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Principal of gases, gas law flow of

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Principal of gases, gas law flow of

  1. 1. PRINCIPAL OF GASES, GAS LAW FLOW OF GASES AND VENTURI PRINCIPAL Presenter Dr Andre Mwana-Ngoie
  2. 2. outline • Introduction • Gas pression • absolute temperature • Boyles low • Charles low
  3. 3. *All substances(Matter) are composed of small particles (molecules); is measured of space; that the molecules occupy (volume) is derived from the space in between the molecules and not the space. The molecules contain themselves
  4. 4. cont • There are 3 states of matter -Solid -Liquid -Gas • The molecules are in constant motion • This motion is different for the 3 states of matter.
  5. 5. cont Solid - Molecules are held close to each other by their attractions of charge. They will bend and/or vibrate, but will stay in close proximity.
  6. 6. cont Liquid - Molecules will flow or glide over one another, but stay toward the bottom of the container. Motion is a bit more random than that of a solid.
  7. 7. cont • Gas - Molecules are in continual straight-line motion. • The kinetic energy of the molecule is greater than the attractive force between them, thus they are much farther apart and move freely of each other. • When the molecules collide with each other, or with the walls of a container, there is no loss of energy.
  8. 8. Gas molecules
  9. 9. cont GAS • distinguished from the solid and liquid states by: -relatively low density and viscosity(‘light’) because molecules are spread apart over a large volume. (density = mass / volume) – Density order: solid > liquid >>> gases
  10. 10. cont – Gases flow freely because there are no effective forces of attraction between the gaseous particles – molecules. – Because of this gases and liquids are described as fluids. – relatively great expansion and contraction with changes in pressure and temperature
  11. 11. cont The spontaneous tendency to become distributed uniformly ... NB ;The main distinguishing property of gases is their ability to be compressed into smaller and smaller because of the ‘empty’ space between the particles. ◦ (almost impossible to compress a solid)
  12. 12. Gas pressure • The pressure of a gas is causes by collisions of the molecules with the walls of the container. • The magnitude of the pressure is related to how hard and how often the molecules strike the wall • The "hardness" of the impact of the molecules with the wall will be related to the velocity of the molecules times the mass of the molecules
  13. 13. cont
  14. 14.  For example - if the number of gaseous particles in a container is doubled, the gas pressure is doubled  because doubling the number of molecules doubles the number of impacts on the side of the container so the total impact force per unit area is also doubled.
  15. 15. This doubling of the particle impacts doubling the pressure is pictured in the two diagrams below. 2 x particles ===> P x 2
  16. 16. Absolute Temperature • The absolute temperature is a measure of the average kinetic energy of its molecules. • If two different gases are at the same temperature, their molecules have the same average kinetic energy If the temperature of a gas is doubled, the average kinetic energy of its molecules is doubled
  17. 17. • Gases have no surface, and no fixed shape or volume, and because of lack of particle attraction, they always spread out and fill any container (so gas volume = container volume). • A gas will fill whatever container that it is in.
  18. 18. eg of this is a bottle of ammonia being opened in a room and the smell traveling throughout the room.
  19. 19. The (advanced) kinetic theory of gases is founded on the following six fundamental postulates: (i)Gases are composed of minute discrete particles (usually molecules). (ii)The particles are in continuous chaotic motion moving in straight lines between very frequent collisions with each other and the sides of the container (approximately 109/s). (iii) The bombardment of the container walls by the particles causes the phenomenon we call pressure (i.e. force of impacts/unit area).
  20. 20. (iv)The collisions are perfectly elastic i.e. no energy loss on collision due to friction. (v)At relatively low pressures the average distance between particles is large compared to the diameter of the particles and therefore the inter- molecular forces between the particles is negligible. (vi)The average kinetic energy of the particles is directly proportional to the absolute temperature on the Kelvin scale (K).
  21. 21. BOYLES LAW • Consider volume of gas within asyringe • Collision btn the molecule and the walls of the container results in an absolute pressure P which in this case is a typical atmospheric pressure=100kPa or 1 bar) . • When volume increase and temperature remains constant .
