Flow of fluid- Pharmaceutical Engineering

Fluid flow-Mention fluid properties such as viscosity, compressibility and surface tension of fluids.
Hydrostatics (Fluidststics) influencing fluid flow.
Fluid dynamics‐ Bernoulli’s theorem, flow of fluids in pipes, laminar and turbulent flow.
A fluid is a substance that continually deforms (flows) under an applied shear stress.

Fluids are a subset of the phases of matter and include liquids, gases.

Fluid flow may be defined as the flow of substances that do not permanently resist distortion

The subject of fluid flow can be divided into fluid static's and fluid dynamics
FLUID STATICS
Consider a column of liquid with two openings Which are provided at the wall of the vessel at different height

The rate of flow through these openings are different due to the pressure exerted at the different heights are different

Consider a stationary column the pressure P is acting on the surface of the fluid, column is maintained at constant pressure by applying pressure

The force acting below and above the point 1 are evaluated

Substituting the force with pressure x area of cross section in the above equation

1. F L O W O F F L UID BY- SANCHIT DHANKHAR

2. D i s cl a ime r Pr e s e nt a ti o n sli d es a r e p r o v i d ed o n stu d e nt' s r e q u e s t fo r p ur po s e o f qu i c k r e f e r e n c e o n l y , h e n c e i t ca n n o t b e r e p l ac ed w it h st a n da r d stu d y m a t e ri a l o r boo k s th a t a r e m e nti o n ed i n s y ll ab u s o f r e s p e c ti ve su b j e c ts . S tu d e nt s a r e ex p e c t ed t o r e f er st a n da r d boo k s fo r stu d y fo r ex a m in a ti o n .

3. Fl u id f l o w M enti o n f l u i d p ro p e rt i e s su c h a s vis co sity , co mpr essi b ility a nd surf ac e te ns i o n o f f l u ids. H ydr o st a ti c s ( Fl u i ds t s t ic s ) infl u e n c i ng f l u i d f l o w . Fl u id d y na m ic s ‐ Bern o u lli’s the o re m, f l ow o f f l u i ds i n p i p es, l a m i n a r a nd turbulent f l o w .

4. V I S C O S I T Y :-

5. F l o w o f F l u i d s

6. FL U I D FLO W A f lui d i s a s ub st anc e t ha t con t inuall y d ef orm s ( f low s ) und er a n appli ed s h e a r st r e ss . F luid s ar e a s ub s et o f t h e pha s es o f ma tt er an d includ e liquid s , ga s e s . F lui d f lo w ma y b e d ef in ed a s t h e f lo w o f s ub st anc es t ha t d o no t p e rman e n t l y r e s i s t di st or t io n T h e s ubj e c t o f f lui d f lo w ca n b e di v id ed in t o f lui d st a t ic' s an d f lui d d y namic s

7. FL U I D ST A T I C S Ø F lui d st a t ic' s d e al s wi t h t h e f luid s a t r e s t i n e quilibriu m Ø B e ha v io r o f liqui d a t r e s t Ø Na t ur e o f pr e ss ur e i t e x e r t s an d t h e v aria t io n o f pr e ss ur e a t di ffe r e n t la y e r s Pr ess ure d i ff e r e nc e s b e t w ee n l a ye rs of li q ui d s h 2 h 1 Poi n t 2 Poi n t 1

8. C o n s i d e r a c ol u m n o f li qu i d w it h t w o o p e n i ngs Wh i c h a r e p r o v i d e d at t he w a l l o f t he v esse l at d i ff ere nt h e i ght T he r a t e o f f lo w t h r o ugh t h es e o p e n i ngs a r e d i ff ere nt due t o t he p r ess ure e x e rt e d a t the d i ff e r e nt h e i g hts a re d i ff e r e nt C o n s i d e r a s t a tion a ry colu m n t he p ress u r e P i s a c ti ng o n t he s u r f a c e o f t he f l u i d, c ol u m n i s m a i n t a i n e d at c o n s t ant p ress u r e by app l y i ng p ress u r e T he f o r c e a c ti ng b e lo w and ab o ve t he p oi nt 1 a r e e va l ua t e d S u b s tituting the f orce w ith p r ess ure x a re a o f c r o s s se c tio n i n t he ab o ve e qua tio n

