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Gas, tubes and flow
ENT/HEAD AND NECK
Gas, tubes and flow
Learning objectives
Viki Mitchell After reading this article, you should be able to: C understand flow characteristics of gas through tubes C understand the characteristics of laminar and turbulent flow and how they relate to the respiratory system C understand the Bernoulli principle and Venturi effect and how they can be incorporated into medical devices
Kate Cheesman
Abstract Gases behave as ‘fluids’ under flow conditions. There are two main flow patterns: laminar and turbulent. Here, we review the flow characteristics of gases and how they relate to the airway and endotracheal tubes. An understanding of these characteristics can be manipulated to improve flow in clinical situations; for example, using a gas with a lower density than air such as heliox reduces turbulent flow and may be helpful in patients with airway obstruction. The Bernoulli principle and Venturi effect have been used to develop fixed-performance masks, jet ventilators and suction devices.
where Q is the flow rate, P is the pressure gradient along the tube, r is the radius of the tube, h is the viscosity of the fluid, and l is the length of the tube. Important features of laminar flow are: the pressure drop down the tube is directly proportional to the flow rate and inversely proportional to the viscosity (not the density) of the fluid resistance is inversely proportional to the 4th power of the radius.
Keywords Bernoulli principle; Coanda effect; fluid flow; heliox; laminar flow; turbulent flow; Venturi effect; viscosity Royal College of Anaesthetists CPD matrix: 3A02
Viscosity (pascal seconds, Pa s) is the property of a fluid that causes it to resist flow, it refers to the ‘stickiness’ of a fluid. When comparing the flow of water through a tube with a more viscous substance such as honey, water flows faster. The velocities of the adjacent layers of the fluid differ, and a ‘slip’ occurs between parallel layers as a result of the shear force acting between them. It is dependent on the intermolecular forces. At higher temperatures the molecules have more kinetic energy and, therefore, it is easier to break the bonds and viscosity decreases and hence the flow increases. The viscosity of Newtonian fluids decreases with increase in temperature and, hence, flow increases. Blood is non-Newtonian and its viscosity is largely dependent on haematocrit, red cell characteristics and blood protein levels. Its viscosity increases in diseases such as leukaemia and flow decreases, which can result in ‘sludging’ in the pulmonary and cerebral vasculature. Treatment often involves fluid ‘hyper-hydration’ to ‘dilute’ the blood and reduce viscosity, thereby increasing flow. In truth, the viscosity of gases increases with increased temperatures as the gas molecules collide more, but this is not significant at clinically experienced temperatures.
Gases and liquids have different physical properties but behave similarly under flow conditions and are both ‘fluids’. An understanding of the principles of fluid mechanics is helpful when looking at flow of gas within the respiratory system. The behaviour of gases is described in terms of pressure, volume and temperature and is governed by the gas laws (Box 1). The general physical principles governing the behaviour of gases are described in Anaesthesia and Intensive Care Medicine 2012; 13(3): 102e105.
Fluid flow Flow is defined as the volume of gas or liquid passing a crosssectional area per unit of time; its dimension is litres per second. It is produced by application of a pressure gradient. The two main patterns of flow are: laminar and turbulent flow. Laminar flow During laminar flow, the molecules of the fluid move in smooth parallel concentric streams without eddies. Molecules at the edge of the tube move more slowly than those in the middle due to the frictional forces between the fluid and the side of the tube; this produces the classical parabolic flow profile (Figure 1). Laminar flow in Newtonian fluids (fluids with constant viscosities) is governed by Poiseuille’s law and the HagenePoiseuille equation: FlowðQÞ ¼
Changing from laminar to turbulent flow (Reynolds number): several factors determine which type of flow predominates, and these are amalgamated into the Reynolds number (Re), a
pPr4 8hl
Gas laws Boyle’s law Charles’s law Gay-Lussac’s law Ideal gas law
Viki Mitchell MBBS FRCA is a Consultant Anaesthetist at University College Hospitals London. Conflicts of interest: none declared.
k, constant; n, number of moles of gas; P, pressure; R, gas constant (8.3143 J/mol/K, where K is the absolute temperature); T, temperature (in Kelvin); V, volume.