  22. 22. • The average kinetic energy of the gas molecules remains constant • This means that the speed of the molecules, remains unchanged . • If the speed remains unchanged, but the volume increases, this means that there will be fewer collisions with the container walls over a a given time • Therefore, the pressure will decrease
  23. 23. • Mathematically Boyle's law can be expressed as P1V1 = P2V2 • V1is the original volume • V2 is the new volume • P1 is original pressure • P2 is the new pressure
  24. 24. Charles law • Effect of a temperature increase at constant volume. • An increase in temperature means an increase in the average kinetic energy of the gas molecules. • There will be more collisions per unit time, furthermore, the momentum of each collision increases (molecules strike the wall harder)
  25. 25.  Therefore, there will be an increase in pressure.  If we allow the volume to change to maintain constant pressure, the volume will increase with increasing temperature . V / T =constant  V is the volume  T is the absolute temperature (measured in Kelvin)
  26. 26. • Important: Charles's Law only works when the pressure is constant. Note: Charles's Law is fairly accurate but gases tend to deviate from it at very high and low pressures.
  27. 27. Combined Law • The combined gas law is a combination of Boyle's Law and Charles's Law; hence its name the combined gas law. • This can be written as PV / T = constant. Since for a given amount of gas there is a constant then we can write P1V1 / T1 = P2V2 / T2.
  28. 28. The Third perfect gas law • The third gas law indicates that at constant volume the absolute pressure on the gas varies directly with the absolute temperature or P / T = constant. • Therefore at constant volume a doubling of temperature results in a doubling of pressure
  29. 29. the combined gas law equation
  30. 30.  P1 is the initial pressure  V1 is the initial volume  T1 is the initial temperature (in Kelvin)  P2 is the final pressure  V2 is the final volume  T2 is the final temperature (in Kelvin)  This equation is useful if you have the current volume, temperature, and pressure of a gas, and if you have two of the three final values of the gas.
  31. 31. Adiabatic changes • For the gas law above one varible must be kept constant. • For these condition to apply heat energy must be added or removed from the gas for the change to occur . • An adiabatic process is one in which the changes in volume and pressure of a given mass of gas take place such that heat is neither allowed to enter nor leave the gas.
  32. 32. • E.g. IF a cylinder is connected to an anaesthetic machine and turned on quickly the pressure in the connecting pipes and gauges rises rapidly. • thus the gas is compressed adiabatically and a large temperature rises with increased risk of fire. • a cylinder is connected to a pressure regulator which is used to set a cooling rate.
  33. 33. For a simple substance, during an adiabatic process in which the volume increases, the internal energy of the working substance must decrease
  34. 34.  Effusion and Diffusion are the two ways that gases mix with other gases.  Diffusion is a process in which a gas enters a container with another gas and the two mix to form a uniform mixture.  Effusion occurs when a gas moves through a small hole in its current container into another container.  An example of diffusion is the ammonia mentioned earlier where the ammonia moves into the room with the air
  35. 35. Dalton's law of partial pressure Two gas laws describe partial pressure. Dalton's law of partial pressure • states that the total pressure of a gas is equal to the sum of its partial pressures(that is, the pressure exerted by each component of the gas mixture.)
  36. 36. • air is composed mostly of nitrogen and oxygen. • Along with these are small components carbon dioxide and gases collectively known as the rare or noble gases. • Hence, the total pressure of a given quantity of air is equal to the sum of the pressures exerted by each of these gases.
  37. 37. Henry's law states • Henry's law • states that the amount of gas dissolved in a liquid is directly proportional to the partial pressure of the gas above the surface of the solution. • This applies only to gases such as oxygen and hydrogen that do not react chemically to liquids.
  38. 38. • On the other hand, hydrochloric acid will ionize when introduced to water: • one or more of its electrons will be removed, and its atoms will convert to ions, which are either positive or negative in charge.
  39. 39. STP  STP is Standard Temperature and Pressure. STP is Oo Celcius and 1 atmosphere of pressure.  Gases properties can be compared using STP as a reference.  To obtain the pressure of gas collected over water the partial pressure of the water must be taken into consideration.  The reason for this is as the gas bubbles through the water the gas picks up water vapor.
  40. 40. • The amount of water vapor the gas picks up only depends on the temperature. • To calculate the pressure of the gas the partial pressure of the water must be subtracted from the pressure in the container.
  41. 41. The ideal gas • The ideal gas law is a combination of all the gas laws. The ideal gas law can be expressed as PV = nRT. • P is the pressure in atm • V is the volume in liters • n is the number of moles • R is a constant • T is the temperature in Kelvin
  42. 42. • The constant R is calculated from a theroretical gas called the ideal gas. The most commonly used form of R is .0821 L * atm / (K * mol). • This R will allow the units to cancel so the equation will work out. • The ideal gas law is the equation of state of a hypothetical ideal gas.