9. F orce act i n g on th e li qu i d = At poi n t 1 + F orc e o n t h e su r f a c e F orc e e xcr e t e d b y t h e liq u i d A bov e poi n t 1 Pr e ss u r e a t po i nt 2 x A r e a = (Pr e ss u r e o n th e s u r f ac e ar ea x s u r f ac e ar e a ) P 1 S = P 2 S + v o l u m e x d ens i t y x g = P 2 S + h e i gh t x ar ea x d e n si t y x g Pr e ss u r e a t po i nt 1 x A r ea = (Pr e ss u r e o n th e s u r f ac e ar ea x s u r f ac e ar e a ) + ( mas s x g )

10. P 1 s = P 2 s + vo l u m e x d e n si t y x g = P 2 s + h ei g h t x a r e a x d e n si t y x g P 2 s + h 1 S ρ g P 1 s = S i n c e s u r f ac e a r e a i s s am e P 1 = P s + h 1 ρ g P r ess u re act i n g o n p o i n t 2 ma y be w r i tt e n a s P 2 = P s + h 2 ρ g Di ffe r e nc e i n t h e pr e ss ur e i s - - P 2 - P 1 = g ( P s + h 2 ρ ) – ( P s + h 1 ρ ) g ∆ P = ( P s + h 2 ρ – P s ∆P = ∆ h ρ g - h 1 ρ ) g [ F= Volu me. ρ g ]

11. F L D U I Y D NA M I C S Ø F luid d y n a m ics d e a ls w ith the s tu d y of f lui d s in m otion Ø T his kno w l e dg e is i m p ort a nt f or li q ui d s , g e l s , oint me nts w hich w ill ch a n g e th e ir f low b e h a v ior w h e n e x p o se d to d i ff e r e nt s tr es s con d itions M I X I NG F L O W T HR OU G H P I PE S F I LLE D I N C O NTA I N E R

12. I m p or t a n c e Identi f ica t ion o f ty pe o f f lo w is i mpo rt a nt i n Ma nuf ac ture o f d o s a ge f o rms ü Ha nd li ng o f drugs f o r adm i n istr a t ion The f lo w o f f l u i d thr o ugh a p i pe ca n be vis co us o r turbu lent a nd it ca n be dete rm i n e d by Rey nolds numb er Rey nolds numb er h a v e no un it

13. R e yn o l d s Ex p e r i m e n t Gla ss tube is co nn e c te d to reserv oi r o f wa ter, r a te o f f lo w o f wa ter is a d juste d by a v al ve , A reserv oi r o f colo re d s ol ut ion is co nn e c te d to o ne e nd o f the gla ss tube wi th h el p o f n o zz le . Colo re d s ol ut ion is intr o du c e d i nto the n o zz l e a s f i ne stre a m thr o ugh jet tub e .

14. w a t er v al v e C olor ed li qu i d L AM I N A R O R V I SC OU S F L O W TUR B U L E NT F L O W

15. TY P E S O F FLO W è Lamina r f lo w i s o n e i n w h i c h t h e fl u i d p a r t i c le s mov e i n l ay e rs o r l am i n a r w i t h o n e l ay e r sli d i n g w i t h ot h e r è T h e re i s n o e xc h a n ge o f fl u i d p a r t i c le s f r o m o n e l ay e r t o ot h e r è A v g v el oc i t y è R e < 200 = 0. 5 V m a x è W h e n v el oc i t y o f t h e wat e r i s i n c r e a se d t h e t h r e a d o f t h e co l o r e d wat e r d is a pp e a rs a n d ma s s o f t h e wat e r g e t s un if o r m l y co l o r e d è T h e re i s com p le t e m i x i n g o f t h e s o l u t i o n a n d t h e fl o w o f t h e fl u i d i s ca lle d a s t urbul e n t f lo w è A v g v el oc i t y = 0. 8 V m a x è R e > 4 00 T h e v e l oc i t y a t w h i ch th e f l u i d chang es f r o m l a mi na r f l ow t o tu r bu l e n t f l ow tha t v e l oc i t y i s ca ll ed a s c r i t ic a l v eloci ty

