Mechanics OF fluid and fluid machinery (PSC).pptx

Introduction to Fluid mechanics

1. MECHANICS OF FLUIDS

2. Fluids fluid, any liquid or gas or generally any material that cannot sustain a tangential, or shearing, force when at rest and that undergoes a continuous change in shape when subjected to such stress. This continuous and irrecoverable change of position of one part of the material relative to another part when under shear stress constitutes flow, a characteristic property of fluids. In contrast, the shearing forces within an elastic solid are maintained in a twisted or flexed position; the solid undergoes no flow and can spring back to its original shape. (See deformation and flow.) Compressed fluids can spring back to their original shape, too, but while compression is maintained, the forces within the fluid and between the fluid and the container are not shear forces. The fluid exerts an outward pressure, called hydrostatic pressure, that is everywhere perpendicular to the surfaces of the container.

3. Concept of Continuum A continuum is an area that can keep being divided and divided infinitely; no individual particles. It is a simplification that makes it possible to investigate the movement of matter on scales larger than the distances between particles. So when studying the movement of the atmosphere the fact that is it made up of atoms is ignored.

4. Physical properties of fluids Though each fluid is different from others in terms of composition and specific qualities, there are some properties that every fluid shares. These properties can be broadly categorized under: Kinematic properties : These properties help in understanding the fluid motion. Velocity and acceleration are the kinematic properties of the fluids. Thermodynamic properties : These properties help in understanding the thermodynamic state of the fluid. Temperature, density, pressure, and specific enthalpy are the thermodynamic properties of fluids. Physical properties: These properties help in understanding the physical state of the fluid such as color and odor.

5. Density The density of a fluid is defined as the ratio of the mass of the fluid to its volume. The density of gases is dependent on pressure and temperature, while the density of liquid remains constant. The density of water is 1000 kg m -3 The density of air is 1.225 kg m -3 . SI Unit=  

6. Specific weight Specific weight is defined as the weight possessed by the unit volume of a fluid. Specific weight is dependent on acceleration due to gravity as it changes from place to place. The specific weight of water is 9.81 × 1000 Nm -3 . SI Unit =  

7. Specific volume In fluid mechanics, specific volume is the reciprocal of density. It can be expressed as the volume that a fluid occupies per unit mass. SI unit =  

8. Specific Gravity It is defined as the ratio of the weight density of a fluid to the weight density of a standard fluid. For liquids standard fluid taken is water, for gases the standard fluid taken is air. S l = S g = =  

9. Vapour Pressure Vapour pressure, also known as vapour equilibrium pressure, can be defined as the pressure exerted (in a system featuring thermodynamic equilibrium) by a vapour with its condensed phases (solid or liquid) in a closed system at a given temperature. The equilibrium vapour pressure is known to serve as an indicator of the evaporation rate of a liquid. The propensity of particles to escape from the liquid (or a solid) is known to be related. A material that, at normal temperatures, has a high vapour pressure is generally referred to as a volatile material. It can be noted that the pressure exhibited above a liquid surface by the vapour is called vapour pressure.

10. 1. Nature of the liquid Liquids have weak intermolecular forces. Heating the molecules of the liquid can help change them to the vapour phase and thus increase the vapour pressure of the liquid. For example, Acetone and benzene have higher vapour pressure than water at a particular temperature. 2. Effect of temperature The vapour pressure of the liquid increases with an increase in its temperature. The molecules of the liquid have higher energy at higher temperatures.

11. Cavitation cavitation, the formation of vapour bubbles within a liquid at low-pressure regions that occur in places where the liquid has been accelerated to high velocities, as in the operation of centrifugal pumps, water turbines, and marine propellers. Cavitation is undesirable because it produces extensive erosion of the rotating blades, additional noise from the resultant knocking and vibrations, and a significant reduction of efficiency because it distorts the flow pattern. The cavities form when the pressure of the liquid has been reduced to its vapour pressure; they expand as the pressure is further reduced along with the flow and suddenly collapse when they reach regions of higher pressure. The sudden growth and collapse of these vapour cavities cause the extreme pressures that pit the metal surfaces exposed to the cavitating liquid.

