Does turbulence increase with radius or decrease

Question

IV lines must be regularly ‘flushed’ to avoid infection and line occlusion. More turbulent flushing better removes any particles attached to a catheter wall, which decreases chances of complications. Which of the following choices would be best suited to flush an IV line?

I was solving some questions on Khan academy and I couldn't figure out one of the questions and this was the answer

A smaller lumen would increase the velocity of flow, increasing turbulence, therefore a low viscosity fluid with a small needle would be best suited

It says a needle with a small diameter will increase turbulence but higher Reynolds number indicates more turbulence
This confused me does turbulence more in tubed with bigger or smaller diameters?

Gert · Accepted Answer

For flow through a pipe/tube the Reynolds number $text{Re}$ is given by:
$$text{Re}=frac{WD}{mu A}$$
where $A=frac{pi D^2}{4}$
so that:
$$text{Re}=frac{4W}{pi mu D}$$
It follows that, all other things being equal, smaller diameters lead to higher turbulence.

Chet Miller · Answer

The key parameter is the shear stress at the wall.  This determines whether an object will be swept off the wall.  For turbulent flow, the wall shear stress for a smooth tube is given by:  $$tau_w=frac{1}{2}rho v^2frac{0.0791}{Re}$$At constant flow rate, this is proportional to diameter to the -3.75 power.  So under these circumstances, smaller diameter is better.
But for fixed pressure drop, $$tau_w=frac{D}{4L}Delta p$$So, in this case, this is proportional to D to the +1 power.  So, larger diameter is better for this case.

niels nielsen · Answer

the flow in IV lines is never fast enough to become turbulent- it is always laminar. The faster the flow and the less viscous the fluid, the thinner becomes the boundary layer that is stuck to the inside of the IV line, and since it is that boundary layer which would contain contaminants, faster flow (still fully laminar!) will do a better job cleaning out the IV lines.

Answered by niels nielsen on August 6, 2021

Does turbulence increase with radius or decrease

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