Gas Flow 1 – Theory

What the curriculum thinks you need to know:

PC_BK_28 Density and viscosity of gases
PC_BK_29 Laminar and turbulent flow: Hagen-Poiseuille equation, Reynold’s number, examples including helium

What you need to know (The theory):


The volume/amount of a fluid (gas or liquid) passing a set point per unit time

Usually measured in Litres per minute in anaesthetics.


Mass of a substance per unit volume

So kilograms per cubic metre would be the appropriate unit here. Note that gases and liquids compress. So by definition their densities can be changed by increasing the pressure and ‘squeezing’ more molecules into a set space.


Measure of the ability to resist deformation by external forces

This is basically a measure of the attractive forces between the atoms/molecules in a substance. The unit is the technically the ‘poiseuille’ but most use the equivalent unit which is the pascal second. The way the viscosity is measured is to place two plates one metre apart and fill the space between them with the substance in question. then one plate is pushed sideways by a force of one pascal.  The distance the plate moves per second is then inversely proportional to the viscosity (the lower the viscosity, the easier the plate moves).

We can classify the types of flow by the way the ‘stream’ of molecules flow. The two classical types of flow:

Laminar flow

You can think of this as ‘ordered’ flow, so much like a good old British queue! All the molecules move in the same direction (parallel to the tube wall). When flow occurs in a tube, the velocity of the molecules in higher in the middle of the tube and slower next to the tube wall. This is due to increased frictional forces nearer to the wall. The flow in the centre of the tube is twice that of the peripheral flow.

The flow rates can in laminar flow are fairly simple to work out as the movement of molecules is ordered and therefore, predictable.

Think of a nice cold drink from your favourite fast food chain, what affects how fast you can drink it through a straw?

  1. The size of the straw. Really thin straws are difficult to drink through. The larger the radius/diameter of the straw, the easier it is to drink.
  2. The length of the straw. Shorter straws are easier. Think of those really long curly straws, they’re really hard to drink through!
  3. How hard you suck! The harder you try to suck up the drink, the faster you can drink it. In technical terms you are creating a larger pressure difference to cause a movement of the drink.
  4. Finally the viscosity of the drink has a large effect. Think of a glass of soft drink vs a thick milkshake. Which is easier to drink through a straw? The more viscous the liquid/gas, the harder it is to make it flow.

So now lets make an equation for this….

Remember, put the things that make flow easier when they increase on top (as they will make the flow bigger!), and put the things that make flow harder on the bottom (they will make the flow smaller!)


The Hagen Poiseuille Equation

Now, notice the similarities to one of physics’ classic equations… Ohm’s Law:


Gas flow vs Electrical Current flow… They’re the same really.

Flow is equivalent to current (which is flow of electrical charge after all)

Pressure difference is equivalent to potential difference or voltage.

Resistance to flow is the same as resistance to current.

Turbulent flow

Contrary to laminar flow, Turbulent flow is disordered and molecules do not travel parallel to the tube wall. The presence of eddy currents make flow inefficient requiring large pressure difference to drive flow. 

Making an equation to work out flow rates in turbulent flow is difficult as it is, by definition, disordered and unpredictable.

We can however make an equation to decide if flow is likely to be laminar or turbulent.

Reynolds Number

A dimensionless number which shows the likelyhood of laminar flow occurring, Less than 2000 is likely to be laminar.

Notice the word likely. Just because the Reynolds number is less than 2000, doesn’t mean flow will be laminar, just that it is more likely


Reynolds Number

High velocity of flow also makes turbulent flow more likely. This makes sense as the higher the kinetic energy the more likely molecules are to fly off in random directions and create eddys. Widening a tube also makes turbulent flow more likely.

The important ones here are viscosity and density.

Notice from the above equation, that a higher density makes your Reynolds number bigger and hence flow more likely to be turbulent. So density is important in turbulent flow.

Viscosity makes laminar flow more likely. Think of this this way, the attractive forces between molecules is higher, stopping ‘rogue’ molecules flying off and creating eddys. So the substance flows as a group.

What you need to know (How it works in practice):


We all know that ‘bigger’ cannulae allow faster flow rates into a patient. The Hagen Pouiselle equation shows this as flow is proportional to radius to the power of 4. So if we double the diameter of the cannula, we increase flow rates by 16 times. Doubling the internal diameter of a cannula is roughly equivalent as going from a 20G (pink) to a 16G (grey). The flow rates on a cannulae don’t exactly go along with this however as there is another variable… Cannula length. The length of the larger venflons tends to be longer, so they don’t get the whole 16x increase.

ETT tubes 

We’re always told to put in the biggest ETT we can fit in.

The Hagen Pouiselle equation supports this. Larger radius allows larger flows. Then, looking at Ohm’s law if we assume a same driving pressure (e.g. work of breathing) then increasing the flow means we must reduce the resistance. Hence decreased resistance to breathing and reduced work of breathing.

Easy way to think about it: Breathing through a drinks straw is hard.

(Nearly) Everyone also cuts their ETT. Why?

Again the Hagen Pouiselle equation tells us if we increase the length of tube, all else being equal, the flow rates will drop. Putting this into Ohm’s law again, if flow/current drops with the same driving force/voltage then resistance increases.

Easy way to think about it: Breathing through a long straw is even more difficult.

Heliox (helium/oxygen mixes)

In situations where airway diameter is limited (bronchospasm being the obvious one), resistance to flow increases and hence a larger pressure difference is needed to maintain gas flow. This eventually leads to exhaustion and the need for mechanical ventilation.

Laminar flow requires less pressure difference to maintain flow. Hence if we can induce laminar flow in bronchospasm, then, theoretically at least, we should be able to decrease work of breathing. To do this we can use Heliox. This is a 70:30 (or 80:20) mix of helium and oxygen. This has a significantly lower density than nitrogen/oxygen mixtures and hence will decrease work of breathing.

Random Exam factoids (i.e. the things the college like asking):

  1. Remember your equations, you would think that a larger diameter tube would make laminar flow more likely, however, if we look at Reynolds equation, larger diameter tubes actually increase Reynolds number making turbulent flow more likely. Note: if flow rates are the same though a tube, then actually, velocity is decreased which makes Reynolds number less… confusing!

© Sam Beckett and Physics4FRCA, 2017. Unauthorized use and/or duplication of this material without express and written permission from this site’s author and/or owner is strictly prohibited.

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