12. Viscosity It is defined as the property of a fluid that offers resistance to the movement of one layer of the fluid over another adjacent layer of the fluid. μ is the constant of proportionality and is known as the coefficient of dynamic viscosity or only viscosity. represents the rate of the shear strain or rate of shear deformation or velocity gradient. therefore, Thus viscosity is also defined as the shear stress required to produce unit rate of shear strain.   Units of viscosity: The units of viscosity are obtained by putting the dimensions of the quantities in the equation. Si unit = MKS unit = CGS unit =   Newton’s law of viscosity: States that the shear stress on a fluid element layer is directly proportional to the rate of shear strain.  

13. Kinematic Viscosity Kinematic viscosity is an important property of fuel, which directly influences the fuel atomization quality and size of the fuel droplet in the spray. In general, kinematic viscosity is measured using the ASTM Standard D445 and EN 3104 test methods. t is defined as the ratio between the dynamic viscosity and density of the fluid. It is denoted by the ν .  

14. Variation of viscosity with temperature Viscosity depends strongly on temperature. In liquids, it usually decreases with increasing temperature, whereas, in most gases, viscosity increases with increasing temperature. The viscous forces in a fluid are due to cohesive forces and molecular momentum transfer. In liquids the cohesive forces predominate the molecular momentum transfer, due to closely packed molecules, and with the increase in temperature, the cohesive forces decrease the result the result of decreasing viscosity. In the case of gases the cohesive forces are small and molecular momentum transfer predominates. With the increase in temperature, molecular momentum transfer increases, and hence viscosity increases.

15. Types of fluids Ideal fluid A fluid is said to be ideal when it cannot be compressed and the viscosity doesn’t fall in the category of an ideal fluid. It is an imaginary fluid which doesn’t exist in reality. Real fluid All the fluids are real as all the fluids possess viscosity. Newtonian fluid When the fluid obeys Newton’s law of viscosity, it is known as a Newtonian fluid. Non-Newtonian fluid When the fluid doesn’t obey Newton’s law of viscosity, it is known as non-Newtonian fluid. Ideal plastic fluid When the shear stress is proportional to the velocity gradient and shear stress is more than the yield value, it is known as ideal plastic fluid. Incompressible fluid When the density of the fluid doesn’t change with the application of external force, it is known as an incompressible fluid. Compressible fluid When the density of the fluid changes with the application of external force, it is known as compressible fluid. Non-Newtonian Fluids Dilatant fluids Pseudoplastic fluids Bingham Plastic fluids Thixotropic R heopectic

16. Surface tension The cohesive forces between liquid molecules are responsible for the phenomenon known as surface tension. The molecules at the surface of a glass of water do not have other water molecules on all sides of them and consequently they cohere more strongly to those directly associated with them (in this case, next to and below them, but not above). It is not really true that a "skin" forms on the water surface; the stronger cohesion between the water molecules as opposed to the attraction of the water molecules to the air makes it more difficult to move an object through the surface than to move it when it is completely submersed. The cohesive forces between molecules in a liquid are shared with all neighboring molecules. Those on the surface have no neighboring molecules above and, thus, exhibit stronger attractive forces upon their nearest neighbors on and below the surface. Surface tension could be defined as the property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of the water molecules.

17. Capillarity Capillarity is an invisible force that works against the force of gravity. It pushes a liquid up in a tube or a narrow pipe. This rising of liquid is the capillary action. We call such liquid capillary water because the water follows the principle of capillarity. Capillary rise Capillary fall  

18. Pressure Fluid pressure is measuring the force per unit area that acts on an object in the fluid or the closed container's surface. Furthermore, the cause of this pressure is due to acceleration, gravity, or forces that are outside the closed container. The application of the pressure is in all directions because the fluid has no definite shape.  

19. Fluid pressure at a point

20. Fluid pressure at a point

21. Fluid pressure at a point

22. Fluid pressure at a point

23. Pressure variation in a fluid at rest Δ A = Cross-sectional area of element ΔZ = Height of fluid element P = Pressure on face AB Z = Distance of fluid element from the free surface

24. Pressure variation in a fluid at rest

25. Absolute pressure: This is defined as the pressure which is measured with reference to absolute vacuum pressure. Gauge pressure: This is defined as the pressure that is measured with the help of a pressure-measuring instrument. Vacuum pressure: This is defined as the pressure below the atmospheric pressure.   Measurement of pressure

26. Differential Pressure: Differential pressure, in general, is a measure of pressure where the reading and reference values are variable. Differential pressure is calculated by subtracting one of these values from the other. If Pipe A flows at 100 psi and Pipe B flows at 30 psi, the differential pressure would be 70 psi. Datum head (Z): Datum head: The head owned by the fluid due to the height above the datum. Unit: Meter (m) Pressure head (h): The pressure head the fluid has due to the pressure generated by the flowing fluid

