001 FLUID_MECHANICS.pptx basic of fluid mechnanics

basic of fluide mechnanics

1. Fluid Mechanics Fundamental Concepts & Applications in Thermal power plants Presented By: Dr. Kuber Nath Mishra Asst. Prof. , DME, OPJU 18/7/2024 1

2. Contents What is a Fluid? Scope of Fluid Mechanics Fluid Properties Types of Fluid Flow Bernoulli's Equation Laminar & Turbulent Flow 18/7/2024 2

3. What is Fluid Mechanics? What is Fluid? FLUID is a substance which deforms continuously under the action of shearing force (however small it is may be). Continuous deformation under the application of stress constitutes flow. Substances with no strength. Includes Gases and Liquids Deformation of fluid Deformation of solid body 18/7/2024 3

4. Difference between Fluid & Solid Solid More compact structure. For a solid the strain is a function of applied stress provided that the elastic limit is not exceeded . The strain in a solid is independent of the time over which the force is applied and if the elastic limit is not exceeded the deformation disappears when the force is removed. Fluid Less compact structure. The rate of strain is proportional to the applied stress. A fluid continues to flow for as long as the force is applied and will not recover its original form when the force is removed. 18/7/2024 4

5. What is Fluid Mechanics? What is Mechanics? The study of motion and the forces which cause (or prevent) the motion. Three types: Statics: The study of forces acting on the particles or bodies at rest. Kinematics (kinetics): The description of motion: displacement, velocity and acceleration. Dynamics: The study of forces acting on the particles and bodies in motion. 18/7/2024 5

6. What is Fluid Mechanics? WHAT IS HYDRAULICS WHAT IS FLUID MECHANICS? Mechanics of fluids It’s that branch of engineering science which deals with the behaviour of fluid under the conditions of rest (fluid statics) & motion (fluid dynamics) Greek word “HUDAR” , means – “WATER” It’s that branch of engineering science deals with water ( at rest or in motion ) Or its that branch of engineering science which is based on experimental observation of water flow. 18/7/2024 6

7. Application Areas of Fluid Mechanics 18/7/2024 7

8. CONCEPT OF FLUID 18/7/2024 8

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10. Compressibility A fluid contracts when more pressure is applied on it and expands when the pressure acting on it is reduced. Fluids act like elastic solids with respect to pressure. Therefore, in an analogous manner to Young’s modulus of elasticity for solids, it is appropriate to define a coefficient of compressibility κ (also called the bulk modulus of compressibility or bulk modulus of elasticity) Compressibility of any substance is the measure of its change in volume under the action of external forces namely pressure 18/7/2024 10

11. Compressibility A large value of κ indicates that a large change in pressure is needed to cause a small fractional change in volume, and thus a fluid with a large κ is essentially incompressible. This is typical for liquids, and explains why liquids are usually considered to be incompressible. The pressure of water at normal atmospheric conditions must be raised to 210 atm to compress it 1 percent, corresponding to a coefficient of compressibility value of κ = 21,000 atm 18/7/2024 11

12. Steady flow: implies no change of properties, velocity, acceleration w.r.t, time at a. particular location. Uniform flow: implies no change of properties, velocity, acceleration w.r.t, location at a particular time. Incompressible flow: implies no change of density. Types of Fluid Flow 18/7/2024 12

13. Bernoulli's Equation It is an approximate relation between pressure, velocity, and elevation. Assumptions: Steady flow Incompressible flow Regions of Inviscid flow Irrotational flow Gravity force is the only body force Flow along a streamline Bernoulli equation can be viewed as “Conservation of Mechanical Energy Principle ” 18/7/2024 13

14. = pressure energy or flow work per unit weight of the fluid = kinetic energy per unit weight of fluid or kinetic head = potential energy per unit weight or potential head   Bernoulli's Equation The sum of kinetic, potential, and flow energies of a fluid particle is constant along a streamline during steady flow when compressibility and frictional effects are negligible. 18/7/2024 14

15. = static pressure or actual thermodynamic pressure = dynamic pressure = hydrostatic pressure Stagnation pressure P stag =   Bernoulli's Equation During the flow the sum total of this energy transported from one point to other is conserved 18/7/2024 15

