The gas laws explain how long a cylinder lasts, fluid mechanics explains what a flowmeter actually measures, and vapour pressure explains how a vaporiser works. The calculators on each card use values encountered in clinical practice.
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Gas laws · Cylinder
Boyle and Gay-Lussac: how long will the cylinder last?
P₁·V₁ = P₂·V₂ · P₁/T₁ = P₂/T₂At constant temperature, pressure and volume are inversely proportional. At constant volume, pressure is directly proportional to absolute temperature.
O₂ is stored in the cylinder as a gas, so the contents fall in direct proportion to the pressure. A 10-litre cylinder at 150 bar delivers roughly 10 × 150 = 1500 L of gas at atmospheric pressure. N₂O, by contrast, liquefies below its critical temperature (36.5 °C): the gauge stays at ≈ 51 bar until the liquid is used up. The contents of an N₂O cylinder can only be known by weighing it.
L
bar
L/min
°C
Usable gas
1500L
Time remaining
4 h 10 min
Pressure at that temp.
150bar
The calculation uses gauge pressure and ignores the 1 atm of gas that remains in the cylinder. The temperature slider shows the pressure, at that temperature, of a cylinder filled at 20 °C (Gay-Lussac).
Partial pressures · Altitude
Dalton: the real pressure of oxygen
Ptotal = P₁ + P₂ + … · PiO₂ = FiO₂ × (PB − 47)Each gas in a mixture exerts the pressure it would exert if it filled the volume alone. 47 mmHg is the saturated water vapour pressure at 37 °C.
O₂ sensors and vaporisers actually respond to partial pressure. As altitude rises, barometric pressure falls, so the same FiO₂ means a lower oxygen pressure. In a city such as Kayseri (≈ 1054 m), PB is about 88% of its sea-level value.
m
PB
—
PiO₂
—
PAO₂ (PaCO₂ 40)
—
Fluids · Flowmeter
Laminar and turbulent flow: what does a Thorpe tube measure?
A Thorpe tube is a glass cone that widens upwards. The bobbin rises until the pressure difference beneath it supports its weight; the pressure difference stays constant and what changes is the width of the annular gap (the orifice). At low flow the narrow, long gap between bobbin and wall behaves like a tube, so viscosity dominates. At high flow the gap widens into a short orifice, so density dominates. That is why each tube is calibrated for its own gas.
L/min
Dominant property
—
True flow
—
Resistance · Airway
Hagen–Poiseuille: the fourth power of the radius
R = 8·μ·L / (π·r⁴)In laminar flow, resistance is directly proportional to length and viscosity and inversely proportional to the fourth power of the radius. In turbulent flow, resistance is approximately proportional to 1/r⁵ (an inverse dependence).
A small reduction in tracheal tube diameter increases resistance substantially. The same principle applies to soda lime granule size (4–8 mesh), to the Thorpe tube and to intravenous cannulae.
mm
Laminar R (vs 8.0)
—
Turbulent R (≈ r⁻⁵)
—
Cross-sectional area
—
Vapour pressure · Vaporiser
Saturated vapour pressure and the splitting ratio
Cchamber = SVP / PB · Fchamber = Fvapour · (PB − SVP) / SVPGas passing through the vaporising chamber is loaded with vapour in proportion to the agent's saturated vapour pressure (SVP). The dial sets the ratio between chamber flow and bypass flow.
A variable-bypass vaporiser splits the fresh gas in two. A small portion is loaded with saturated vapour in the chamber; the rest passes through the bypass, and the two streams rejoin at the outlet. Because vaporisation absorbs latent heat, the liquid cools and its SVP falls; a bimetallic strip compensates by narrowing the bypass. Desflurane's SVP is very close to atmospheric pressure (669 mmHg, boiling point 22.8 °C): a Tec 6–type device heats the agent to 39 °C and injects a metered amount at ≈ 2 atm.
%
L/min
Splitting ratio
—
Output (at altitude)
—
Liquid consumption
—
Solubility · Pharmacokinetics
Henry's law and the blood/gas partition coefficient
Cdissolved = k · Pgas · λ = Cblood / CgasThe amount of gas dissolved in a liquid is proportional to the partial pressure above the liquid. O₂ solubility coefficient ≈ 0.003 mL·dL⁻¹·mmHg⁻¹; dissolved O₂ ≈ 0.003 × PaO₂ (mL/dL).
