FLOW OF FLUID

SEM III
PHARMACEUTICAL ENGINEERING
FLOW OF FLUID ( REYNOLD'S NUMBER , BERNOULLI'S EQUATION , ORIFICE METER )

1. FLOW OF FLUID BY PROF. TAUFIK MULLA ASSISTANT PROFESSOR DEPARTMENT OF PHARMACEUTICS SPBC COLLEGE OF PHARMACY

2. Matter – 3 types Solid Liquid Gas If we apply pressure on solid material – it move from one place to another place but do not change its shape. But if we apply pressure on liquid / gas – it move from one place to another place and shape of material can be changed. Pressure means – shear stress

3. What is Fluid ???? a substance that has no fixed shape like a gas or a liquid. a fluid is a substance that continually deforms (change) under an applied shear stress (force tending to cause change shape e.g. chewing food between teeth) , or external force. Fluids are a phase of matter and include liquids, gases and plasmas Properties of Fluid - Viscosity Surface tension Density

4. Viscosity Viscosity is a measure of a fluid’s resistance to flow. It describes the internal friction of a moving fluid. A fluid with large viscosity resists motion because its molecular makeup gives it a lot of internal friction. A fluid with low viscosity flows easily because its molecular makeup results in very little friction when it is in motion.

5. Surface Tension Surface tension is a contractive tendency of the surface of a fluid that allows it to resist an external force.“ Surface tension is the tendency of the surface of a liquid to behave like a stretched elastic membrane. Fluid tends to attend the minimum surface area as possible. Why? The reason behind this is that while a molecule inside the fluid bulk is pulled in each and every direction by the adjacent molecules But at the surface of the fluid , the case is different. the adhesive forces causes downward pull on the molecule due to coherent. So the molecule on the surface tends to move down.

6. Density Density depends on the mass of an individual molecule and the number of such molecules that occupy a unit of volume. For liquids, density depends primarily on the particular liquid and, to a much smaller extent, on its temperature. For gas, density depends on the molecular weight, absolute pressure, and absolute temperature. The  density  of a fluid is defined as its mass per unit volume and indicates its resistance to an accelerating force.

7. FLOW OF FLUID Fluid flow defined as flow of substance that do not permanently resist distortion (changes of state of natural). Fluid is a substance which continuously flow under applied shear stress. (pressure) E.g. liquid , gases Flow fluid we can observe by – Handling of liquid – transportation of solvent, solution , suspension is simple, cheap and problematic as compared to solid material in industry

8. Fluid can be study by fluid statics and fluid dynamics. Fluid statics – study behavior of liquid when it in resting Fluid dynamics – study behavior of liquid when its in motion Flow of fluid involved in different area of pharmaceutical industry like :- Passing of reactant (liquid / gas) in reactant system Transferring of broth/ culture media in fermenter Packaging of liquid dosage form in suitable container Transferring of sterile water for preparation of parenteral. Mixing of solid and liquid for suspension.

9. FLUID STATICS Fluid static's deals with the fluids at rest in equilibrium and Behavior of liquid at rest. Nature of pressure it exerts and the variation of pressure at different layers. Pressure differences between layers of liquids. 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.

10. Force acting on the liquid At point 1 = Force on the surface + Force excreted by the liquid Above point 1. Application of fluid static – Used in manometer Pressure difference is measured in term of difference in height of column

11. manometer Device used for measurement of pressure difference. 3 types of manometer Simple Differential Inclined manometer also classified as : Simple manometer Piezometer U-tube manometer single column manometer Vertical single column Inclined single column Differential manometer U – tube differential manometer Inverted U – tube differential manometer

12. Simple manometer Most commonly used manometer in various industry It’s a U shape glass tube filled with liquid (A) of density ρ A kilogram / meter cube. Above liquid A, arms are filled with liquid B of density ρ B kilogram / meter cube. Liquid A and B are immiscible. If we apply two different pressure P1 and P2 on two arms. Meniscus of liquid A will be higher in one arm than other. Pressure at point 1 is P 1 pascal and pressure at point 5 is P2 pascal. By the principle of fluid statics, pressure at point 2 will be as follow: Pressure at point 2 = P1 +( m+R ) ρ Bg ------ 1 ( m+R ) = distance from point 3 to 4 and 4 to 5. Arms

13. Point 2 and 3 are at same level so, the pressure at point 3 will be as follows : Pressure at point 3 = P 1 + ( m+R ) ρ Bg - ---------- 2 Pressure at point 4 (from right side) = P 2 + gm ρ B ---------- 3 Pressure at point 4 (from left side) = P 1 + ρ B ( m+R ) – ρ ARg ------------ 4 Equation 3 to 4 represent the pressure at point 4 only. P 1 + ρ B ( m+R ) – ρ ARg = P 2 + gm ρ B P 1 – P 2 = gm ρ B - ρ B ( m+R ) + ρ ARg ‘ ∆P = m ρ Bg – m ρ Bg – R ρ Bg + RpAg ∆P = R( pA – pB )g

14. Conclusion from equation – Easy to measure R value (meter) The value of ∆P pascal is independent of value of m and also the dimension of the U tube. Application – Measuring the consumption of gases in chemical reaction. Used in conjunction with flow meter for the measurement of flow of fluid. Venturi meter and orifice meter used for measurement of pressure head using manometer.