16. Bernoulli's Equation - Applications 18/7/2024 16

17. Laminar & Turbulent Flow Reynold’s experiments involved injecting a dye streak into fluid moving at constant velocity through a transparent tube. Fluid type, tube diameter and the velocity of the flow through the tube were varied. 18/7/2024 17

18. Dye followed a straight path. Dye followed a wavy path with streak intact. Dye rapidly mixed through the fluid in the tube Laminar & Turbulent Flow 18/7/2024 18

19. Reynolds classified the flow type according to the motion of the fluid Laminar Flow : every fluid molecule followed a straight path that was parallel to the boundaries of the tube. Turbulent Flow: every fluid molecule followed very complex path that led to a mixing of the dye. Transitional Flow: every fluid molecule followed wavy but parallel path that was not parallel to the boundaries of the tube. 18/7/2024 19

20. Reynolds found that conditions for each of the flow types depended on: 1. The velocity of the flow (U) 2. The diameter of the tube (D) 3. The density of the fluid ( ).   4. The fluid’s dynamic viscosity ( ).   He combined these variables into a dimensionless combination now known as the Flow Reynolds’ Number (Re) where:   Reynolds Number 18/7/2024 20

21. Velocity Distribution in Turbulent Flow In laminar flows the fluid momentum is transferred only by viscous shear; a moving layer of fluid drags the underlying fluid along due to viscosity. The velocity distribution in turbulent flows has a strong velocity gradient near the boundary and more uniform velocity (on average) well above the boundary. 18/7/2024 21

22. The more uniform distribution well above the boundary reflects the fact that fluid momentum is being transferred not only by viscous shear. The chaotic mixing that takes place also transfers momentum through the flow. The movement of fluid up and down in the flow, due to turbulence, more evenly distributes the velocity: low speed fluid moves upward from the boundary and high speed fluid in the outer layer moves upward and downward. This leads to a redistribution of fluid momentum . Velocity Distribution in Turbulent Flow 18/7/2024 22

23. Turbulent flows are made up of two regions: An inner region near the boundary that is dominated by viscous shear, i.e., An outer region that is dominated by turbulent shear (transfer of fluid momentum by the movement of the fluid up and down in the flow). Turbulent Shear Stress 18/7/2024 23

24. Turbulent Shear Stress     Where h is the eddy viscosity or turbulent viscosity which reflects the efficiency by which turbulence transfers momentum through the flow. 18/7/2024 24

25. Fluid Flow in Power Plants 18/7/2024 25

26. Types of power plants (involving fluid flow) 18/7/2024 26

27. Thermal power plant (Rankine cycle based power generation ) 18/7/2024 27

28. Ideal Reheat Rankine cycle (Thermal power plant cycle) 18/7/2024 28

29. Fluids flow cases in thermal power plants 18/7/2024 29 Liquid Liquid+ gas mixture & Liquid Gas + liquid mixture & Liquid Vapour Liquid and Liquid

30. Flow through pipes or internal flow Liquid or gas flow through pipes or ducts is commonly used in heating and cooling applications and fluid distribution networks. The fluid in such applications is usually forced to flow by a fan or pump through a flow section. Friction in pipes is directly related to the pressure drop and head loss during flow The pressure drop is then used to determine the pumping power requirement. The terms pipe, duct, and conduit are usually used interchangeably for flow sections. In general, flow sections of circular cross section are referred to as pipes (when the fluid is a liquid), and flow sections of noncircular cross section as ducts (when the fluid is a gas). Small diameter pipes are usually referred to as tubes. 18/7/2024 30

31. Energy Losses in Pipe flow The loss of energy in Pipes is calculated in terms of Meters of Head of the same liquid. An equivalent additional Pump work is required to maintain the same head. The energy losses in pipes is categorised broadly into Major and Minor losses The Major loss is incurred due to surface friction against the flow in the pipe 18/7/2024 31

32. Circular pipes can withstand large pressure differences between the inside and the outside without undergoing any significant distortion, but noncircular pipes cannot 18/7/2024 32 Trivia

33. Fluid velocity in a pipe 18/7/2024 33 The fluid velocity in a pipe changes from zero at the wall because of the no-slip condition to a maximum at the pipe center. In fluid flow, it is convenient to work with an average velocity V avg , which remains constant in incompressible flow when the cross-sectional area of the pipe is constant The average velocity in heating and cooling applications may change because of c hanges in density with temperature . In practice, the fluid properties are taken at some average temperature and treat them as constants.