16. R EY N OL D S NU MBE R I n Re y n o l ds e x p e r i m e n t t h e fl o w co n d i t i o n s a re a ffe ct e d by Ø Di am e t e r o f p i pe Ø A v e r a ge v el oc i t y Ø De n si t y o f li q u i d Ø V is co si t y o f t h e fl u i d T h i s f o u r f acto rs a re com b i n e d i n o n e wa y a s R e yn ol ds nu m b e r R e= Ø I n e r t ia l f orc es a re d u e t o ma s s a n d t h e v el oc i t y o f t h e fl u i d p a r t i c le s t r y i n g t o d iff u s e t h e fl u i d p a r t i c le s Ø v i s cou s f orc e i f t h e f r i ct i o n a l f o r c e d u e t o t h e v is co si t y o f t h e fl u i d w h i c h mak e t h e mot i o n o f t h e fl u i d i n p a r a llel . D u ρ η I N ER T I AL F O R C E S = ------------------------------ V IS C OU S F O R C E S

17. ¬ A t lo w ve loci ties the i n ert ia l f o r c es a re less w h e n compa re d to the fr ic t ion a l f o r c es ¬ Re su lti ng f lo w wil l be vis co us i n n a ture ¬ Oth er h a nd w h e n i n ert ia l f o r c es a re pre d o m i n a nt the f l u i d la yers bre a k up due to the i n c re a se i n ve loci ty h e n c e turbu lent f lo w t a kes plac e . ¬ If R e < 200 the f lo w I s aid to be la m i n a r ¬ If R e > 400 the f lo w is s aid to be turbu lent ¬ If R e lies b et w ee n 200 to 400 the f lo w c h a nge b et w ee n la m i n a r to turbu lent

18. APP L I C A T I O NS Ø R e yn ol ds nu m b e r i s u se d t o p re d i c t t he na t u r e o f t he f lo w Ø S to c k s l aw e qua tio n i s m o d i f i e d t o i n c l ude R e yn ol ds nu m b e r t o s t udy t he r a t e o f se d i me n t a tio n i n s u s p e n s io n Wh e n v e lo c it y i s p lott e d aga i n s t t he d i s t an c e f r o m t he w a l l f ollo w i ng c o n c l u s io ns c an be d r a w n Ø T he f lo w o f f l u i d i n t he m i dd l e o f t he p i pe i s f a s t e r t h e n t he f l u i d n e ar t o t he w a l l Ø A t t he a c t ual s u r f a c e o f t he p i pe – w a l l t he v e lo c it y o f t he f l u i d i s z er o

19. Pi p e w al l R e la t i v e d is t a n c e f ro m th e c e nt er o f th e p i p e U / U m a x T u r bu l e n t f lo w V isco u s f lo w

20. BE RN O U LL I 'S T H EO R E M W h e n t h e pr i n c i p a l s o f t h e l a w o f e n e rgy i s a pp lie d t o t h e fl o w o f t h e fl u i ds t h e r es u l t i n g e q u at i o n i s a B e r n o u lli ' s t h e o r e m Ø C o n si d e r a p u m p wo r k i n g un d e r is ot h e r ma l co n d i t i o n s b e tw ee n p o i n t s A a n d B Ø B e r n o u lli ' s t h e o r e m s tat e m e n t , " I n a s t e a dy s tat e t h e tota l e n e rgy p e r un i t ma s s con s i st s o f pr e ss ur e, k in e t i c an d po t e n t ia l e n e rgi es ar e con st an t " K i n e t i c e n e r g y = u 2 / 2 g P u m p Pr e ss u r e e n e r g y = P a / ρ A g F ric t io n e n e r g y = F