  43. 43. The modern form of the equation is:. where p is the absolute pressure of the gas; V is the volume; is the amount of substance; R is the Regnault constant, better known as universal gas constant; and T is the absolute temperature In SI units, p is measured in pascals; V in cubic metres; n in moles; and T in kelvin. R has the value 8.314472 J·K−1·mol−1 .
  44. 44. Deviations from real gases • The equation of state given here applies only to an ideal gas, or a real gas that behaves like an ideal gas. • Since it neglects both molecular size and intermolecular attractions, • the ideal gas law is most accurate for monatomic gases at high temperatures and low pressures
  45. 45. • This can be clearly seen in the diagram • If the gases conformed to the ideal gas law equation PV=nRT, the product PV should be constant with increasing pressure at constant temperature, clearly this is not the case.
  46. 46. • for any gas the lower its pressure and the higher its temperature, the more closely it will be 'ideal', i.e. closely obey the ideal gas equation • PV=nRT • Also the smaller the molecular mass or the weaker the intermolecular forces, the gas will be closer to ideal behaviour.
  47. 47. Flow of gases – Flow by definition is the quantity of the gas or fluid which passes a point in unit time. In equation form, F = Q/t – where F is equal to the mean flow – Q = the quantity (mass or volume) and – T = time. – The rate of change of a parameter, such as Q, is specified as Q dot or
  48. 48. Laminar Flow: Definition: laminar flow -- "Streamline flow of a fluid in which the fluid moves in layers without fluctuations or turbulence so that successive particles passing the same point have the same velocity. – It occurs at low Reynolds numbers, i.e. low velocities, high viscosities, low densities or small dimensions.... Laminar flow may be visualized in accord with the diagram below.
  49. 49. • The flow is greatest in the centre as the side of the tube is approached the flow becomes slower until it approaches zero • In order to drive a fluid through the tube the pressure different must be present across the end. • This principal can be used to measure resistance with gas flow
  50. 50. • The relationship above illustrates that Pressure is proportiona to Flow [ P ] and P/Q= R, • where R presents the resistance of the tube.
  51. 51. If the flow is constant, i.e. is constant then the magnitude of the resistance caused by the constriction can be determined from P1 and P2. The resistance would be (P1-P2)/ Q = R.
  52. 52. Graphs for turbulent and lamumina flow For turbulent flow, a nonlinear relationship exists between flow and pressure as shown below: Relationships between flow and pressure: (laminar)
  53. 53. Turbulent flow • Turbulent flow may occur if there is sharp increase in the flow through the tube. • These fluctuations are superimposed on the underlying regular (average) flow. • Other factors affecting the type of flow include viscosity, density and the diameter of the tube. • These factors may be combined to give index known Reynolds number.
  54. 54. • Reynolds number = (v Pd) /n , • where v is the linear fluid velocity • ,P is the density, • d is the tube diameter, and • n is the viscosity
  55. 55. – Recalling that the Reynolds number is a ratio of inertia forces (momentum) to viscous forces, – smaller Reynolds numbers are consistent with relatively larger viscous forces which would predispose to laminar flow. – Larger Reynolds numbers then indicate dominance of momentum forces which predispose to turbulence.
  56. 56. ◦ Generally, Reynolds numbers less than about 2000 correspond to laminar flow, ◦ whereas Reynolds number is greater than about 3000 characterize turbulent flow ◦ Reynolds numbers between 2000 and 3000 reflect unstable flow that can transition between laminar and turbulent characteristics.
  57. 57. – Furthermore, with turbulent flow, since pressure to flow relationships do not exhibit linearity, resistance will not be constant. – In the turbulent flow case, resistance measurements must be specified in terms of the particular flow rate. – Physiologically, during breathing, airflow resistance will depend on the air flow rate assuming turbulence
  58. 58. Graphs for turbulent For turbulent flow, a nonlinear relationship exists between flow and pressure as shown below:
  59. 59. factors predisposed to relatively laminar vs. turbulent flow behavior ***Effect of reducing the tube diameter on the flow Small changes in the diameter of an endotrachial tube would have large effects on resistance and then flow, assuming constant pressure. – Hemodynamically, changes in vasomotor tone, causing vasoconstriction, have similar large effects.