34. Laminar and Turbulent Flow 18/7/2024 34 Fluid flow is streamlined at low velocities - The flow regime in this case is said to be laminar , characterized by smooth streamlines and highly ordered motion The flow is T urbulent at higher velocities , where it is characterized by velocity fluctuations and highly disordered motion . The transition from laminar to turbulent flow does not occur suddenly ; rather, it occurs over some region in which the flow fluctuates between laminar and turbulent flows before it becomes fully turbulent Trivia : Most flows encountered in practice are turbulent. Laminar flow is encountered when highly viscous fluids such as oils flow in small pipes or narrow passages.

35. Reynolds Number 18/7/2024 35 Reynolds Experiment

36. Osborne Reynolds discovered that the flow regime depends mainly on the ratio of inertial forces to viscous forces in the fluid. This ratio is called the Reynolds number and is expressed for internal flow in a circular pipe as Where V avg = average flow velocity (m/s), D = characteristic length of the geometry (diameter in this case, in m), and 𝜈 = 𝜇/𝜌 = kinematic viscosity of the fluid (m 2 /s). Reynolds number is a dimensionless quantity Also, kinematic viscosity has units m2/s, and can be viewed as viscous diffusivity or diffusivity for momentum . 18/7/2024 36 Reynolds Number

37. At large Reynolds numbers, the inertial forces, which are proportional to the fluid density and the square of the fluid velocity, are large relative to the viscous forces, Thus the viscous forces cannot prevent the random and rapid fluctuations of the fluid.- Turbulent Flow At small or moderate Reynolds numbers, however, the viscous forces are large enough to suppress these fluctuations and to keep the fluid “in line.” – Laminar Flow The Reynolds number at which the flow becomes turbulent is called the critical Reynolds number, The value of the critical Reynolds number is different for different geometries and flow conditions. For internal flow in a circular pipe, the generally accepted value of the critical Reynolds number is Re = 2300 18/7/2024 37 Reynolds Number

38. For flow through noncircular pipes, the Reynolds number is based on the hydraulic diameter D h defined as Hydraulic diameter: 18/7/2024 38 where A c is the cross-sectional area of the pipe and p is its wetted perimeter . The hydraulic diameter is defined such that it reduces to ordinary diameter D. for different cross sections of pipe and ducts, Reynolds Number

39. Trivia 18/7/2024 39 Water exiting a tube: ( a ) laminar flow at low flow rate, ( b ) turbulent flow at high flow rate, and ( c ) same as ( b ) but with a short shutter exposure to capture individual eddies

40. Moody Chart The friction factor in fully developed turbulent pipe flow depends on the Reynolds number and the relative roughness 𝜀/D , which is the ratio of the mean height of roughness of the pipe to the pipe diameter. Lewis F. Moody (1880–1953) presented the Darcy friction factor for pipe flow as a function of Reynolds number and 𝜀 /D over a wide range. It is probably one of the most widely accepted and used charts in engineering. Although it is developed for circular pipes, it can also be used for noncircular pipes by replacing the diameter with the hydraulic diameter. 18/7/2024 40

41. 18/7/2024 41 Moody Chart Commercially available pipes differ from those used in the experiments in that the roughness of pipes in the market is not uniform and it is difficult to give a precise description of it These values are for new pipes, and the relative roughness of pipes may increase with use as a result of corrosion, scale buildup, and precipitation. As a result, the friction factor may increase by a factor of 5 to 10. Actual operating conditions must be considered in the design of piping systems. Also, the Moody chart involves several uncertainties (the roughness size, experimental error, curve fitting of data, etc.), and thus the results obtained should not be treated as “exact.” They are is usually considered to be accurate to ±15 percent over the entire range in the figure.

