Chapt 1 flow of fluid lect 1st 2 nd.pptx

pharmaceutical engineering
III rd sem chapt1 ppt

1. FLOW OF FLUIDS Presented by: Arti J. Darode Asst . Professor (Pharmaceutics Dept ) Faculty of Nagpur College of Pharmacy, Nagpur

2. 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 FLOW

3. FLUID STATICS Fluid static's deals with the fluids at rest in equilibrium Behavior of liquid at rest Nature of pressure it exerts and the variation of pressure at different layers Pressure differences between layers of liquids h1 h2 P o i n t 1 P o i n t 2

4. 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 opening s are different due to the pressure exerted at the different height Consider a stationary column the pressure p s 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 F o r c e acti n g on the li q uid A t point 1 = Force on the surface F o r c e e x c r e t e d b y the li q uid A b o v e point 1 P ress ure a t point 1 x A re a = Pressure on the surface x area + m a ss x a ccele r a tio n +

5. P 1 s = P 2 s + volume x density x acceleration P 1 s = = P 2 s + height x area x density x acceleration P 2 s + h 1 S ρ g Since surface area is same P 1 = P s + h 1 ρ g Pressure acting on point 2 may be written as P 2 = P s + h 1 ρ g Difference in the pressure is obtained by P 2 - P 1 = g (P s + h 2 ρ ) – ( P s + h 1 ρ) g ∆P = ( P s + h 2 ρ – P s - h 1 ρ ) g ∆P = ∆ h ρ g [ F = V o l u m e. ρ . g]

6. Fluid dynamics Fluid dynamics deals with the study of fluids in motion This knowledge is important for liquids, gels, ointments which will change their flow behavior when exposed to different stress conditions MIXING FLOW THROUGH PIPES FILLED IN CONTAI N ER

7. Types of flow Ide n tifi c a ti o n o f type o f fl o w is i m p o r t a n t in Manufacture of dosage forms Handling of drugs for administration The flow of fluid through a closed channel can be viscous or turbulent and it can be observed by Reynolds experiment Glass tube is connected to reservoir of water, rate of flow of water is adjusted by a valve, a reservoir of colored solution is connected to one end of the glass tube with help of nozzle. Colored solution is introduced into the nozzle as fine stream

8. w a t e r v a l v e Col o r e d liquid LAMINAR OR VISCOUS FLOW TUR B ULENT FLOW Colored water

9. Laminar flow is one in which the fluid particles move in layers or laminar with one layer sliding with other. There is no exchange of fluid particles from one layer to other When velocity of the water is increased the thread of the colored water disappears and mass of the water gets uniformly colored, indicates complete mixing of the solution and the flow of the fluid is called as turbulent flow The velocity at which the fluid changes from laminar flow to turbulent flow that velocity is called as critical velocity

10. Inertial forces are due to mass and the velocity of the fluid particles trying to diffuse the fluid particles Viscous force if the frictional force due to the viscosity of the fluid which make the motion of the fluid in parallel . Reynolds number In Reynolds experiment the flow conditions are affected by Diameter of pipe A v e r a g e v el o cit y Density of liquid Viscosity of the fluid This four factors are combined in one way as Reynolds number Re ynolds n u m b e r is o b t a in e d b y the f oll o w i n g e q u a t io n D u ρ Inertial forces = ------------------------------ = η Vis c ous f o r ce s Mass X Acceleration of liquid flowing ---------------------------------------------------------- Shear stress x area

11. A t low v el o c i t i e s t h e i n ertia l f o r ce s a r e less whe n c o m p a r e d t o the frictional forces Resulting flow will be viscous in nature Other hand when inertial forces are predominant the fluid layers break up due to the increase in velocity hence turbulent flow takes place. If Re < 2000 the flow I said to be laminar If Re > 4000 the flow is said to be turbulent If Re lies between 2000 to 4000 the flow change between laminar to turbulent

12. Types of flow The velocity at which the fluid changes from laminar flow to turbulent flow that velocity is called as critical velocity è A v g v eloc i ty è Re < 2000 = 0.5 V m a x è Laminar flow is one in which the fluid particles move in layers or laminar with one layer sliding with other è Turbulent flow is When velocity of the water is increased the thread of the colored water disappears and mass of the water gets uniformly colored è There is complete mixing è There is no exchange of fluid particles from one layer to other of the solution and the flow of the fluid is cal l ed as turbulent flow è Avg velocity = 0.8 V max è Re > 4 000

13. Ap p li ca t i o n s Reynolds number is used to predict the nature of the flow S t o k e ’ s l a w equ a ti o n is modified t o include R e y no l d s number to study the rate of sedimentation in suspension When velocity is plotted against the distance from the wall following conclusions can be drawn  The flow of fluid in the middle of the pipe is faster then the fluid near to the wall  The velocity of fluid approaches zero as the pipe wall is approached  At the actual surface of the pipe wall the velocity of the fluid is zero

14. Pi p e w all Relative distance from the center of the pipe U / U max The velocity of the fluid is zero at the wall surface there should be some layer in viscous flow near the pipe wall which acts as stagnant layer if the flow is turbulent at the center and viscous at the surface a buffer layer exist, this buffer layer changes between the viscous to turbulent flow V isc o us fl o w T urbu l e n t f l o w

