Basic physics for the anaesthetist

Basic definitions

It is now customary in medical practice to employ the International System (Système Internationale; SI) of units. Common exceptions to the use of the SI system include measurement of arterial pressure and, to a lesser extent, gas pressure. The mercury column is used to calibrate electronic arterial pressure measuring devices and so ‘mmHg’ is retained. Sea-level atmospheric pressure is often referred to as 760 mmHg or 1.013 bar (or approximately 1 bar). Low pressures are expressed usually in kilopascals (kPa), whilst higher pressures are referred to in bar (100 kPa = 1 bar).

The fundamental quantities in physics are mass, length and time, from which other measures can be derived ( Table 15.1 ). Expressed in basic SI units they are as follows:

• Mass (m). The unit of mass is the kilogram (kg).

• Length (l). The unit is the metre (m).

• Time ( t ) . Measured in seconds (s).

From these basic definitions, several units of measurement may be expressed as derived units:

• Volume has units of m ³ .

Density is defined as mass per unit volume:

Velocity is defined as the distance travelled per unit time:

Acceleration is defined as the rate of change of velocity:

Force is that which is required to give mass an acceleration:

The SI unit of force is the newton (N). One newton is the force required to give a mass of 1 kg an acceleration of 1 m s ^–1 :

Weight is the force of the earth's attraction for a body, even if we incorrectly express it as mass. When a body falls freely under the influence of gravity, it accelerates at a rate of 9.81 m s ^–2 ( g ):

Momentum is defined as mass multiplied by velocity:

Note that force is also the rate of change of momentum.

Work is undertaken when a force moves an object:

Energy is the capacity for undertaking work. Thus it has the same units as those of work. Energy can exist in several forms, such as mechanical (kinetic energy (KE) or potential energy (PE)), thermal or electrical, and all have the same units.

Power ( P ) is the rate of doing work. The SI unit of power is the watt:

Pressure is defined as force per unit area:

As 1 Pa is a rather small unit, it is more common in medical practice to use the kilopascal (kPa): 1 kPa ≈ 7.5 mmHg.

Basic mathematical functions

The following mathematical functions relevant to anaesthetic practice are described:

• The straight line

• The rectangular hyperbola

• The exponential

• Rate of change, differentiation

• Area under a curve, integration

For clarity mathematical notation often uses the period as the symbol for product (multiplication). This is used in this chapter when necessary.

The straight line ( Fig. 15.1A ) is a direct relationship between two variables with a constant slope. A relevant example is:

CO ₂ volume production is directly proportional to its partial pressure. Similarly,

where the output voltage from an amplifier is directly proportional to the input voltage, multiplied by the gain, G. These lines go through the origin, but there may be an offset on either axis, for the line

where m is the slope and c is the offset value of y when x = 0; an example here might be a version of Ohm's law:

where the voltage drop across a resistor R carrying a current I is V ₁ – V ₂ .

The rectangular hyperbola ( Fig. 15.1B ) occurs when the product of two variables is constant. A relevant example is Boyle's law at a given temperature T:

Note the curve does not cross either axis, but approaches them asymptotically at each extreme. If the temperature of the gas is raised, the curve is shifted upwards and outwards, indicating greater thermal energy.

An exponential function is one where the magnitude of a variable is proportional to the rate of change of that variable:

and represents many natural and engineering processes. A tear-away exponential, representing bacterial growth for example, is shown in Fig. 15.2A, and a negative exponential ( Fig. 15.2B ) is one where the magnitude of the variable is decreasing; a relevant example here is plasma drug concentration after a bolus injection:

It touches the y-axis and does not touch the x-axis. Useful time values to characterise the behaviour of the variable include the half-life t _1/2 when C = C ₀ /2, and the time constant τ (tau) when C = C ₀ /e. A third variation on the exponential is shown in Fig. 15.2C and represents lung filling, for example.