27. Measurement of pressure The devices that are used for measuring pressure are called pressure gauges. Gauge pressure is the pressure relative to atmospheric pressure. For the pressures above atmospheric pressure, gauge pressure is positive. For the pressures below atmospheric pressure, gauge pressure is negative. The pressure gauge is also known as a pressure meter or vacuum gauge. A manometer is a device that uses the surface area and weight of a liquid column to measure and indicate pressure. Most gauges calculate the pressure relative to atmospheric pressure as the zero point. Hence, this form of reading is known as gauge pressure. Pressure gauges are analog as well as digital.

28. Applications of Pressure Gauge Pressure gauges are used to measure the pressure of liquids, vapors, solids, and gases. It is used for the inspection of air brakes on trucks. Pressure gauges are used in chemical, petrochemical, sanitary, pharmaceutical, and process industries. Pressure gauges are used in HVAC, refrigeration, ventilation, food, and beverage industries They are also used in eliminating the potential leak paths.

29. The pressure of a fluid is measured by the following devices 1. Manometers 2. Mechanical Gauges Manometers Manometers are defined as devices used for measuring the pressure at a point in a fluid by balancing the column of fluid by the same or another column of the fluid. They are classified as Simple Manometers Differential Manometers Mechanical Gauges (Pressure Gauges) Mechanical Guges are defined as devices used for measuring the pressure by balancing the fluid column by the spring or dead weight. They are commonly known as pressure gauges. Commonly used pressure gauges are Diaphragm pressure gauges Bourdon tube pressure gauges Deadweight pressure gauges Bellows pressure gauges

30. Simple manometers A simple manometer consists of a glass tube having one of its ends connected to a point where pressure is to be measured and the other end remains open to the atmosphere. Common types of simple manometers are Piezometer U-tube manometer Single column Manometer

31. Simple manometers 1. Piezometer It is the simplest form of manometer used for measuring gauge pressure. One end of this manometer is connected to the point where pressure is to be measured and other end is open to the atmosphere as shown in the figure. The rise of liquid gives the pressure head at the point. If at a point a the height of liquid say water h in piezometer tube then pressure at A is  

32. Simple manometers 2. U-tube manometer It consists of a glass tube bent in a U-shape, one end of which is connected to a point at which pressure is to be measured and the other end remains open to the atmosphere as shown in the figure. The tube generally contains mercury or any other liquid whose specific gravity is greater than the specific gravity of the liquid whose pressure is to be measured.

33. Simple manometers 2. U-tube manometer 1. For gauge pressure Let B be the point at which pressure is to be measured whose value is p. The datum line is A - A Pressure is the same for the horizontal surface. Hence the pressure above the horizontal datum line in both left and right column are same. ⸫  

34. Simple manometers 2. U-tube manometer 2. For vacuum pressure The level of the heavy liquid in the manometer will be as shown in figure Pressure above A-A in the left column = Pressure head in right column = 0 ⸫  

35. Simple manometers 3. Single Column Manometer It is a modified form of u tube manometer. In which a reservoir has a large cross-sectional area (about 100 times) compared to the tube area connected to one of the limbs of the manometer. Due to the large cross-sectional area of the reservoir, for any variation in pressure, the change in the liquid level in the reservoir will be very small which may be neglected and hence the pressure is given by the height of liquid in the other limb. The limb may be vertical or inclined, thus there are two types of single-column manometer Vertical single-column manometer Inclined single-column manometer

36. Simple manometers 3.1 Vertical Single Column Manometer  

37. Simple manometers 3.1 Vertical Single-Column Manometer Fall of heavy liquid in reservoir will cause a rise of heavy liquid level in the right limb, ⸫ ie , ------------- (equation 1) Now consider the datum line Y-Y as shown in figure. Then pressure in the right limb above Y-Y Pressure in the left limb above Y-Y Equating the pressure, we get As the area A is very large as compare to a, hence ratio a/A becomes very small and can be neglected  

38. Simple manometers 3.2 Inclined Single Column Manometer This manometer is more sensitive, due to the inclination the distance moved by the heavy liquid in the right limb will be more. We know that Substituting the value of , we get  