Kate Cheesman FRCA BSc is an Anaesthetic SpR with the North Central London Rotation. Her interests include Obstetric and ENT Anaesthesia. Conflicts of interest: none declared.
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
PV ¼ k (at constant temperature) V=T ¼ k (at constant pressure) P=T ¼ k (at constant volume) PV ¼ nRT
Box 1
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Ó 2014 Elsevier Ltd. All rights reserved.
ENT/HEAD AND NECK
Laminar and turbulent flow P1
P2
P1
P2
Vmax P1 › P2
Velocity
Velocity
During laminar flow (smooth, steady flow) the flow profile is parabolic, with the fluid travelling most quickly at the centre of the tube and not moving at the edges of the tube. During turbulent flow (fluctuating and agitated flow) the flow profile is essentially flat, with all fluid travelling at the same velocity except at the tube edges where flow velocity is zero. Figure 1
dimensionless value that is a measure of the ratio of inertial forces to viscous forces:
Pressure gradient and flow
Re ¼
Laminar flow
where Re is the Reynolds number, v is the linear velocity of the fluid, r is the density (mass per unit volume), h is the viscosity, and d is the diameter of the tube. Laminar flow occurs at Re less than 2000, where viscous forces are dominant. There is a period of ‘transitional flow’ between Re 2000 and 4000, where pressure is related both directly to the flow rate (laminar) and to the square root of the flow rate (turbulent). At Re >4000, turbulent flow occurs.
ΔP
gradient = resistance = ΔP = 8ηl flow π
Turbulent flow During turbulent flow, the molecules swirl in eddies and vortices rather than in an orderly way, so that they have a rotational as well as a linear velocity (Figure 1). Irregularities and corners in the tube facilitate turbulence. Conversion from laminar flow to turbulent flow approximately halves the flow for a given pressure drop (Figure 2). The rate of turbulent flow is a function of fluid density, not viscosity like laminar flow. There is no precise equation to calculate turbulent flow.
Flow Turbulent flow ΔP Δ Gradient (resistance) is not constant but increases with flow and at any given flow is related to density
Clinical application These characteristics are important in the airways. Laminar flow requires less pressure change for the same flow rate, hence less energy expenditure. The smaller the airway, the greater the increase in resistance; for example, if the diameter of a trachea is reduced by half, the flow through it is reduced by a factor of 16. This explains why a paediatric airway is so dramatically affected by tracheal oedema or secretions inside the tracheal tube. In the airways, laminar flow usually occurs only in the small conducting airways, where the Re is low. Flow tends to be turbulent in the trachea and larynx, where the velocity of airflow is
Flow ΔP, pressure gradient along the tube; η, viscosity of the fluid; l, length of the tube; r, radius of the tube; ρ, density
Figure 2
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
rvd h
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Ó 2014 Elsevier Ltd. All rights reserved.
ENT/HEAD AND NECK
high. Transitional flow Re 2000e4000 occurs in most of the bronchial tree. These factors are important in the partially obstructed upper airway.