If we want to express the rate of change of a process using a function of time f(t) (as earlier to define an exponential function for example), calculus allows us to perform a mathematical procedure of differentiation to give df(t)/dt. The differential of velocity (ms ^–1 ) with respect to time is acceleration (ms ^–2 ) The reader is referred to other texts ( ; ) for more detail.

Sometimes it is useful to know the area under a curve, and the opposite mathematical procedure is integration. Examples include calculation of energy of a gas by the area under the P–V curve in Fig. 15.1B or the area under a thermal dilution curve in the calculation of cardiac output.

Fluids

Substances may commonly exist in solid, liquid or gaseous form. Other states exist and may be encountered directly or indirectly by anaesthetists, including plasma and non-classical states such as glass and liquid-crystal. These forms or phases differ from each other according to the random movement of their constituent atoms or molecules. In solids, molecules oscillate about a fixed point, whereas in liquids the molecules possess higher velocities and therefore higher KE; they move more freely and thus do not bear a constant relationship in space to other molecules. The molecules of gases possess even higher KE and move freely to an even greater extent.

Both gases and liquids are termed fluids. Liquids are incompressible and at constant temperature occupy a fixed volume, conforming to the shape of a container; gases have no fixed volume but expand to occupy the total space of a container. Nevertheless, the techniques for analysing the behaviour of liquids and gases (or fluids in general) in terms of their hydraulic and thermodynamic properties are very similar.

In the process of vaporisation, random loss of liquid molecules with higher kinetic (thermal) energies from the liquid, occurs while vapour molecules randomly lose thermal (kinetic) energy and return to the liquid state. Heating a liquid increases the KE of its molecules, permitting a higher proportion to escape from the surface into the vapour phase. The acquisition by these molecules of higher KE requires an energy source, and this usually comes from the thermal energy of the liquid itself, which leads to a reduction in its thermal energy as vaporisation occurs and hence the liquid cools. Vaporisation is discussed in more detail later.

Collision of randomly moving molecules in the gaseous phase with the walls of a container is responsible for the pressure exerted by a gas. The difference between a gas and a vapour will also be discussed later.

Behaviour of gases

There are three gas laws that determine the behaviour of gases and which are important to anaesthetists. These are derived from the kinetic theory of gases; they depend on the assumption that the substances concerned are perfect gases (rather than vapours), and they assume a fixed mass of gas.

Boyle's law states that, at constant temperature, the volume ( V ) of a given mass of gas varies inversely with its absolute pressure ( P ):

$PV=k_1$

Charles’ law states that, at constant pressure, the volume of a given mass of gas varies directly with its absolute temperature ( T ):

$V=k_{2}T$

The third gas law (sometimes known as Gay-Lussac's law) states that, at constant volume, the absolute pressure of a given mass of gas varies directly with its absolute temperature:

$P=k_{3}T$

Combining these three gas laws:

$PV=kT$

or

$\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}$

where suffixes 1 and 2 represent two conditions different in P , V and T of the gas. Note that where a change of conditions occurs slowly enough for T ₁ = T ₂ , conditions are said to be isothermal , and the combined gas law could be thought of as another form of Boyle's law.

Boyle's law can be used to derive Dalton's law of partial pressures to describe a mixture of gases in a container. This states that in such a mixture the pressure exerted by each gas is the same as that which it would exert if it alone occupied the container. Dalton's law can be used to compare volumetric fractions (concentrations) to calculate partial pressures, which are an important concept in anaesthesia. Thus in a cylinder of air at an absolute pressure of 100 bar, the pressure exerted by nitrogen is equal to 79 bar, as the fractional concentration of nitrogen is 0.79.

Avogadro's hypothesis, also deduced from the kinetic theory of gases, states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.

Avogadro's number is the number of molecules in 1 g molecular weight of a substance and is equal to 6.022 × 10 ²³ .