39. Differential Manometers Differential manometers are the devices used for measuring the difference of pressure between two points in a pipe or in two different pipes. A differential manometer consists of U-tube, containing heavy liquid whose two ends are connected to the points, whose difference of pressure is to be measured. Most commonly used types of manometers U-tube differential manometers a) Two pipes at different levels b) Two pipes at same levels 2. Inverted u tube manometers

40. Differential Manometers 1. a U-tube differential manometer Two pipes at different levels The points A and B are at different levels and contain liquids of different specific gravity. gr these points are connected to the U-tube manometer Let pressure at A and B are and , taking datum line X-X Pressure above X-X in the left limb, Pressure above X-X in the left limb,  

41. Differential Manometers 1. a U-tube differential manometer A and B at the same levels In the figure, the two points A and B are at the same level and contains the same liquid of density Equating the two pressure   x A B

42. Differential Manometers 2 . Inverted U-tube D ifferential M anometer It consists of an inverted u tube, Containing a light liquid. The two ends of the tube are connected to the points whose difference of pressure is to be measured. It is used for measuring difference of low pressures. In the figure manometer is connected to the two points A and B. Let the pressure at A is more than the pressure at B.

43. Differential Manometers 2 . Inverted U-tube D ifferential M anometer   Taking x-x as datum line pressure in the left limb below X-X Pressure in the right limb below X-X Equating the two pressure  

44. Barometers A barometer is a scientific instrument used to measure air pressure in a certain environment. Pressure tendency can forecast short-term changes in the weather. Evangelista Torricelli is universally credited with inventing the barometer in 1643.

45. Types of Pressure Gauges Depending on the usability and purpose, whether commercial or industrial, the most common pressure gauges are designed. Some of the pressure gauges are: Bourdon Tube Pressure Gauge Diaphragm Pressure Gauge Capsule Pressure Gauge Absolute Pressure Gauge Differential Pressure Gauge Bellows Pressure Gauge

46. Bourdon Tube Pressure Gauge A bourdon tube is the most commonly used pressure gauge. It is a mechanical instrument that measures the pressure without an electric supply. It is made of steel to resist wear and corrosion. A bourdon tube pressure gauge can measure pressure from 0.6 to 7000 bar (8 to 10000 psi). It is compatible with liquid or gaseous media for vacuum, as well as low and high-pressure applications. It is a compact instrument that is ideal for heavy vibration applications and dynamic pressure load.

47. Diaphragm Pressure Gauge It is the device used to measure the pressure of fluid in a system. It is purposefully designed to measure low-pressure intensities. A diaphragm pressure gauge is also known as a membrane pressure gauge. This device uses the deflection of a flexible thin membrane known as the diaphragm. The pressure is indicated by using a needle, which is moved with the help of a pinion arrangement with the diaphragm.

48. Capsule Pressure Gauge In this type of pressure gauge, two corrugated diaphragms are welded together at their periphery to form a capsule. This capsule is the main element in sensing the pressure. A hole is present in one of the diaphragms in the center which lets the medium enter. The diaphragms expand or contract upon the application of pressure. The capsule pressure gauge is used for calculating the pressure of gases and is utilised for calculating the pressure of substances with up to 600 mbar.

49. Absolute Pressure Gauge These are the instruments ideally used to measure the pressure independent of the natural fluctuations in atmospheric pressure. A reference measure of vacuum is fixed to the side of the measuring element and is not subject to pressure. Hence, it has zero pressure with no variation. They are mainly used in scientific laboratories. Altitude does not affect the absolute pressure gauges, hence they are used in aeronautics, Heating, ventilation, and air conditioning systems, and distillation processes.

50. Differential Pressure Gauge The difference between the pressure in two chambers separated by an element that moves back and forth according to the changes in pressure is measured by the differential pressure gauge. A diaphragm present in the differential pressure gauge separates the media chamber from the vacuum chamber. When the pressure increases, the diaphragm deforms into the vacuum chamber. The deformation and change are converted into a pressure value.

51. Bellows Pressure Gauge Bellows pressure gauges are the devices used to measure low-pressure applications. The bellows in the devices are made of thin-walled springy metal connected tubes that form a shape similar to an accordion; this is sealed in the free end of the gauge.