Variable orifice flowmeter
Heliox A helium and oxygen mixture can be used to increase flow at the level of the obstruction, where turbulent flow predominates. Heliox is a mixture of helium (70%) and oxygen (30%), and is one fifth the density of a nitrogen (70%) and oxygen (30%) mixture (helium is 0.166, nitrogen 1.165 kg/m3). Because the viscosities of these mixtures are similar, no clinical difference is seen during laminar flow. Heliox improves gas flow only if flow is turbulent, so it is advantageous to use heliox if there is narrowing of the upper airway, but not if there is bronchospasm because the distal airways exhibit laminar flow. However, if bronchoconstiction is severe and affects the whole bronchial tree, airflow may become turbulent and heliox may have a role. Tracheal tubes Using fluid mechanics, the variability of flow through different tracheal tubes can be understood. Although tracheal tubes offer resistance to airflow, they do not add resistance to the airway because they replace the inherent resistance from the nose and trachea, which accounts for 30e40% of normal airway resistance. If the diameter of a tracheal tube is halved, the flow is reduced by a factor of 16. Length of the tube is also important because resistance is directly proportional. A curved tube (i.e. south polar or RAE) increases the resistance, as does an angled catheter mount, thereby increasing the likelihood of turbulent flow. A short (cut), wide, straight tube provides least resistance to flow and allows for easy suction and clearance of airway secretions, hence the preference in intensive care patients. However, there are disadvantages to large tubes, including difficulty in inserting the tube initially owing to obscuring of the laryngeal inlet, thereby increasing the risk of trauma and failed intubation as well as increasing the incidence of sore throat and hoarseness with tubes with an internal diameter >7 mm. The additional inspiratory work of breathing due to a small tube is overcome by positive pressure ventilation. In patients who are breathing spontaneously, 6- and 7-mm tracheal tubes are well tolerated, and the extra work of breathing compared with a more conventional 8- or 9-mm tube is likely to be a problem only in patients with critical respiratory compromise.
At low flows (left) viscosity of the gas is important as flow is laminar, at high flows (right) density is important as flow is orificial Figure 3
area of the ring-shaped gap or annulus between the bobbin and the tube wall is proportional to the height of the bobbin. At low flows, the gap is small and the restriction is approximately tubular, and so flow is laminar and is dependent on viscosity.
The Bernouilli effect
P1 V1
P2 V2
Flow through orifices In the ideal orifice, the length is smaller than the radius. Flow through an orifice (Q) is always turbulent and is inversely proportional to the square root of density (r): FlowðQÞ ¼
1 Or
Rotameter Rotameters are widely used for measuring the flow rates of gases. They are known as variable orifice flowmeters because they consist of a tapered vertical tube and a bobbin or ball (Figure 3). The pressure of the gas flowing upwards supports the bobbin, and an equilibrium position is reached when the pressure is exactly equal to the weight of the bobbin. The cross-sectional
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
Fluid velocity (and kinetic energy) increases as it passes a constriction. Because total energy state must remain constant, potential energy falls and this is reflected in a pressure drop P, pressure; V, linear velocity
Figure 4
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Ó 2014 Elsevier Ltd. All rights reserved.
ENT/HEAD AND NECK
The Coanda effect
The Venturi mask
A
B
B
The fluid clings to the area of low pressure A past the constriction and is diverted preferentially down one arm of a Y-tube
A As 100% O2 is passed through constriction A, it entrains air via the vents B. The degree of entrainment is controlled by the flow of O2 and the size of the vents (B), but is independent of the patient’s minute ventilation; i.e. 24% oxygen mask requires a flow rate of 2 l/min and entrains 38 l/min of room air
Figure 6
entrainment, which is controlled by the flow of oxygen and the size of the entrainment vents but is independent of the patient’s minute volume. For example, the 24% oxygen mask requires a flow rate of 2 litres per minute and entrains 38 litres of air per minute.
Figure 5
At higher flows, the width of the gap is wider than its length, and so it behaves as an orifice and flow becomes a function of gas density, hence turbulent flow. Gas density decreases with decreasing barometric pressure; at high altitude, turbulent flow will be increased. Rotameters are calibrated for a specific density, and so will under-read at high flows in such situations.