Under conditions of standard temperature and pressure (STP) (0°C and 1.013 bar), 1 g molecular weight (i.e. 28 g of nitrogen or 44 g of carbon dioxide) of any gas occupies a volume of 22.4 litres (L).

These data are useful in calculating, for example, the quantity of gas produced from liquid nitrous oxide. The molecular weight of nitrous oxide is 44. Thus 44 g of N ₂ O occupy a volume of 22.4 L at STP. If a full cylinder of N ₂ O contains 3.0 kg of liquid, then vaporisation of all the liquid would yield:

$\begin{array}{c}\frac{22.4\times 3.0\times 1000L}{44}\\ =1527\text{L at STP}\end{array}$

The gas laws can be applied to calculate its volume at, say, room temperature, bearing in mind that the Kelvin scale of temperature should be used for such calculations.

If the temperature of a vapour is low enough, then sufficient application of pressure to it will result in its liquefaction. If the vapour has a higher temperature, implying greater molecular KE, no amount of compression liquefies it. The critical temperature of such a substance is the temperature above which that substance cannot be liquefied by compression alone because the molecules have too much KE to allow liquefaction. A substance in such a state is considered a gas, whereas a substance in ‘gaseous’ form below its critical temperature is a vapour. The critical pressure is that which must be applied to the substance to liquefy it at the critical temperature.

The critical temperature of oxygen is −118°C, that of nitrogen is −147°C, and that of air is −141°C. Thus at room temperature, cylinders of these substances contain gases. In contrast, the critical temperature of carbon dioxide is 31°C and that of nitrous oxide is 36.4°C. The critical pressures are 73.8 and 72.5 bar, respectively; at higher pressures, cylinders of these substances at UK room temperature contain a mixture of gas and liquid. Fig. 15.3 shows the pressure-volume isotherms for a substance at, below and above its critical temperature.

A ‘full’ cylinder of oxygen on an anaesthetic machine contains compressed gaseous oxygen at a pressure of 137 bar gauge pressure. If the cylinder of oxygen slowly empties and the temperature remains constant, the volume of gas contained is related linearly to its absolute pressure (by Boyle's law). In practice, linearity is not followed because temperature falls as a result of adiabatic expansion of the compressed gas; the term adiabatic implies a change in the condition (pressure, volume and temperature) of a gas without exchange of heat energy with its surroundings.

By contrast, a nitrous oxide cylinder contains liquid nitrous oxide in equilibrium with its vapour. The pressure in the cylinder remains relatively constant at the saturated vapour pressure for that temperature as the cylinder empties to the point at which liquid has totally vaporised. Rapid emptying of the cylinder will reduce the cylinder temperature and hence the vapour pressure. Subsequently, there is a linear decline (linear assumes constant temperature) in pressure proportional to the decline in volume of gas remaining within the cylinder.

Filling ratio

The degree of filling of a nitrous oxide cylinder is expressed as the mass of nitrous oxide in the cylinder divided by the mass of water that the cylinder could hold. Normally a cylinder of nitrous oxide is filled to a ratio of 0.75 in a temperate climate. This should not be confused with the volume of liquid nitrous oxide in a cylinder. A ‘full’ cylinder of nitrous oxide at room temperature is filled to the point at which approximately 90% of the interior of the cylinder is occupied by liquid, the remaining 10% being occupied by nitrous oxide vapour. Incomplete filling of a cylinder is necessary because thermally induced expansion of the liquid in a totally full cylinder may cause cylinder rupture. Because vapour pressure increases with temperature, it is necessary to have a lower filling ratio in tropical climates (0.67) than in temperate climates.