52. Pressure on plane and curved surfaces

53. Vertical plane surface submerged in liquid

54. Centre of pressure

55. Center of Pressure

56. Centre of pressure (h*) Horizontal Surface submerged   Inclined plane surface A= Total area of the inclined surface   Force on a curved surface  

57. KINEMATICS OF FLUID FLOW EULERIAN APPROACH LEGRANGIAN APPROACH

58. KINEMATICS OF FLUID FLOW EULERIAN APPROACH The velocity, acceleration, pressure, density, etc are described at a point in the flow field. The Eulerian method is commonly used in fluid mechanics. Known as control volume approach. LEGRANGIAN APPROACH A single fluid particle is followed during its motion and its velocity, acceleration, density, etc. Mixing of fluid Known as the control mass approach.

59. CLASSIFICATION OF FLOW STEADY FLOW Steady flow is defined as that type of flow in which the fluid characteristics like velocity, pressure, density, etc., at a point do not change with time. Ie ,   UNSTEADY FLOW Unsteady flow is defined as that type of flow in which the fluid characteristics like velocity, pressure, density, etc., at a point change with time.  

60. CLASSIFICATION OF FLOW UNIFORM FLOW Uniform flow is defined as that type of flow in which the velocity at any given time does not change with respect to space(i.e., length of direction of flow)   NON UNIFORM FLOW Non-uniform flow is defined as that type of flow in which the velocity at any given time changes with respect to space(i.e., length of direction of flow)  

61. Which of the following represents uniform steady flow? Ans. Flow through a long pipe at constant rate Flow through an expanding tube at an increasing rate. Flow through an expanding tube at constant rate Flow through a long pipe at decreasing rate Flow through a long pipe at constant rate

62. CLASSIFICATION OF FLOW LAMINAR FLOW TURBULENT FLOW

63. CLASSIFICATION OF FLOW LAMINAR FLOW Laminar flow or streamline flow in pipes (or tubes) occurs when a fluid flows in parallel layers, with no disruption between the layers. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with all particles moving in straight lines parallel to the pipe walls. Any lateral mixing (mixing at right angles to the flow direction) occurs by the action of diffusion between layers of the liquid. Diffusion mixing can be slow however if the diameter of the pipe of the tube is small then this diffusive mixing can be very significant. TURBULENT FLOW Turbulent flow is a flow regime characterized by chaotic property changes. This includes a rapid variation of pressure and flows velocity in space and time. In contrast to laminar flow, the fluid no longer travels in layers, and mixing across the tube is highly efficient. Flows at Reynolds numbers larger than 4000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers below 2300 usually remain laminar. Flow in the range of Reynolds numbers 2300 to 4000 and known as transition.

64. CLASSIFICATION OF FLOW ROTATIONAL FLOW Rotational flow, also known as swirling or vortical flow, is a type of fluid motion characterized by the presence of vortices or rotational components within the flow field. Unlike irrotational flow, where fluid particles move without rotating, rotational flow involves the swirling or circular motion of fluid particles around a central axis. This rotation creates regions of high and low velocity, generating dynamic and complex flow patterns. Examples of Rotational Flow Rotational flow can occur in various scenarios, such as when a fluid is stirred or agitated, or when it flows past a curved surface or an obstruction. It is also commonly observed in natural phenomena like tornadoes, whirlpools, and turbulent flows. The presence of vortices in rotational flow can have significant effects on fluid behaviour , such as changes in pressure distribution, mixing and diffusion rates, and the development of shear forces. IRROTATIONAL FLOW Irrotational flow refers to a type of fluid motion in which the fluid particles move without rotating as they travel through the flow field. In other words, there are no vortices or swirling motions present in the irrotational flow. Instead, the fluid particles move smoothly and consistently, following streamlines that do not intersect or cross each other. In irrotational flow, the velocity of the fluid particles can vary from point to point, but the direction of motion remains consistent along a streamlined flow. This means that the fluid particles do not experience any rotational or angular velocity as they move. Irrotational flow is often associated with laminar flow, which is characterized by well-ordered, parallel layers of fluid moving without disruption. The various examples of Irrotational flow are: Flow around an idealized streamlined body (such as an airfoil) at low angles of attack, Flow through a long, straight pipe with laminar flow, Flow over a flat plate with a laminar boundary layer, Flow in a closed circuit with no obstructions or disturbances, Potential flow around a submerged body in an inviscid fluid, Flow through a diffuser or converging-diverging nozzle with steady, smooth motion.