  60. 60. ***length*** • At constant pressure reducing the length of the tube increase the flow of gas. • flows may be laminar in which fluids move in thin layers or turbulence reflecting irregular motion with the velocity fluctuations • Flow may change from lamina to turbulent if a consriction is reached resulting in increased fluid velocity
  61. 61. **viscosity** • Viscosity of the fluid affect the flow.eg blood viscosity increases if the patients haemoglobin or fibrinogen raise • Raise in viscosity reduces blood flow giving risk of vascular occlusion. • Viscosity increases at low temperature, increasing age and following treatment with low molecular weight dextan.
  62. 62. [Hagen-Poiseulle equation]
  63. 63. Clinical consideration • An important clinical consideration has to do with a change in the relationship between flow and pressure as flow transitions from laminar to turbulent. • In particular, for turbulence flow inside pathways that have rough internal edges, flow appears about proportional to the square root of pressure or a doubling of flow requires a quadrupling of pressure.
  64. 64. Clinical aspect • Laminar and turbulent flow in anesthesia: The diagram above notes the critical flows for air and for an anesthetic mixture containing nitrous oxide (60%) and oxygen. • Transition between laminar and turbulent flow exhibits dependencies on gas velocity. • Furthermore gas velocity will be dependent on other factors including volume flow, tubing diameter and airway diameters.
  65. 65. • Within the patient airway, gases tend to be more humidified and at a higher temperature, factors that reduced density ,Critical flow values then will exhibit dependencies on temperature and humidity. • The figure above indicates that the critical flow represented in l/min correlates fairly well with airway diameter (mm).
  66. 66. • For example anesthetic flow through a 10mm internal diameter endotracheal tube would transition from laminar to turbulent flow when the flow rate would increase to above about 10 l/min. • Similarly if the tracheal diameter is about 15 mm, then the transitional flow to turbulence would occur at flow rates above about 15 l/min.
  67. 67. • Within normal breathing cycle, higher flows, peaking at over 50 l/min would be associated with turbulence while laminar flow would be typical elsewhere in the respiratory cycle.
  68. 68. • The figure above indicates a greater likelihood that air flow would remain laminar compared to the combination of nitrous oxide + oxygen. • Within the respiratory tract, the narrower, smaller flow pathways in the lung, typically in the lower part of the respiratory tract, would predispose to laminar flow.
  69. 69. cont • Corrugated surface of anaesthetic tubing induces turbulence at a lower flow than a smooth tube • Any sharp bends or angle increase the incidence of turbulence flow, • Eg turbulence at the connector of an endotracheal tube
  70. 70. Elbow adapter between anesthetic circuit and endotracheal tube .
  71. 71. • For "quiet breathing", much of the respiratory tract flow would be laminar; however speaking or coughing or sighing (deep breath) would induce turbulence. Sharp tubing bends and rougher(corrugated) internal surfaces also predispose to turbulence as suggested at the connecting site for an endotracheal tube (below):
  72. 72. Venturi effect • Some equipments have a tube with a constriction in which across section area gradually decreases and then increase, this instrument is a venturi meter • If the pressure along the tube is measured it is found that the pressure at the narrowest part is lower than other areas • This fall of pressure at the constriction (narrow)is called venturi effect.
  73. 73. • The Venturi effect is the reduction in fluid pressure that results when a fluid flows through a constricted section of pipe. • The Venturi effect is named after Giovanni Battista Venturi (1746–1822). • The Venturi effect is a jet effect;
  74. 74. • Eg as with an (air) funnel, or a thumb on a garden hose, the velocity of the fluid increases as the cross sectional area decreases, with the static pressure correspondingly decreasing.
  75. 75. How does it arises • Flowing fluid contains energy in two forms kinetic energy associated with flow and potential energy associated with pressure. • At a constriction there is a considerable increase of fluid velocity hence a gain in kinetic energy. • A gain in kinetic energy can only occur if there is a fall in potential energy ,This is because the total energy present must remain constant.
  76. 76. • According to the laws governing fluid dynamics, a fluid's velocity must increase as it passes through a constriction to satisfy the conservation of mass, • while its pressure must decrease to satisfy the conservation of energy. • Thus any gain in kinetic energy a fluid may accrue due to its increased velocity through a constriction is negated by a drop in pressure.