21. Ø At p oi n t a o n e k ilo g ra m o f li qu i d i s ass u m ed t o b e e nt e ri n g a t p oi n t a , Pr e ss u r e e n e r g y = P a /g ρ A Wh e r e P a = Pr e ss u r e a t p oi n t a g = A cc e l e ra t io n du e t o g ra v i t y ρ A = D e n si t y o f th e li qu i d Po t e nt ia l e n e r g y o f a b o d y i s d ef i n ed a s th e e n e r g y p oss e ss ed b y th e b o d y b y th e v ir tu e o f i t s p osi t io n Po t e nt ia l e n e r g y = X A K i n e t i c e n e r g y o f a b o d y i s d ef i n ed a s th e e n e r g y p oss e ss ed b y th e b o d y b y v ir tu e o f i t s mo t io n , k i n e t i c e n e r g y = U A / 2 g 2 T o t a l e n e r g y a t p oi n t A = Pr e ss u r e e n e r g y + Po t e nt ia l e n e r g y + K . E T o t a l e n e r g y a t p oi n t A = P a V + X A + U A / 2 g 2

22. A ccor d i n g t o th e Be r n o u lli ' s th e or em th e t o t a l e n e r g y a t p oi n t A i s co n s t a n t T o t a l e n e r g y a t p oi n t A = P A V +X A + ( U A / 2 g ) = C o n s t a n t 2 Af t er th e s y s t em r e ac h es th e s t e a d y s t a t e, w h e n e v er o n e k ilo g ra m o f li qu i d e nt e r s a t p oi n t A, a n o th er o n e k ilo g ra m o f li qu i d l e a v es a t p oi n t B T o t a l e n e r g y a t p oi n t B = P B V + X B + U B / 2 g 2 P A V + X A + ( U A 2 / 2 g ) + E n e r g y a dd ed b y th e pu m p = P B V + X B + ( U B 2 / 2 g ) T h e or e t icall y al l k i nd s o f th e e n e r g i es i nv ol v ed i n f l u i d f lo w s h o u l d b e acco unt e d , pu m p h a s a dd ed c e r t ai n amo un t o f e n e r g y

23. D u r i n g t h e t r a n s p o rt s om e e n e rgy i s co n v e r t e d t o h e a t d u e t o f r i ct i o n a l Fo r c e s E n e rg y lo s s du e t o f ric t io n i n t h e lin e = F E n e rg y add ed b y pum p = W P a / ρ A + X A + U A 2 / 2 g – F + W = P B / ρ B + X B + U B / 2 g 2 T his e q u a tion is c a ll e d a s Be rnoulli's e q u a tion

24. E N E RGY LOS S A cc o r d i ng t o t he l aw o f c o nv ers a tio n o f e n er gy, e n er gy ba l an c e have t o be p r o p er l y c a l c u l a t e d f l u i ds e xp er i e n c e s e n er gy lo sse s i n se v er al w ays w h il e f lo w i ng t h r o ugh p i p es , t h e y a r e Ø Fr i c tio nal lo sse s Ø L o sse s i n t he f itti ng Ø E n l a r g eme nt lo sse s Ø C o n t r a c tio n lo sse s

25. A pplica t io n o f B E R NO U LL I ' S T H EO R E M Ø U s ed i n th e m e a sur e m e n t o f r a t e o f f lui d f l o w usin g f l o wm e t e r s Ø It app li ed i n th e w o rkin g o f th e c e ntri f u ga l p u m p , i n thi s kin e ti c e n e r g y i s co n ve rt ed i n t o p r e ssur e.

26. THANK-YOU