Entonox

Entonox is the trade name for a compressed gas mixture containing 50% oxygen and 50% nitrous oxide. The mixture is compressed into cylinders containing gas at a pressure of 137 bar gauge pressure (see later). The nitrous oxide does not liquefy because the two gases in this mixture dissolve in each other at high pressure. In other words, the presence of oxygen reduces the critical temperature of nitrous oxide. The critical temperature of the mixture is −7°C, the ‘pseudocritical temperature’. Cooling of a cylinder of Entonox to a temperature below −7°C results in separation of liquid nitrous oxide, and its use results in oxygen-rich gas being released initially, followed by a hypoxic nitrous oxide-rich gas. Consequently it is recommended that when an Entonox cylinder may have been exposed to low temperatures, it should be stored horizontally for a period of not less than 24 h at a temperature of 5°C or above. In addition, the cylinder should be inverted several times before use.

Pressure

Although the use of SI units of measurement is generally accepted in medicine, a variety of ways of expressing pressure are still used, reflecting custom and practice. Arterial pressure is still referred to universally in terms of mmHg because a column of mercury is still used occasionally to measure arterial pressure and to calibrate electronic devices.

Measurement of central venous pressure is sometimes referred to in cmH ₂ O because it can be measured using a manometer filled with saline, but it is more commonly described in mmHg when using an electronic transducer system. Note that, although we speak colloquially of cmH ₂ O or mmHg, the actual expression for pressure measured by a column of fluid is P = ρ. g .H, where ρ is fluid density, g is acceleration as a result of gravity and H is the height of the column. Because mercury is 13.6 times more dense than water, a mercury manometer can measure a given pressure with a much shorter length of column of fluid. For example, atmospheric pressure ( P _B ) exerts a pressure sufficient to support a column of mercury of height 760 mm ( Fig. 15.4 ):

$\begin{array}{c}1\text{atmospheric pressure}=760\text{mmHg}\\ =1.01325\text{bar}\\ =760\text{torr}\\ =1\text{atmosphere absolute}\left(\text{ata}\right)\\ =14.7{\text{lb in}}^{-2}\\ =101.325\text{kPa}\\ =10.33{\text{metres of H}}_{2}O\end{array}$

In considering pressure, it is necessary to indicate whether or not atmospheric pressure is taken into account. Thus a diver working 10 m below the surface of the sea may be described as compressed to a depth of 1 atmosphere or working at a pressure of 2 atmospheres absolute (2 ata).

To avoid confusion when discussing compressed cylinders of gases, the term gauge pressure is used. Gauge pressure describes the pressure of the contents above ambient pressure. Thus a full cylinder of oxygen has a gauge pressure of 137 bar, but the contents are at a pressure of 138 bar absolute.

Gas regulators

Pressure relief valves

The Heidbrink valve is a common component of many anaesthesia breathing systems. In the Magill breathing system, the anaesthetist may vary the force in the spring(s), thereby controlling the pressure within the breathing system ( Fig. 15.5 ). At equilibrium the force exerted by the spring is equal to the force exerted by gas within the system:

$\mathrm{Force}\left(F\right)=gas\mathrm{pressure}\left(P\right)\times \mathrm{disc}\mathrm{area}\left(A\right)$

Modern anaesthesia systems contain a variety of pressure relief valves, in each of which the force is fixed so as to provide a gas escape mechanism when pressure reaches a preset level. Thus an anaesthetic machine may contain a pressure relief valve operating at 35 kPa situated on the back bar of the machine between the vaporisers and the breathing system to protect the flowmeters and vaporisers from excessive pressures. Modern ventilators contain a pressure relief valve set at 7 kPa to protect the patient from barotrauma. A much lower pressure is set in relief valves which form part of anaesthetic scavenging systems, and these may operate at pressures of 0.2–0.3 kPa to protect the patient from negative pressure applied to the lungs.

Pressure-reducing valves (pressure regulators)

Pressure regulators have two important functions in anaesthetic machines:

• They reduce high pressures of compressed gases to manageable levels (acting as pressure-reducing valves).

• They minimise fluctuations in the pressure within an anaesthetic machine, which would necessitate frequent manipulations of flowmeter controls.