Coanda effect The Coanda effect describes the channelling of fluid. Imagine the Venturi principle without the vents to allow entrainment of another fluid: there is still a pressure drop but no entrainment, instead the pressure drop causes the fluid to ‘cling’ to the solid edge where the pressure is lowest. If a tube is divided into two tubes e i.e. a Y shape e fluid is channelled preferentially down one tributary. It is thought to explain the maldistribution of air in the pulmonary tree following a constriction in a bronchiole, as the flow will stream along one fork of the division, leading to unequal distribution of gas flow (Figure 6). The Coanda effect can be used to produce valveless ventilators, which are useful in ventilating small children, where resistance to flow needs to be minimal. A
The Bernoulli effect and Venturi principle The Bernoulli effect is the reduction in pressure when a fluid accelerates through a constriction. The velocity, and therefore kinetic energy, increases. By the law of the conservation of energy, the total energy must remain the same; potential and therefore pressure are reduced (Figure 4). A Venturi tube is one that has a restriction followed by a dilatation. At the level of the restriction where there is a pressure drop, a second fluid can be ‘entrained’ through a side vent, resulting in a mixture of fluids with a fixed ratio.
FURTHER READING Dimech J, Sturman J. Measurement of respiratory function: ventilation. Anaesthesia and Intensive Care Medicine 2008; 9: 432e6. Koh KF, Hare JD, Calder I. Small tubes revisited. Anaesthesia 1998; 53: 46e50. Mandal N. Measurement of volume and flow in gases. Anaesthesia and Intensive Care Medicine 2008; 10: 52e6. Thomas G, Stamatakis S. Physics of gases. Anaesthesia and Intensive Care Medicine 2008; 10: 48e51.
Clinical application Fixed-performance oxygen masks, suction, the Sanders injector, and scavenging equipment are all based on entrainment (Figure 5). Fixed-performance masks (Venturi masks) can deliver a fractional inspired oxygen concentration of 0.24e0.60. Oxygen is passed through a narrow orifice on the mask, which generates a jet of the gas that entrains a constant proportion of air. The concentration of oxygen delivered depends on the degree of air
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
228
Ó 2014 Elsevier Ltd. All rights reserved.
Gas, tubes and flow
Learning objectives
Viki Mitchell After reading this article, you should be able to: C understand flow characteristics of gas through tubes C understand the characteristics of laminar and turbulent flow and how they relate to the respiratory system C understand the Bernoulli principle and Venturi effect and how they can be incorporated into medical devices
Kate Cheesman
Abstract Gases behave as ‘fluids’ under flow conditions. There are two main flow patterns: laminar and turbulent. Here, we review the flow characteristics of gases and how they relate to the airway and endotracheal tubes. An understanding of these characteristics can be manipulated to improve flow in clinical situations; for example, using a gas with a lower density than air such as heliox reduces turbulent flow and may be helpful in patients with airway obstruction. The Bernoulli principle and Venturi effect have been used to develop fixed-performance masks, jet ventilators and suction devices.
where Q is the flow rate, P is the pressure gradient along the tube, r is the radius of the tube, h is the viscosity of the fluid, and l is the length of the tube. Important features of laminar flow are: the pressure drop down the tube is directly proportional to the flow rate and inversely proportional to the viscosity (not the density) of the fluid resistance is inversely proportional to the 4th power of the radius.
Keywords Bernoulli principle; Coanda effect; fluid flow; heliox; laminar flow; turbulent flow; Venturi effect; viscosity Royal College of Anaesthetists CPD matrix: 3A02
Viscosity (pascal seconds, Pa s) is the property of a fluid that causes it to resist flow, it refers to the ‘stickiness’ of a fluid. When comparing the flow of water through a tube with a more viscous substance such as honey, water flows faster. The velocities of the adjacent layers of the fluid differ, and a ‘slip’ occurs between parallel layers as a result of the shear force acting between them. It is dependent on the intermolecular forces. At higher temperatures the molecules have more kinetic energy and, therefore, it is easier to break the bonds and viscosity decreases and hence the flow increases. The viscosity of Newtonian fluids decreases with increase in temperature and, hence, flow increases. Blood is non-Newtonian and its viscosity is largely dependent on haematocrit, red cell characteristics and blood protein levels. Its viscosity increases in diseases such as leukaemia and flow decreases, which can result in ‘sludging’ in the pulmonary and cerebral vasculature. Treatment often involves fluid ‘hyper-hydration’ to ‘dilute’ the blood and reduce viscosity, thereby increasing flow. In truth, the viscosity of gases increases with increased temperatures as the gas molecules collide more, but this is not significant at clinically experienced temperatures.
