Radius to the 4th power

Ohm's law, right?

poiselles law states that airway resistance (assuming laminar flow) is related to the length of the tube the radius of a tube and the viscocity of the gas

so

R=8Ln/pi x r to the 4th power

R=resistance

L= length of tube

n=viscocity of the gas

pi and 8 are constants.

r= radius

i remember a formula just for resistance that we got in lecture that seemed simpler it was

R=1/r4th resistance is inversely proportional to 1/radius 4th power

so.

what this means is

if you double the size of the tube, resistance to flow decreases 16x's.

so if you tube someone with an 8.0 tube vs a 4.0 your work of breathing (as it relates to flow through the ett) would decrease by 16x's. this is assuming that airflow through the tube is laminar and not turbulent.

am i on the right track, someone help me.

d

See below.

Poiselles law = Π(radius to 4th power)(ΔP) / 8 (viscosity)(length of tube)

This assumes that flow is laminar, when it is turbulent; however, radius becomes even more important, as it is raised to the 5th power. Moreover, liquid (gases are liquids too) density becomes more important than viscosity.

How is this relevant to anesthesia?

Well think blood pressure control (modulated largely by muscular arterioles)

airway diameter during the respiratory cycle (increased with inspiration and less with expiration - closing volumes)

IVs (larger bore leads to greater flow)

endotracheal tubes (for the same reason as IVs)

As you can see, this formula has a huge impact on the choices you make clinically. Don't forget the other factors that influence flow, but you are correct that radius yields the greatest impact. Hope this helps.

Ahh, so size does matter!

Ahh, so size does matter!

and radius to the 5th power is important in which one?!?!?!?!?!?!?!? LOL

turbulent flow equation...

and radius to the 5th power is important in which one?!?!?!?!?!?!?!? LOL

turbulent flow equation...

Thank you to all who replied to my question. I was pretty much on board with what everyone was answering but sometimes it is nice to take it out of text and see it in another light. I am sure I can come up with some more brain busters here in a few weeks since I started my second semester and it is full of fun classes such as physiology. Wish me luck for I am going to need it

Tia

the big deal I see here is that it doesnt take much change in radius to get a big change in resistance. its just somthing to know

R4 is also used in the same way in hemodynamic equiations as the radius of arteriols that affect systemic vascular resistance. All these calculations are based on Ohm's Law: flow= pressure/resistance.

Tia,

When you hang a bag of IV fluids and you raise the bag to increase the flow is an example of Pouislle's law. When you use an 18 gauge catheter as opposed to a 22 gauge is an example of Pouiselle's as you are increasing the radius. In pediatrics the smaller diameter of the airway causes increased resistance, again an application. There are many more applications.