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!

Yeah, in a nutshell , size does matter.

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



turbulent flow equation...

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