Gases and liquids have different physical properties but behave similarly under flow conditions and are both ‘fluids’. An understanding of the principles of fluid mechanics is helpful when looking at flow of gas within the respiratory system. The behaviour of gases is described in terms of pressure, volume and temperature and is governed by the gas laws (Box 1). The general physical principles governing the behaviour of gases are described in Anaesthesia and Intensive Care Medicine 2012; 13(3): 102e105.
Fluid flow Flow is defined as the volume of gas or liquid passing a crosssectional area per unit of time; its dimension is litres per second. It is produced by application of a pressure gradient. The two main patterns of flow are: laminar and turbulent flow. Laminar flow During laminar flow, the molecules of the fluid move in smooth parallel concentric streams without eddies. Molecules at the edge of the tube move more slowly than those in the middle due to the frictional forces between the fluid and the side of the tube; this produces the classical parabolic flow profile (Figure 1). Laminar flow in Newtonian fluids (fluids with constant viscosities) is governed by Poiseuille’s law and the HagenePoiseuille equation: FlowðQÞ ¼
Changing from laminar to turbulent flow (Reynolds number): several factors determine which type of flow predominates, and these are amalgamated into the Reynolds number (Re), a
pPr4 8hl
Gas laws Boyle’s law Charles’s law Gay-Lussac’s law Ideal gas law
Viki Mitchell MBBS FRCA is a Consultant Anaesthetist at University College Hospitals London. Conflicts of interest: none declared.
k, constant; n, number of moles of gas; P, pressure; R, gas constant (8.3143 J/mol/K, where K is the absolute temperature); T, temperature (in Kelvin); V, volume.
Kate Cheesman FRCA BSc is an Anaesthetic SpR with the North Central London Rotation. Her interests include Obstetric and ENT Anaesthesia. Conflicts of interest: none declared.
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
PV ¼ k (at constant temperature) V=T ¼ k (at constant pressure) P=T ¼ k (at constant volume) PV ¼ nRT
Box 1
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Ó 2014 Elsevier Ltd. All rights reserved.
ENT/HEAD AND NECK
Laminar and turbulent flow P1
P2
P1
P2
Vmax P1 › P2
Velocity
Velocity
During laminar flow (smooth, steady flow) the flow profile is parabolic, with the fluid travelling most quickly at the centre of the tube and not moving at the edges of the tube. During turbulent flow (fluctuating and agitated flow) the flow profile is essentially flat, with all fluid travelling at the same velocity except at the tube edges where flow velocity is zero. Figure 1
dimensionless value that is a measure of the ratio of inertial forces to viscous forces:
Pressure gradient and flow
Re ¼
Laminar flow
where Re is the Reynolds number, v is the linear velocity of the fluid, r is the density (mass per unit volume), h is the viscosity, and d is the diameter of the tube. Laminar flow occurs at Re less than 2000, where viscous forces are dominant. There is a period of ‘transitional flow’ between Re 2000 and 4000, where pressure is related both directly to the flow rate (laminar) and to the square root of the flow rate (turbulent). At Re >4000, turbulent flow occurs.
ΔP
gradient = resistance = ΔP = 8ηl flow π
Turbulent flow During turbulent flow, the molecules swirl in eddies and vortices rather than in an orderly way, so that they have a rotational as well as a linear velocity (Figure 1). Irregularities and corners in the tube facilitate turbulence. Conversion from laminar flow to turbulent flow approximately halves the flow for a given pressure drop (Figure 2). The rate of turbulent flow is a function of fluid density, not viscosity like laminar flow. There is no precise equation to calculate turbulent flow.