42. 18/7/2024 42 At very large Reynolds numbers, the friction factor curves on the Moody chart are nearly horizontal, and thus the friction factors are independent of the Reynolds number Moody Chart

43. 18/7/2024 43 Moody Chart : Major interpretations For laminar flow, the friction factor decreases with increasing Reynolds number, and it is independent of surface roughness. The friction factor is a minimum for a smooth pipe (but still not zero because of the no-slip condition) and increases with roughness. The Colebrook equation in this case (𝜀 = 0) reduces to the Prandtl equation expressed as 1/√ f = 2.0 log( Re√ f ) - 0.8. The transition region from the laminar to turbulent regime (2300 < Re < 4000) is indicated by the shaded area in the Moody chart The data in this range are the least reliable. At small relative roughness, the friction factor increases in the transition region and approaches the value for smooth pipes. At very large Reynolds numbers (to the right of the dashed line on the Moody chart) the friction factor curves corresponding to specified relative roughness curves are nearly horizontal, and thus the friction factors are independent of the Reynolds number The flow in that region is called fully rough turbulent flow or just fully rough flow because the thickness of the viscous sublayer decreases with increasing Reynolds number, and it becomes so thin that it is negligibly small compared to the surface roughness height.

44. Types of fluid flow problems Determining the pressure drop (or head loss) when the pipe length and diameter are given for a specified flow rate (or velocity) Soln : Problems of this type are straightforward and can be solved directly by using the Moody chart. 2. Determining the flow rate when the pipe length and diameter are given for a specified pressure drop (or head loss) Soln : In problems of the second type, the diameter is given but the flow rate is unknown. A good guess for the friction factor in that case is obtained from the completely turbulent flow region for the given roughness. This is true for large Reynolds numbers, which is often the case in practice. Once the flow rate is obtained, the friction factor is corrected using the Moody chart or the Colebrook equation, and the process is repeated until the solution converges. (Typically only a few iterations are required for convergence to three or four digits of precision.) 18/7/2024 44

45. 3. Determining the pipe diameter when the pipe length and flow rate are given for a specified pressure drop (or head loss) Soln : In problems of this type, the diameter is not known and thus the Reynolds number and the relative roughness cannot be calculated. Therefore, we start calculations by assuming a pipe diameter. The pressure drop calculated for the assumed diameter is then compared to the specified pressure drop, and calculations are repeated with another pipe diameter in an iterative fashion until convergence 18/7/2024 45 Types of fluid flow problems

46. Loss of head due to friction in pipes (Major loss) 18/7/2024 46 Fictitious water level Actual water level Fictitious water level - Actual water level= Head loss due to friction Additional length Additional Surface Additional friction losses additional pressure drop Additional pumping cost

47. Darcy Wisbech Equation for calculation of loss of Head due to friction in pipes 18/7/2024 47 Consider a Uniform horizontal pipe having a steady flow and Let a1-1 and 2-2 be two sections in this pipe. p1= pressure intensity at section 1-1 p2= Pressure intensity at section 2-2 V1, V2 = Velocity at sections 1-1 and 2-2 resp. L = length between 1-1 and 2-2 d= diameter of the pipe f’ = frictional resistance per unit length

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50. Loss of head in pipes (Minor losses) The fluid in a typical piping system passes through various fittings, valves, bends, elbows, tees, inlets, exits, expansions, and contractions in addition to the straight sections of piping. These components interrupt the smooth flow of the fluid and cause additional losses because of the flow separation and mixing they induce. In a typical system with long pipes, these losses are minor compared to the head loss in the straight sections (the major losses) and are called minor losses. Although this is generally true, in some cases the minor losses may be greater than the major losses. This is the case, for example, in systems with several turns and valves in a short distance. 18/7/2024 50

51. Loss of head in pipes (Minor losses) The head loss introduced by a completely open valve, for example, may be negligible. But a partially closed valve may cause the largest head loss in the system, as evidenced by the drop in the flow rate. Flow through valves and fittings is very complex, and a theoretical analysis is generally not plausible. Therefore, minor losses are determined experimentally, usually by the manufacturers of the components. 18/7/2024 51