  77. 77. • As the tube widens the fluid velocity falls together with its kinetic energy hence the potential energy and the pressure rises. • IF you have a pressure gauge at the constriction which is removed and leave the tube open at this area • The pressure at this point is below atmospheric pressure , air or fluid will be entrained through this opening(INJECTOR)
  78. 78. • Kinetic energy can also be converted to heat energy by the friction of the moving fluid with its container • For the system to work efficiently the friction force which cause change in pressure between two terminal end must be small so that negligible amount of heat energy is lost. • This will balance the two energy.
  79. 79. An equation for the drop in
  80. 80. Bernoulli's theorem • Bernoulli's theorem: • P1 + 1/2P v1 2 = P2 + 1/2 Pv2 2 • where v = flow velocity, P1or 2 = pressure andP = density. • (this form is for a horizontal "tube" such that gravitational contributions may be omitted) • Also, A1v1=A2v2 where A is the circular cross- sectional area and v = flow velocity
  81. 81. application • The Venturi oxygen mask is based on the Venturi principal in that relatively rapidly moving oxygen molecules pull along (entrainment) air molecules by two processes:
  82. 82. 1. the first process is based on the Bernoulli effect in which there is a relative reduction in pressure associated with the higher oxygen velocity from the injector – 2. and the second involves friction between the high-speed oxygen molecules in the lower speed air molecules which has the effect of pulling air molecules into the higher speed stream of oxygen(JET INTRAINMENT) – Translational momentum transfer occurs as the air molecules increased their velocity.
  83. 83. This injector therefore dilutes oxygen with air provides clinically useful concentraions
  84. 84. Venturi Mask (oxygen molecules: blue; air molecules green
  85. 85. • Entrainment ratio can be calculated as a function of the entrainment flow to the driving (oxygen) flow. Entrainment ratio = (entrainment flow) / (driving flow). • If the ratio were 8:1, then 8 l/min of air would be entrained by the driving gas (oxygen) of 1 l/min.
  86. 86. • Factors that could change the entrainment ratio include • transient obstruction at the outlet of te venturi, (reduce) • change back pressure, which would ultimately change the flow and so the resulting oxygen concentration delivered
  87. 87. Bernoulli's Principle • Bernoulli's Principle states that as the speed of a moving fluid increases, the pressure within the fluid decreases. • for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure ( a decrease in the fluid's potential energy . )
  88. 88. • For Bernoulli's Principle to apply, the fluid is assumed to have these qualities: -fluid flows smoothly -fluid flows without any swirls (which are called "eddies") -fluid flows everywhere through the pipe (which means there is no "flow separation") -fluid has the same density everywhere (it is "incompressible" like water)
  89. 89. • As a fluid passes through a pipe that narrows or widens, the velocity and pressure of the fluid vary. • As the pipe narrows, the fluid flows more quickly. • Bernoulli's Principle tells us that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases!
  90. 90. Narrow pipe widens As cross- sectional area increases, velocity drops and pressure slightly increases Rocket nozzle Exhaust is shot at high speed out of narrow opening
  91. 91. • Bernoulli's principle can be derived from the principle of conservation of energy. • This states that, in a steady flow, the sum of all forms of mechanical energy in a fluid along a streamline is the same at all points on that streamline. • This requires that the sum of kinetic energy and potential energy remain constant.
  92. 92. • If the fluid is flowing out of a reservoir the sum of all forms of energy is the same on all streamlines because in a reservoir the energy per unit mass (the sum of pressure and gravitational potential ρ g h) is the same everywhere. • Fluid particles are subject only to pressure and their own weight[
  93. 93. • If a fluid is flowing horizontally and along a section of a streamline, where the speed increases it can only be because the fluid on that section has moved from a region of higher pressure to a region of lower pressure; • if its speed decreases, it can only be because it has moved from a region of lower pressure to a region of higher pressure. Consequently, within a fluid flowing horizontally, the highest speed occurs where the pressure is lowest, and the lowest speed occurs where the pressure is highest.
  94. 94. • This demonstration of Bernoulli's Principle . While blowing through the narrow part, remove your finger that is holding the ball inside the inverted funnel. • The ball will hover in the funnel until your breath runs out.
  95. 95. A ping pong ball is contained in an inverted funnel. Blowing into the small tube end of the funnel causes the ping pong ball to rise to the top (narrow end) of the funnel.
  96. 96. references • Basic physics and measurements in anaesthesia by P d davis • Textbook of Anaesthesia by smith • www.wekipedia.com

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