Flow Turbulent flow ΔP Δ Gradient (resistance) is not constant but increases with flow and at any given flow is related to density
Clinical application These characteristics are important in the airways. Laminar flow requires less pressure change for the same flow rate, hence less energy expenditure. The smaller the airway, the greater the increase in resistance; for example, if the diameter of a trachea is reduced by half, the flow through it is reduced by a factor of 16. This explains why a paediatric airway is so dramatically affected by tracheal oedema or secretions inside the tracheal tube. In the airways, laminar flow usually occurs only in the small conducting airways, where the Re is low. Flow tends to be turbulent in the trachea and larynx, where the velocity of airflow is
Flow ΔP, pressure gradient along the tube; η, viscosity of the fluid; l, length of the tube; r, radius of the tube; ρ, density
Figure 2
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
rvd h
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Ó 2014 Elsevier Ltd. All rights reserved.
ENT/HEAD AND NECK
high. Transitional flow Re 2000e4000 occurs in most of the bronchial tree. These factors are important in the partially obstructed upper airway.
Variable orifice flowmeter
Heliox A helium and oxygen mixture can be used to increase flow at the level of the obstruction, where turbulent flow predominates. Heliox is a mixture of helium (70%) and oxygen (30%), and is one fifth the density of a nitrogen (70%) and oxygen (30%) mixture (helium is 0.166, nitrogen 1.165 kg/m3). Because the viscosities of these mixtures are similar, no clinical difference is seen during laminar flow. Heliox improves gas flow only if flow is turbulent, so it is advantageous to use heliox if there is narrowing of the upper airway, but not if there is bronchospasm because the distal airways exhibit laminar flow. However, if bronchoconstiction is severe and affects the whole bronchial tree, airflow may become turbulent and heliox may have a role. Tracheal tubes Using fluid mechanics, the variability of flow through different tracheal tubes can be understood. Although tracheal tubes offer resistance to airflow, they do not add resistance to the airway because they replace the inherent resistance from the nose and trachea, which accounts for 30e40% of normal airway resistance. If the diameter of a tracheal tube is halved, the flow is reduced by a factor of 16. Length of the tube is also important because resistance is directly proportional. A curved tube (i.e. south polar or RAE) increases the resistance, as does an angled catheter mount, thereby increasing the likelihood of turbulent flow. A short (cut), wide, straight tube provides least resistance to flow and allows for easy suction and clearance of airway secretions, hence the preference in intensive care patients. However, there are disadvantages to large tubes, including difficulty in inserting the tube initially owing to obscuring of the laryngeal inlet, thereby increasing the risk of trauma and failed intubation as well as increasing the incidence of sore throat and hoarseness with tubes with an internal diameter >7 mm. The additional inspiratory work of breathing due to a small tube is overcome by positive pressure ventilation. In patients who are breathing spontaneously, 6- and 7-mm tracheal tubes are well tolerated, and the extra work of breathing compared with a more conventional 8- or 9-mm tube is likely to be a problem only in patients with critical respiratory compromise.
At low flows (left) viscosity of the gas is important as flow is laminar, at high flows (right) density is important as flow is orificial Figure 3
area of the ring-shaped gap or annulus between the bobbin and the tube wall is proportional to the height of the bobbin. At low flows, the gap is small and the restriction is approximately tubular, and so flow is laminar and is dependent on viscosity.