52. 18/7/2024 52 For a constant-diameter section of a pipe with a minor loss component, the loss coefficient of the component is determined by measuring the additional pressure loss it causes and dividing it by the dynamic pressure in the pipe. Loss of head in pipes (Minor losses)

53. Minor losses are usually expressed in terms of the loss coefficient K L (also called the resistance coefficient), defined as Loss coefficient: where h L is the additional irreversible head loss in the piping system caused by insertion of the component, and is defined as hL = ΔPL/𝜌 g. 18/7/2024 53 Loss of head in pipes (Minor losses)

54. When the inlet diameter equals the outlet diameter, the loss coefficient of a component can also be determined by measuring the pressure loss across the component and dividing it by the dynamic pressure, When the loss coefficient for a component is available, the head loss for that component is determined from 18/7/2024 54 Loss of head in pipes (Minor losses) The loss coefficient, in general, depends on the geometry of the component and the Reynolds number, just like the friction factor.

55. Minor losses are also expressed in terms of the equivalent length L equiv , defined as where f is the friction factor and D is the diameter of the pipe that contains the component . The head loss caused by the component is equivalent to the head loss caused by a section of the pipe whose length is L equiv . Therefore, the contribution of a component to the head loss is accounted for by simply adding L equiv to the total pipe length 18/7/2024 55

56. 18/7/2024 56 For constant diameter pipes throughout the system

57. Loss at entrance of a pipe 18/7/2024 57 The head loss at the inlet of a pipe is almost negligible for well-rounded inlets ( KL = 0.03 for r / D > 0.2) but increases to about 0.50 for sharp-edged inlets. A sharp-edged inlet acts like a flow constriction. The velocity increases in the vena contracta region (and the pressure decreases) because of the reduced effective flow area and then decreases as the flow fills the entire cross section of the pipe

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61. 18/7/2024 61 Graphical representation of flow contraction and the associated head loss at a sharp-edged pipe inlet.

62. Pumps and Turbines 18/7/2024 62

63. Pumps and turbines in daily life 18/7/2024 63

64. Pump terminology 18/7/2024 64 The net head of a pump, H, is defined as the change in Bernoulli head from inlet to outlet

65. PIPING NETWORKS AND PUMP SELECTION 18/7/2024 65 Pipes in Series and parallel For pipes in series, the flow rate is the same in each pipe, and the total head loss is the sum of the head losses in the individual pipes. For pipes in parallel, the head loss is the same in each pipe, and the total flow rate is the sum of the flow rates in individual pipes

66. The analysis of piping networks, no matter how complex they are, is based on two simple principles : 1. Conservation of mass throughout the system must be satisfied. This is done by requiring the total flow into a junction to be equal to the total flow out of the junction for all junctions in the system. Also, the flow rate must remain constant in pipes connected in series regardless of the changes in diameters. 18/7/2024 66

67. 2. Pressure drop (and thus head loss) between two junctions must be the same for all paths between the two junctions. This is because pressure is a point function and it cannot have two values at a specified point. In practice this rule is used by requiring that the algebraic sum of head losses in a loop (for all loops) be equal to zero. (A head loss is taken to be positive for flow in the clockwise direction and negative for flow in the counterclockwise direction.) Trivia: the analysis of piping networks is very similar to the analysis of electric circuits (Kirchhoff’s laws), with flow rate corresponding to electric current and pressure corresponding to electric potential. However, the situation is much more complex here since, unlike the electrical resistance, the “flow resistance” is a highly nonlinear function. 18/7/2024 67

68. Piping Systems With pumps and Turbines 18/7/2024 68 When a pump moves a fluid from one reservoir to another, the useful pump head requirement is equal to the elevation difference between the two reservoirs plus the head loss

69. When a piping system involves a pump and/or turbine, the steady-flow energy equation on a unit-mass basis is expressed as In terms of head where h pump , u = w pump , u /g is useful pump head delivered to the fluid, h turbine , e = w turbine , e /g is turbine head extracted from the fluid, 𝛼 is the kinetic energy correction factor whose value is about 1.05 for most flows, h L is the total head loss in the piping. 18/7/2024 69