15. Bernoulli's theorem P u mp P ress ure e ne r gy = P a / ρ A g A Friction energy = F Ø When the principals of the law of energy is applied to the flow of the fluids the resulting equation is called Bernoulli's theorem Consider a pump working under isothermal conditions between points A and B Ø Bernoulli's theorem states that in a steady state the total energy per unit mass consists of pressure, kinetic and potential energies are constant B Kinetic en e rgy = u 2 / 2g

16. At point a one kilogram of liquid is assumed to be entering at this point, pressure energy at joule can be written as Pressure energy = P a /g ρ A Where P a = Pressure at point a g = Acceleration due to gravity ρ A = D ensity of t h e liquid Potential energy of a body is defined as the energy possessed by the body by the virtue of its position Potential energy = X A Kinetic energy of a body is defined as the energy possessed by the body by virtue of its motion, kinetic energy = U A / 2g 2 T o t a l e n e r g y a t p o i n t A = P r ess u r e e n e r g y + P o t e n t i a l e n e r gy + Kinetic energy

17. A Total energy at point A = P a /g ρ A + X A + U 2 / 2g According to the Bernoulli's theorem the total energy at point A is constant Total energy at point A = P a /g ρ A +X A + U 2 / 2g = Constant Energy added by the pump = + wJ A After the system reaches the steady state, whenever one kilogram of liquid enters at point A, another one kilogram of liquid leaves at point B T o t a l ene r g y a t poi n t B = P B / g ρ B + X B + U 2 / 2g B INPUT = OUT PUT A P a / g ρ A + X A + U 2 / 2g = P B / g ρ B + X B + U B 2 / 2g Theoretically all ki n ds of the energies involved in fluid flow should be accounted, pump has added certain amount of energy

18. nces During the transport some energy is converted to heat due to frictional Forces Loss of energy due to friction in the line = - F J A P a / g ρ A + X A + U 2 / 2g – F + W = P B / g ρ B + X B + U B 2 / 2g Bernou l l i's equation Applications Used in the measurement of rate of fluid flow It applied in the working of the centrifugal pump, in this kinetic energy is converted in to pressure. Ø Used in the measurement of rate of fluid flow using flowmeters Ø It applied in the working of the centrifugal pump, in this kinetic energy is converted in to pressure .

19. nces 22 Energy losses Facu l t y of Phar m acy © Rama i ah Uni v ers i t y of A pp li ed Sc i e According to the law of conversation of energy , energy balance have to be properly calculated Fluids experiences energy losses in several ways while flowing through pipes, they are Ø Frictional losses Ø Losses in the fitting Ø Enlargement losses Ø Contraction losses

20. During flow of fluids frictional forces causes a loss in pressure. Type of fluid flow also influences the losses. In general pressure drop will be PR E SSU R E D R O P α V E L O C IT Y (u) α Density of fluid( ρ) α Length of the pipe (L) α 1 / diameter of the pipe (D) These relationships are proposed in Fanning equation for calculating friction losses Fanning equation ∆p = 2 f u 2 Lρ / D F = frictional factor For viscous flow pressure drop Hagen –Poiseullie equation = 32 Luη / D 2 F Frictional losses rmac i s t.blogs p ot. c om

21. LastbenchPharmacist.blogspot.com Losses in fitting Fanning equation is applicable for the losses in straight pipe. When fitting are introduced into a straight pipe, They cause disturbance in the flow, Which result in the additional loss of energy losses in fitting may be due to Change in direction Change in the type of fittings Equivalent fitting = Equivalent fitting x internal diameter F or glob e v a l v e = 300 x 50 = 15 m e t e r T e e fitti n g Equivalent length = 90 Globe valve equivalent length = 300 That means globe valve is equal to 15 meters straight line, so this len g th is s u b s tit u t e d in f anni n g eq u a ti o n F L a a c s u l t t b y o e f n P c h a h r m P a h c a y rmac i s t.blogs p ot. c om

22. LastbenchPharmacist.blogspot.com Enlargement loss If the cross section of the pipe enlarges gradually, the fluid adapts itself to the changed section with out any disturbance. So no loss of energy If the cross section of the pipe changes suddenly then loss in energy is observed due to eddies. These are greater at this point than straight line pipe Then u 2 < u 1 F or s u d d e n e n l a r g eme n t = ∆ H = u 1 – u 2 / 2g o H = loss of head due to sudden enlargement F L a a c s u l t t b y o e f n P h c a h r m P a h c a y rmac i s t.blogs p ot. c om

23. Contraction losses If the cross section of the pipe is reduced suddenly the fluid flow is disturbed, the diameter of the fluid stream is less than the initial column this point is known as vena contracta

24. Summary A fluid is a substance that continually deforms (flows) under an applied shear stress Fluid static's deals with the fluids at rest in equilibrium Fluid dynamics deals with the study of fluids in motion The flow of fluid through a closed channel can be viscous or turbulent and it can be observed by Reynolds experiment Bernoulli's theorem states that in a steady state the total energy per unit mass consists of pressure, kinetic and potential energies are constant According to the law of conversation of energy, energy balance have to be properly calculated