The Bernouilli effect
P1 V1
P2 V2
Flow through orifices In the ideal orifice, the length is smaller than the radius. Flow through an orifice (Q) is always turbulent and is inversely proportional to the square root of density (r): FlowðQÞ ¼
1 Or
Rotameter Rotameters are widely used for measuring the flow rates of gases. They are known as variable orifice flowmeters because they consist of a tapered vertical tube and a bobbin or ball (Figure 3). The pressure of the gas flowing upwards supports the bobbin, and an equilibrium position is reached when the pressure is exactly equal to the weight of the bobbin. The cross-sectional
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
Fluid velocity (and kinetic energy) increases as it passes a constriction. Because total energy state must remain constant, potential energy falls and this is reflected in a pressure drop P, pressure; V, linear velocity
Figure 4
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Ó 2014 Elsevier Ltd. All rights reserved.
ENT/HEAD AND NECK
The Coanda effect
The Venturi mask
A
B
B
The fluid clings to the area of low pressure A past the constriction and is diverted preferentially down one arm of a Y-tube
A As 100% O2 is passed through constriction A, it entrains air via the vents B. The degree of entrainment is controlled by the flow of O2 and the size of the vents (B), but is independent of the patient’s minute ventilation; i.e. 24% oxygen mask requires a flow rate of 2 l/min and entrains 38 l/min of room air
Figure 6
entrainment, which is controlled by the flow of oxygen and the size of the entrainment vents but is independent of the patient’s minute volume. For example, the 24% oxygen mask requires a flow rate of 2 litres per minute and entrains 38 litres of air per minute.
Figure 5
At higher flows, the width of the gap is wider than its length, and so it behaves as an orifice and flow becomes a function of gas density, hence turbulent flow. Gas density decreases with decreasing barometric pressure; at high altitude, turbulent flow will be increased. Rotameters are calibrated for a specific density, and so will under-read at high flows in such situations.
Coanda effect The Coanda effect describes the channelling of fluid. Imagine the Venturi principle without the vents to allow entrainment of another fluid: there is still a pressure drop but no entrainment, instead the pressure drop causes the fluid to ‘cling’ to the solid edge where the pressure is lowest. If a tube is divided into two tubes e i.e. a Y shape e fluid is channelled preferentially down one tributary. It is thought to explain the maldistribution of air in the pulmonary tree following a constriction in a bronchiole, as the flow will stream along one fork of the division, leading to unequal distribution of gas flow (Figure 6). The Coanda effect can be used to produce valveless ventilators, which are useful in ventilating small children, where resistance to flow needs to be minimal. A
The Bernoulli effect and Venturi principle The Bernoulli effect is the reduction in pressure when a fluid accelerates through a constriction. The velocity, and therefore kinetic energy, increases. By the law of the conservation of energy, the total energy must remain the same; potential and therefore pressure are reduced (Figure 4). A Venturi tube is one that has a restriction followed by a dilatation. At the level of the restriction where there is a pressure drop, a second fluid can be ‘entrained’ through a side vent, resulting in a mixture of fluids with a fixed ratio.
FURTHER READING Dimech J, Sturman J. Measurement of respiratory function: ventilation. Anaesthesia and Intensive Care Medicine 2008; 9: 432e6. Koh KF, Hare JD, Calder I. Small tubes revisited. Anaesthesia 1998; 53: 46e50. Mandal N. Measurement of volume and flow in gases. Anaesthesia and Intensive Care Medicine 2008; 10: 52e6. Thomas G, Stamatakis S. Physics of gases. Anaesthesia and Intensive Care Medicine 2008; 10: 48e51.
Clinical application Fixed-performance oxygen masks, suction, the Sanders injector, and scavenging equipment are all based on entrainment (Figure 5). Fixed-performance masks (Venturi masks) can deliver a fractional inspired oxygen concentration of 0.24e0.60. Oxygen is passed through a narrow orifice on the mask, which generates a jet of the gas that entrains a constant proportion of air. The concentration of oxygen delivered depends on the degree of air
ANAESTHESIA AND INTENSIVE CARE MEDICINE 15:5
228
Ó 2014 Elsevier Ltd. All rights reserved.