , bu t s t i l l r ema in

t he s t r a i gh t l i ne a t t he e a r l i e r pa r t . Nex t , t he d i spe r s i on s t a r t ed t o

i nc r ea se , i nd i ca t i ng t he t u rbu l en t f l ow . These obse rva t i ons a r e conc luded

a s t he s t r e aml ine s i s unde rgo ing a change o f t ype o f f l ow , wh ich i s f r om

l amina r f l ow , t r ans i t i on f l ow to t u rbu l en t f l ow .

The re a r e a f ew ca r e l e s s m i s t ake s t ha t have been done du r ing t h i s

expe r imen t . Mos t o f a l l , t he a ccu racy o f co l l e c t i ng t he f l u id f l owing ou t

o f t he t ube w i th in 3 s econds i s a b i t i naccu ra t e . The one who co l l e c t t he

f l u id m igh t no t beg in r i gh t when t he pe r son mon i to r i ng t he s t opwa tch

s t a r t ed t i ck ing on i t , and he / she migh t a l so no t s t op co l l e c t i ng exac t l y

a f t e r t he t h i rd s econd . The re fo re , t he va lue s c a l cu l a t ed i n r e su l t s s ec t i on

migh t no t be exac t l y 100% co r r ec t .

CONCLUSION

As a conc lu s ion , a s wa t e r f l ow r a t e i s i nc r ea s ing , t he Reyno lds

number w i l l au toma t i ca l l y i nc r ea se a s we l l , and t he r ed dye l i ne change

f rom s t r a igh t l i ne t o sw i r l i ng s t r e aml ine s . L ikewi se , i t i s p roven t ha t

Reyno lds number i s d imens ion l e s s , s i nce no un i t i s r ep re sen t i ng t he va lue

o f Reyno lds number . Lamina r f l ow i s ob t a ined i f t he Reyno lds number i s

l e s s t han 2300 ; meanwhi l e t he Reyno lds number fo r t u rbu l en t f l ow i s more

t han 4000 . The Reyno lds number fo r t r ans i t i on f l ow i s i n be tween 2300

un t i l 4000 .

RECOMMENDATIONS

The re a r e some r ecommenda t i ons t o make su re t h i s expe r imen t wou ld

a t t a i n more accu ra t e and p r ec i s e r e su l t s i n t he fu tu r e :

Check whe the r t he wa t e r i n t he t ube f l ows i n a co r r ec t way and we

shou ld a l so make su re t ha t t he f l ow i s s t ab l e be fo re measu r ing t he

f l ow r a t e by mon i to r i ng t he t ime t aken fo r co l l e c t i ng an amoun t o f

wa t e r i n t he vo lume t r i c measu r ing t ank .

Befo re i n j ec t i ng t he dye i n to t he f l u id , we shou ld make su re t he dye

i s no t t oo much and no t t oo i n su f f i c i en t . I t w i l l be ha rd t o s t ab l e t he

f l u id t o ge t a l amina r f l ow .

The expe r imen t shou ld be r epea t ed tw ice t o ge t be t t e r r e su l t .

The pe r son co l l e c t i ng t he wa t e r shou ld synch ron i ze we l l w i th t he

t ime keepe r .

REFERENCES

Flu id Mechan i c s by Dr . Andrew S l e igh ( J . F r anz in i /E . F innemore ) ,

McGraw Hi l l .

F . M. Whi t e , F lu id Mechan i c s (Mc-Graw Hi l l , I nc . , New York ,

1994 ) .

J . Baggett and L . Trefethen, “Low-dimensional models of

subcr i t ica l t rans i t ion to turbulence,”Phys. F lu ids 9 , 1043

(1997) .

www.pipef low.co.uk

APPENDICES