Modern anaesthetic machines are designed to operate with an inlet gas supply at a pressure of 3–4 bar (usually 4 bar in the UK), as do hospital pipelines, and therefore no pressure regulators are required between them. In contrast, the contents of cylinders of all medical gases (i.e. oxygen, nitrous oxide, air and Entonox) are at much higher pressures. Thus a pressure-reducing valve is required between the cylinder and the anaesthetic machine flowmeter.

The principle on which the simplest type of pressure-reducing valve operates is shown in Fig. 15.6 . High-pressure gas enters through the valve and forces the flexible diaphragm upwards, tending to close the valve and prevent further ingress of high-pressure gas.

If there is no tension in the spring, the relationship between the reduced pressure (p) and the high pressure ( P ) is very approximately equal to the ratio of the areas of the valve seating ( a ) and the diaphragm ( A ):

$pA=Pa$

or

$\frac{p}{P}=\frac{a}{A}$

By tensing the spring, a force F is produced which offsets the closing effect of the valve. Thus p may be increased by increasing the force in the spring.

Without the spring, the simple pressure regulator has the disadvantage that reduced pressure decreases proportionally with the decrease in cylinder pressure. The addition of a force from the spring considerably reduces but does not eliminate this problem. During high flows, the input to the valve may not be able to keep pace with the output. This can cause the regulated pressure to fall. A two-stage regulator can be employed to overcome this.

Pressure demand regulators

These are regulators in which gas flow occurs when an inspiratory effort is applied to the outlet port. The Entonox valve is a two-stage regulator, and its mode of action is demonstrated in Fig. 15.7 . The first stage is identical to the reducing valve described earlier. The second-stage valve contains a diaphragm. Movement of this diaphragm tilts a rod, which controls the flow of gas from the first-stage valve. The second stage is adjusted so that gas flows only when pressure is below atmospheric.

Flow of fluids

Viscosity (η) is the constant of proportionality relating the stress (τ) between layers of flowing fluid (or between the fluid and the vessel wall) and the velocity gradient across the tube or vessel, dv/dr.

Hence:

$\tau =\eta \frac{dv}{dr}$

or

$\eta =\frac{\mathrm{shear}\mathrm{stress}}{\mathrm{velocity}\mathrm{gradient}}$

In this context, velocity gradient is equal to the difference between velocities of different fluid layers divided by the distance between layers ( Fig. 15.8A ). The units of the coefficient of viscosity are Pascal seconds (Pa s).

Fluids for which η is constant are referred to as Newtonian fluids. However, most biological fluids are non-Newtonian, an example of which is blood; viscosity changes with the rate of flow of blood (as a result of change in distribution of cells) and, in stored blood, with time.

Viscosity of liquids diminishes with increase in temperature, whereas viscosity of a gas increases with increase in temperature. An increase in temperature is due to an increase of KE of fluid molecules. This can be thought of as causing a freeing up of intermolecular bonds in liquids and an increase in intermolecular collisions in gases.

Laminar flow through a tube is illustrated in Fig. 15.8B . In this situation there is a smooth, orderly flow of fluid such that molecules travel with the greatest velocity in the central axial stream, whilst the velocity of those in contact with the wall of the tube may be virtually zero. The linear velocity of axial flow is twice the average linear velocity of flow.

In a tube in which laminar flow occurs, the relationship between flow and pressure is given by the Hagen–Poiseuille formula:

$\dot{Q}=\frac{\pi \Delta P{r}^4}{8\eta l}$

where Q̇ is the flow, Δ P is the pressure gradient along the tube, r is the radius of the tube, η is the viscosity of fluid and l is the length of the tube.

The Hagen–Poiseuille formula applies only to Newtonian fluids and to laminar flow. In non-Newtonian fluids such as blood, increase in velocity of flow may alter viscosity because of variation in the dispersion of cells within plasma.