70. Pump work between two reservoirs 18/7/2024 70 When the reservoir at inlet and outlet have free surfaces of the (open to atmosphere), the energy equation is solved for the required useful pump head, yielding Once the useful pump head is known, the mechanical power that needs to be delivered by the pump to the fluid and the electric power consumed by the motor of the pump for a specified flow rate are determined from where 𝜂pump–motor is the efficiency of the pump–motor combination, which is the product of the pump and the motor efficiencies. The pump– motor efficiency is defined as the ratio of the net mechanical energy delivered to the fluid by the pump to the electric energy consumed by the motor of the pump, and it typically ranges between 50 and 85 percent

71. Centrifugal pump curves The head loss of a piping system increases (usually quadratically) with the flow rate. A plot of required useful pump head h pump,u as a function of flow rate is called the system (or demand) curve. The head produced by a pump is not a constant either. Both the pump head and the pump efficiency vary with the flow rate, and pump manufacturers supply this variation in tabular or graphical form 18/7/2024 71

72. Characteristic pump curves for centrifugal pumps, the system curve for a piping system, and the operating point 18/7/2024 72

73. Flow rate of a pump increases as the required head decreases The intersection point of the pump head curve with the vertical axis typically represents the maximum head (called the shutoff head) the pump can provide While the intersection point with the horizontal axis indicates the maximum flow rate (called the free delivery ) that the pump can supply. The efficiency of a pump is highest at a certain combination of head and flow rate. 18/7/2024 73

74. Therefore, a pump that can supply the required head and flow rate is not necessarily a good choice for a piping system unless the efficiency of the pump at those conditions is sufficiently high The pump installed in a piping system will operate at the point where the system curve and the characteristic curve intersect. This point of intersection is called the operating point. The useful head produced by the pump at this point matches the head requirements of the system at that flow rate. Also, the efficiency of the pump during operation is the value corresponding to that flow rate. 18/7/2024 74

75. Pump Cavitation and Net Positive Suction Head (NPSH) When pumping liquids, it is possible for the local pressure inside the pump to fall below the vapor pressure of the liquid, Pv . When P < Pv , vapor-filled bubbles called cavitation bubbles appear. In other words, the liquid boils locally, typically on the suction side of the rotating impeller blades where the pressure is lowest 18/7/2024 75

76. Pump Cavitation and NPSH After the cavitation bubbles are formed, they are transported through the pump to regions where the pressure is higher, causing rapid collapse of the bubbles. It is this collapse of the bubbles that is undesirable, since it causes noise, vibration, reduced efficiency, and most importantly, damage to the impeller blades. Repeated bubble collapse near a blade surface leads to pitting or erosion of the blade and eventually catastrophic blade failure. 18/7/2024 76

77. NPSH To avoid cavitation, we must ensure that the local pressure everywhere inside the pump stays above the vapor pressure. Since pressure is most easily measured (or estimated) at the inlet of the pump, C avitation criteria are typically specified at the pump inlet . It is useful to employ a flow parameter called net positive suction head (NPSH) , defined as the difference between the pump’s inlet stagnation pressure head and the vapor pressure head, 18/7/2024 77

78. NPSH : Significance Pump manufacturers test their pumps for cavitation in a pump test facility by varying the volume flow rate and inlet pressure in a controlled manner. Specifically, at a given flow rate and liquid temperature, the pressure at the pump inlet is slowly lowered until cavitation occurs somewhere inside the pump. The value of NPSH is calculated using Equation and is recorded at this operating condition. The process is repeated at several other flow rates, and the pump manufacturer then publishes a performance parameter called the required net positive suction head ( NPSH required ), defined as the minimum NPSH necessary to avoid cavitation in the pump. The measured value of NPSH required varies with volume flow rate, and therefore NPSH required is often plotted on the same pump performance curve as net head. 18/7/2024 78

79. Avoiding Cavitation 18/7/2024 79 The volume flow rate at which the actual NPSH and the required NPSH intersect represents the maximum flow rate that can be delivered by the pump without the occurrence of cavitation.

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