15. Differential manometer This manometer used to find difference of two pressure at two different point / pipe. Rarely occasionally this manometer is used. Very sensitive and mainly used to measure small pressure difference. Also known as two fluid U-tube manometer. Contain two immiscible liquid A and B having same density. At both limbs it having a chamber. meniscus of liquid in chamber does not change with change in R value. LIMBS

16. By using principle of Simple manometer equation will be like : ∆P = P 1 – P 2 = R (Pc – P A )g Equation indicate small difference in (Pc – P A ), larger reading of R on manometer for given ∆P. Micromanometer based on liquid column principle. It measure reading with high precision and accurately and its very sensitive. Doesn’t require any calibration as it’s a free from error.

17. Inclined manometer Many applications require accurate measurement of low pressure such as drafts and very low differentials, primarily in air and gas installations. In these applications the manometer is arranged with the indicating tube inclined. This enables the measurement of small pressure changes with increased accuracy. P1 –P2 = g R ( ρ A - ρ B) sin α

18. Fluid dynamics Deals with the study of fluid in motion. Study of flow property of fluid is important for those who work in pharmaceutical , chemical industry. Mfg. of syrup , gel , ointment , cream and paste or liquid preparation. This fluid change their behavior when exposed to different stress condition like : Mfg. of dosage form – mixing , flowing through pipes and filled in container Handling of drug for administration – pouring of liquid , extrusion of ointment That’s why flow property is a important quality control parameter for mfg. of dosage form. The flow of fluid through a pipe can be viscous and it can be determined by Reynolds number. Reynolds number have no unit. mixing Flow through pipe Filled in container

19. TYPES OF FLOW LAMINAR FLOW Fluid particle move in a straight layer. No exchange of fluid particle from one layer to another. Also called as streamline flow. It occur when small pipes and low flow rate involved. Shear stress depend upon viscosity of fluid. Avg. velocity = 0.5 Vmax

20. TYPES OF FLOW TURBULENT FLOW When velocity increase, fluid particles move in random manner. This type of flow called as turbulent flow. In this complete mixing of fluid particles are observed. This flow happen generally at high flow rate with larger pipe. Avg. velocity = 0.8 Vmax

21. TYPES OF FLOW TRANSITIONAL FLOW It’s a mixture of laminar and turbulent flow. Turbulence observe at the center of the pipe. Laminar flow observe at near the edge.

22. REYNOLD’S NUMBER Its a dimensionless number. Turbulent flow and laminar flow is determined by Reynold’s number. It’s a ratio of inertial force to viscous force. Re = inertial force / viscous force Inertial force = mass X acceleration of liquid flowing Viscous force = shear stress X area Formula for Reynold’s number as follows : Re = Dup / n Where, D = diameter of pipe (m) u = velocity of flow (m/s) p = density of fluid (kg/m3) n = viscosity of fluid

23. Reynolds experiment Glass tube connect with reservoir of water. Rate of water flow through tube increase or decrease by valve. Reservoir of colored solution connected at one end of glass tube with nozzle. Colored solution entered in glass tube as fine stream. By performing this experiment we can conclude below details : GLASS TUBE

24. When velocity of water is low, water will move in line parallel to tube. i.e. laminar flow If velocity of water is high, it move in wave form. i.e. transitional flow. If velocity of water is more, it do not move in straight line. i.e. turbulent flow. The flow is – Laminar flow = Re < 2000 Transitional flow = 2000 < Re < 4000 Turbulent flow = Re > 4000

25. Application – Reynold’s number is used To predict nature of flow To study flow of incompressible fluid in closed pipe. Heat transfer in liquid also depend on flow. To study sedimentation rate of suspension.

26. Mathematical problem When liquid is flow through a pipe having diameter 200mm. Tube with mean velocity of oil 2m/sec. if density of liquid is 910 kg/m3. and viscosity is 0.35 N.S/m2. then what will be the type of the flow. Re = Dup / n D = 200 mm = 0.2 . U = 2 . P = 910 / 0.35 = 1040.

27. BERNOULLI’S THEOREM / EQUATION Principle of conservation of energy is applied to the flow of fluid , resulting equation called as Bernoulli’s equation. This theorem state that total energy (pressure energy, kinetic energy and potential energy) per unit mass in steady state are constant. It based on conversation of energy when applied to flow of fluid. It said that, in steady state – ideal flow of incompressible fluid – total energy per unit mass – also include pressure energy , kinetic energy and datum energy at any point of fluid is CONSTANT.