In turbulent flow, fluid no longer moves in orderly planes but swirls and eddies around in a haphazard manner as illustrated in Fig. 15.9 . Essentially, turbulent flow is less efficient in the transport of fluids because energy is wasted in the eddies, in friction and in sound (bruits). Although viscosity is the important physical variable in relation to the behaviour of fluids in laminar flow, turbulent flow is more markedly affected by changes in fluid density.

The relationship between pressure and flow is linear in the laminar region, but as velocity increases, a point is reached (the critical point or critical velocity) at which the flow becomes turbulent ( Fig. 15.10 ). The critical point depends upon several factors, which are related by the formula used for calculation of (the dimensionless) Reynolds’ number:

$\mathrm{Reynol}{d}^{\prime }s\mathrm{number}=\frac{v\rho r}{\eta }$

where v is the fluid linear velocity, r is the radius of the tube, ρ is the fluid density and η is its viscosity.

Studies with cylindrical tubes have shown that if Reynolds’ number exceeds 2000, flow is likely to be turbulent, whereas if less than 2000, flow is usually laminar. However, localised areas of turbulent flow can occur at lower Reynolds’ numbers when there are changes in fluid direction or changes in cross-sectional area of the tube.

The flow rate in turbulent flow (Q̇) is dependent on the following:

• Square root of the pressure difference driving the flow (ΔP)

• Square of the radius of the vessel (r)

• Square root of density (ρ) of the fluid – that is:

$\dot{Q}\propto \frac{\sqrt{\Delta P}.r^2}{\sqrt{\rho }}$

A tube typically has a length many times its diameter, whereas in an orifice the diameter of the fluid pathway exceeds the length. Flow through an orifice is much more likely to be turbulent.

Turbulence and flow resistance in physiology and anaesthetic practice

In the upper respiratory tract there is often turbulent flow at high flow rates in the trachea, with flow gradually becoming laminar as branching of airways occurs and airway diameter and flow velocity reduce. In addition an obstruction in the upper respiratory tract causes downstream turbulence; thus for the same respiratory effort (driving pressure), a lower tidal volume is achieved than when flow is laminar. The extent of turbulent flow may be reduced by reducing gas density; clinically this is sometimes achieved by administration of oxygen-enriched helium rather than oxygen alone (the density of oxygen is 1.31 kg m ⁻³ and that of helium is 0.16 kg m ⁻³ ). This reduces the likelihood of turbulent flow and reduces the respiratory effort required.

In anaesthetic breathing systems a sudden change in diameter of tubing or irregularity of the wall may be responsible for a change from laminar to turbulent flow. Thus tracheal and other breathing tubes should possess smooth internal surfaces, gradual bends and no constrictions. Resistance to breathing is much greater when a tracheal tube of small diameter is used ( Fig. 15.11 ). Tubes should be of as large a diameter and as short as possible.

In the circulation, high-velocity pulsatile flow from the left ventricle to the aorta, a large diameter vessel, predisposes to turbulent blood flow. Similarly in the bronchial tree, as the vessels bifurcate and become smaller and the velocity of flow diminishes as the cardiac output is divided, flow becomes laminar.

The Venturi, the injector and Bernoulli

A Venturi is a tube with a section of smaller diameter than either the upstream or the downstream parts of the tube. The principles governing the behaviour of fluids flowing through a Venturi were formulated by Bernoulli in 1778, some 60 years earlier than described by Venturi himself. In any continuum the energy of the fluid may be described by the Bernoulli equation, which suggests that the sum of energies (potential (PE) and kinetic (KE)) possessed by the fluid is constant – that is:

assuming that the predominant fluid flow is horizontal, such that gravitational PE can be ignored.