An agent that is poorly soluble in blood (low λ) raises its alveolar partial pressure quickly, so induction and emergence are fast. The effect depends on the partial pressure in the brain, not on the amount in the blood. The bars below are drawn to scale.
Agent
Blood/gas
Olive oil/gas
MAC %
SVP 20 °C
Desflurane
0.42
19
6.0
669
N₂O
0.47
1.4
104
gas
Sevoflurane
0.65
47
2.0
157
Isoflurane
1.4
91
1.15
238
Halothane
2.4
224
0.75
243
MAC: reference values for adults around age 40 in O₂ at 1 atm; values vary with age. N₂O MAC exceeds 100%. Olive oil/gas is not the same as adipose tissue/gas. SVP: mmHg.
Wall tension · Bag, alveolus
Laplace's law
P = 2T / r (sphere) · P = T / r (cylinder)T: wall tension, r: radius.
When a reservoir bag is overdistended its radius increases; although wall tension rises, the pressure levels off at a plateau. Under ISO 5362, a bag inflated to four times its nominal volume must hold a pressure between 30 and 60 cmH₂O. This plateau depends on the bag material; it does not replace the APL valve or guarantee protection against barotrauma. The ISO limit is a test condition, not a clinically safe pressure threshold. In the alveolus, surfactant lowers surface tension in small alveoli and so stops a small alveolus from emptying into a larger one.
Respiratory mechanics · Ventilator
The equation of motion of the respiratory system
Paw = V / C + R · V̇ + PEEPtotElastic component (volume / compliance) + resistive component (resistance × flow) + end-expiratory pressure.
In a passive patient, an inspiratory hold after a constant-flow volume-controlled breath brings flow to zero. Ppeak − Pplat is resistive pressure; resistance is R = (Ppeak − Pplat) / flow. Driving pressure is ΔP = Pplat − total PEEP, and static compliance is C = Vt / ΔP. In a single-compartment model, τ = R × C; about 95% of the passive volume change occurs within 3τ.
A = log₁₀(I₀/I) = ε · c · d · I = I₀ · 10−ε·c·dAbsorbance (A) is proportional to the molar decadic absorption coefficient, the concentration and the length of the light path.
A pulse oximeter takes the ratio of the pulsatile absorption of 660 nm (red) and 940 nm (infrared) light: R = (AC₆₆₀/DC₆₆₀) / (AC₉₄₀/DC₉₄₀). R ≈ 0.4 corresponds to SpO₂ ≈ 100%, and R = 1 to ≈ 85%. A capnometer measures CO₂ by infrared absorption at 4.26 µm, and anaesthetic agents in the 3.3 µm or 8–9 µm band (8–9 µm is free from methane and CO₂ interference).
P + ½ρv² + ρgh = constantAt a constriction the velocity rises and the lateral pressure falls; the low pressure draws ambient air in through a side port (entrainment).
A Venturi mask entrains room air with an O₂ jet to deliver a target FiO₂. Use the specified O₂ flow, keep air-entry ports clear and ensure that total flow meets inspiratory demand. Back pressure and high patient demand can alter delivered FiO₂. Gas entrainment is also used in nebulizers and some scavenging systems.
Physics page · Part 2 · Pharmacokinetics
Pharmacokinetics and low flow
The alveolar partial pressure of an inhaled agent rises at a rate set by its solubility in blood, by cardiac output and by ventilation. At low flow, the composition of gas in the circuit differs from that of the fresh gas: as the patient takes up O₂ and agent, the agent concentration in the circuit differs from the dial setting.
Wash-in and wash-out (FA/FI)
Alveolus + vessel-rich group + muscle + fat: a four-compartment physiological model, solved numerically every 0.3 seconds. At the cut-off time, agent delivery stops and the curve begins to show wash-out.
L/min
L/min
%
min
Low-flow anaesthesia
Circle system + FRC ≈ 6 L. The patient consumes 250 mL/min of O₂; sevoflurane uptake follows Lowe's square-root-of-time approximation (uptake ∝ 1/√t). At the start the circuit is full of fresh gas and contains no agent.
L/min
%
%
kg
TRY
Absorbent: as fresh gas flow falls below minute ventilation, a larger share of the exhaled gas passes through the absorber; at low flow the absorbent is exhausted sooner, so its colour and FiCO₂ require close monitoring.