28. At point A , 1kg of liquid is assumed to enter in pipe. At that point liquid experience pressure energy , kinetic energy and datum energy (potential). It represented as – pressure energy = P A / gp A P A = pressure in pascal at point A g = acceleration due to gravity m/s2 p A = density of liquid kg/m3

29. Potential energy = it possessed by body by behavior of its configuration or position. Point A is placed at height X A meter above datum plane. potential energy = X A Kinetic energy = it possessed by body by behavior of its motion. consider u A as velocity of liquid m/s at point A. kinetic energy = u A2 / 2g At point A total energy as follows : total energy = pressure energy + potential energy + kinetic energy As per Bernoulli’s theorem , total energy at point A is constant. The equation will be : = CONSTANT

30. Once the system reaches to steady state, flow become steady at each point in pipe. And the 1kg of liquid leaves at point B. Energy content of 1 kg liquid at point B written as : P B = pressure at point B p B = density at point B kg/m3 X B = height of point B from datum u B = velocity at point B m/s

31. If there is no loss or gain of energy then principle of energy conversation applied at point A & B. Input = Output Theoretically all types of energy involved in fluid flow should be accountable. During transportation of fluid , pump has added some amount of energy is W joule and Some energy converted to heat due to frictional forces so energy loss is F joule. The final equation of energy conservation written as

32. This equation called as Bernoulli’s equation. APPLICATION Measuring flow rate of fluid using head meter like orifice meter , venture meter. Applied in working of centrifugal pump

33. ENERGY LOSS 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  Frictional losses  Losses in the fitting  Enlargement losses  Contraction losses

34. FRICTIONAL LOSS 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 Directly proportional to VELOCITY of fluid (u) Directly proportional to Density of fluid(ρ) Directly proportional to Length of the pipe (L) inversely proportional to diameter of the pipe (D) These relationships are proposed in Fanning equation for calculating friction losses Fanning equation Δ p = 2fu2L ρ / D F = frictional factor For viscous flow pressure drop Hagen – Poiseullie equation = 32 Lu η / D2 (n = viscosity of liquid)

35. 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 Tee fitting Equivalent length = 90 Globe valve equivalent length = 300 Equivalent length of fitting = Equivalent length x internal diameter For globe valve = 300 x 50 = 15 meter That means globe valve is equal to 15 meters straight line, so this length is substituted in fanning equation

36. ENLARGMENT 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 Than u2< u1 For sudden enlargement = Δ H = (u1 – u2 )2 / 2g Δ H = loss of head due to sudden enlargement

37. CONTRACTION LOSS 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 value of diameter this point of minimum cross section is known as vena contracta . the velocity of fluid at smaller cross section will be greater than at larger cross section, u2> u1

38. ORIFICE METER Principle: Orifice meter is a thin plate containing a narrow and sharp aperture When a fluid stream is allowed to pass through a narrow constriction the velocity of the fluid increase compared to up stream This results in decrease in pressure drop and the difference in the pressure may be read from a manometer The velocity of the fluid at thin constriction may be written as U0 =C0 √ 2g ΔH ΔH = difference in height, can be measured by manometer C0 = constant U0 = velocity of fluid at the point of orifice meter

39. Construction; It is consider to be a thin plate containing a sharp aperture through which fluid flows Normally it is placed between long straight pipes For present discussion plate is introduced into pipe and manometer is connected at points A and B Working: Orifice meter is referred as the variable head meter, ie it measure the variation in the pressure across a fixed construction placed in the path of flow

40. When fluid is allowed to pass through the orifice the velocity of the fluid at point B increase, as a result at point A pressure will be increased Difference in the pressure is measured by manometer Bernoulli's equation is applied to point A and point B for experimental conditions √μ02 –μ A2 =C0 √2g Δ H μ0 = velocity of fluid at orifice μA = velocity of fluid at point A C0 = constant If the diameter of the orifice is 1/5 or less of the pipe diameter then μA is neglected so, μ0 = C0 √2g Δ H Applications Velocity at either of the point A and B can be measured Volume of liquid flowing per hour can be determined

41. Venturi meter Principle: Venturi meter consist of two tapered sections in the pipe line with a gradual constriction at its centre. when fluid stream is allowed to pass through the narrow throat the velocity of the fluid increases at the venturi compared to velocity of the upstream. This results in decrease in the pressure head. This resulting decrease in the pressure head is measured directly from the manometer.

42. Disadvantages Expensive Need technical expert Not flexible Occupies more space Advantages Power loss is less Head loss is negligible Applications: It is commonly used for liquids, specially for water. It can also be used for the measurement of gases.