In a Venturi ( Fig. 15.12 ), in order that fluid flow be continuous, its velocity must increase through its narrowed throat ( v ₂ > v ₁ ). This is associated with an increase in KE and Bernoulli's equation shows that there is an associated reduction in PE and therefore in pressure. Beyond the constriction, velocity decreases back to the initial value and the pressure rises again. In Fig. 15.12 , at point A, the energy in the fluid energy consists of potential (pressure) and kinetic (velocity), but at point B the amount of KE has increased because of the increased velocity, and the pressure is reduced here. A Venturi has a number of uses, including that of a flow measurement device. For optimum performance of a Venturi, it is desirable for fluid flow to remain laminar, and this is achieved by gradual opening of the tube beyond the constriction. In this way, if a U tube manometer is placed with one limb sampling the pressure at point A and the other at point B, then if the flow remains laminar, the Hagen–Poiseuille equation suggests a linear relationship between the pressure difference and the flow, hence the device can be used as a flowmeter. This contrasts with an orifice, at the outflow of which the flow is usually turbulent. Although an orifice can also be used as a flowmeter, the relationship between pressure difference and flow is non-linear, and it must be carefully calibrated. Another use of a Venturi is as a device for entraining fluid from without. If a flow of oxygen is fed into a Venturi through a nozzle, the low pressure induced at the throat may be used to entrain air, thus giving a metered supply of oxygen-enriched air or acting as an injector by multiplying the amount of air flowing through the Venturi towards the patient's lungs. If, instead, a hole is made in the side of the Venturi at the throat, then the low pressure at that point may form the basis of a suction device ( Fig. 15.13 ).

The injector principle may be seen in anaesthetic practice in several types of Venturi oxygen masks which provide oxygen-enriched air. With an appropriate flow of oxygen (usually exceeding 4 L min ^–1 ), there is a large degree of entrainment of air. This results in a total gas flow that exceeds the patient's peak inspiratory flow rate, thus ensuring that the inspired oxygen concentration remains relatively constant, and it prevents an increase in apparatus dead space which always accompanies the use of low-flow oxygen devices. The same principle is used in:

• Nebulisers. These are used to entrain water from a reservoir. If the water inlet is suitably positioned, the entrained water may be broken up into a fine mist by the high gas velocity.

• Ventilators. It can also be used as the principle of a driving gas in a ventilator ( Fig. 15.14 ).

  

The Coanda effect

The Coanda effect describes a phenomenon whereby when a jet of fluid (gas or liquid) flows across a flat surface it will tend to cling either to the surface. This occurs because of the lower pressure occurring around the jet (see earlier). If this pressure is balanced (by ambient surrounding pressure), then the jet carries on in a straight line. However, if an object (surface) reduces the rate at which this pressure is balanced, an effective negative pressure exists between the jet and the surface, leading to the clinging effect. The most visible demonstration of this is the way water from a tap clings to the surface of a sink. If the jet is passing through a Y junction, the flow tends to be bi-stable – it flows down one or other limb, not both. This is exploited in fluid-logic ventilators – small pressures applied perpendicular to the jet distal to the restriction may enable gas flow to be switched from one side to another ( Fig. 15.15 ). The effect is also of relevance to echocardiography as intracardiac jets may follow more discrete paths than otherwise expected, thereby altering jet sizes and Doppler-based measurements.

Heat

Heat is the energy that may be transferred from a body at a hotter temperature to one at a colder temperature. Its units are therefore joules. As discussed earlier, energy takes a number of forms and, if account is taken of energy losses, they are interchangeable. For example, if heat energy is applied to an engine, mechanical energy is the output. In a refrigeration cycle, mechanical energy is put in and heat is extracted from the cold compartment to the environment. Temperature is a measure of the tendency of an object to gain or lose heat.

Vaporisation

In a liquid, molecules are in a state of continuous motion because of their KE and are held in the liquid state because of intermolecular attraction by van der Waal's forces. Some molecules may develop velocities sufficient to escape from these forces, and if they are close to the surface of a liquid, these molecules may escape to enter the vapour phase. Increasing the temperature of a liquid increases its KE and a greater number of molecules escape. As the faster moving molecules escape into the vapour phase, the net velocity of the remaining molecules reduces; thus the energy state and therefore temperature of the liquid phase are eventually reduced. The amount of heat required to convert a unit mass of liquid into a vapour without a change in temperature of the liquid is termed the latent heat of vaporisation.