65. CLASSIFICATION OF FLOW COMPRESSIBLE FLOW The volume of real fluids changes when they are expanded or compressed by an external force or the change of pressure or temperature. The property of volume change is called compressibility and a fluid whose volume changes is called compressible fluid. INCOMPRESSIBLE FLOW On the other hand, an incompressible fluid is a fluid which is not compressed or expanded, and its volume is always constant. In reality, a rigorous incompressible fluid does not exist. However, when a flow is less affected by compressibility, as a flow of air or water around us, the flow can be considered as an incompressible fluid flow.

66. CLASSIFICATION OF FLOW 1-D FLOW It is that type of flow in which the flow parameter such as velocity is a function of time and one space coordinate only. 2-D FLOW It is that type of flow in which the flow parameter such as velocity is a function of time and three space coordinates. 3-D FLOW It is that type of flow in which the flow parameter such as velocity is a function of time and two space coordinates.

67. Bernoulli Equation: The total mechanical energy of the moving fluid comprising the gravitational potential energy of elevation, the energy associated with the fluid pressure and the kinetic energy of the fluid motion, remains constant. Assumptions Flow is steady. Fluid is incompressible. Fluid is non-viscous (inviscid) Equation is applicable along a streamline. Effect of friction is neglected. Only pressure and gravity forces are taken into account. Velocity is uniform over the cross-section.    

68. Bernoulli Equation:   P (Static Pressure) = It represents the actual thermodynamical pressure of the fluid. (Dynamic pressure) = It represents the pressure rise when the fluid in motion is brought to a stop isentropically. pressure at a point according to the reference point selected.   The sum of static, dynamic, and hydrostatic pressure is called total pressure. Therefore Bernoulli’s equations state that the total pressure along a streamline is constant. Stagnation pressure: it represents the pressure at a point where the fluid is brought to a complete stop.  

69. Bernoulli Equation: Limitations Steady flow: Only applicable to a steady flow. it should not be used during periods of change in the flow conditions. Frictionless flow: Friction due to the smallest fluid velocity change must be ignored. No shaft work: The Bernoulli equation was derived from a force balance on a particle moving along a streamline. Therefore, the Bernoulli equation is not applicable in a flow section that involves a pump, turbine, fan, or any other machine or impeller since such devices destroy the streamlines and carry out energy interactions with the fluid particles. Incompressible flow No heat transfer Flow along a streamline

70. Bernoulli Equation: Application working of airplane: An airplane works on the principle of Bernoulli’s theorem. When an airplane flies, the wings create a low-pressure area above them. This low-pressure area sucks the air from below the wings and creates lift. Working of a venturi: A venturi is a device that is used to measure the flow rate of a fluid. It works on the principle of Bernoulli’s theorem. The fluid is accelerated as it passes through a narrow constriction in the venturi. This causes a decrease in pressure which can be measured. working of a pitot tube: A pitot tube is used to measure the rate of a fluid. It works on the principle of Bernoulli’s theorem. The fluid is accelerated as it passes through a narrow constriction in the pitot tube. This causes a decrease in pressure which can be measured. Action of atomizer: An atomiser is a device that is used to spray a liquid in the form of fine droplets. It works on the principle of Bernoulli’s theorem. The liquid is accelerated as it passes through a narrow constriction in the atomiser . This causes a decrease in pressure which vaporises the liquid and breaks it up into fine droplets.

71. HGL and EGL Hydraulic Grade Line The line that represents the sum of the static pressure and the elevation heads is called the hydraulic grade line   Energy Grade Line The line that represents the total head of the fluid is called the energy grade line. Dynamic Head: The difference between the heights of EGL and HGL is equal to the dynamic head  

72. Continuity Equation The conservation of mass principle for a control volume can be expressed as: The net mass transfer to or from a control volume during a time interval Δ t is equal to the net change (increase or decrease) in the total mass within the control volume during Δ t Assumption of Continuity Equation The tube has a single entry and single exit. The fluid flowing in the tube is non-viscous. The flow is incompressible. The fluid flow is steady.

73. Momentum equation Newton’s second law states that the acceleration of a body is proportional to the net force acting on it and is inversely proportional to its mass, and that the rate of change of the momentum of a body is equal to the net force acting on the body. Therefore, the momentum of a system remains constant when the net force acting on it is zero, and thus the momentum of such systems is conserved. This is known as the conservation of momentum principle.

74. Energy Equation Energy can be transferred to or from a closed system by heat or work, and the conservation of energy principle requires that the net energy transfer to or from a system during a process be equal to the change in the energy content of the system. Control volumes involve energy transfer via mass flow also, and the conservation of energy principle, also called the energy balance  

75. STREAM LINES