In a closed vessel containing liquid and gas, a state of equilibrium is reached when the number of molecules escaping from the liquid is equal to the number of molecules re-entering the liquid phase. The vapour concentration is then said to be saturated at the specified temperature. Saturated vapour pressure of liquids is independent of the ambient pressure but increases with increasing temperature.

The boiling point of a liquid is the temperature at which its saturated vapour pressure becomes equal to the ambient pressure. Thus on the graph in Fig. 15.16 the boiling point of each liquid at 1 atmosphere is the temperature at which its saturated vapour pressure is 101.3 kPa.

If we consider the simplest form of vaporiser ( Fig. 15.17 ), the concentration ( C ) of anaesthetic in the gas mixture emerging from the outlet port is dependent upon:

• The saturated vapour pressure of the anaesthetic liquid in the vaporiser. A highly volatile agent such as desflurane is present in a much higher concentration than a less volatile agent (i.e. with a lower saturated vapour pressure) such as halothane or isoflurane.

• The temperature of the liquid anaesthetic agent, as this determines its saturated vapour pressure.

• The splitting ratio – that is, the flow rate of gas through the vaporising chamber ( F _v ) in comparison with that through the bypass ( F – F _v ). Regulation of the splitting ratio is the usual mechanism whereby the anaesthetist controls the output concentration from a vaporiser.

• The surface area of the anaesthetic agent in the vaporiser, which must be maximised using baffles and wicks to maximise gas exposure to liquid agent.

• Duration of use. As the liquid in the vaporising chamber evaporates, its temperature and thus its saturated vapour pressure decrease. This leads to a reduction in concentration of anaesthetic in the mixture leaving the exit port unless temperature compensation methods are used. Classically, this is a bimetallic strip acting as a partial valve at the point where the flow splits to reduce bypass flow as temperature falls. (This is where the name TEC originates – TEmperature Compensated.)

• The flow characteristics through the vaporising chamber. In the simple vaporiser illustrated, gas passing through the vaporising chamber may fail to mix completely with vapour as a result of streaming because of poor design. This lack of mixing is flow dependent.

• Altitude . If the saturated vapour pressure (SVP) of the agent in the vaporising chamber is P _S , and the ambient pressure is P _A , then the concentration of the agent in the chamber is P _S /P _A , according to Dalton's law of pressures (see Fig. 15.17 ). The addition of the bypass gas makes the output a fraction f of this concentration, and the output is f.P _S /P _A . If the vaporiser is used at altitude, because of a reduced ambient pressure. the output concentration is higher than at sea level. However, the pharmacological effect of the agent is dependent on its partial pressure f. P _S , so no vaporiser recalibration is required.

• Back pressure (pumping effect). Some gas-driven mechanical ventilators produce an increase in pressure in the outlet port and back bar of the anaesthetic machine. The increased pressure during inspiration compresses the gas in the vaporiser; some gas in the region of the inlet port of the vaporiser is forced into the vaporising chamber, where more vapour is added to it. Subsequently there is a temporary surge in anaesthetic concentration when the pressure decreases at the end of the inspiratory cycle. This effect does not occur with efficient vaporisers because gas in the outlet port is already saturated with vapour. However, when pressure reduces at the end of inspiration, some saturated gas passes in retrograde fashion out of the inspiratory port and mixes with the bypass gas. Thus a temporary increase in total vapour concentration may still occur in the gas supplied to the patient. Methods of overcoming this problem include the following:

  • Incorporation of a one-way valve in the outlet port

  • Construction of a bypass chamber and vaporising chamber which are of equal volumes so that the gas in each is compressed or expanded equally

  • Construction of a long inlet tube to the vaporising chamber so that retrograde flow from the vaporising chamber does not reach the bypass channel

Humidity and humidification