I know that from the equation of Reynolds number that as the

I know that from the equation of Reynolds number that as the diameter increases the Reynolds number increases and as the velocity of flow increases Reynolds number increases too increasing the likelihood of turbulent flow. But I don\'t understand why in narrowed blood vessel(stenosis) why we have turbulent flow although the diameter is actually decreased. I know velocity is increased in this case but does that mean that velocity effect Reynolds number more in this case? if so, can you please explain why.

Solution

Yes you are right about the part which says as the diameter increases the Reynolds number increases and as the velocity of flow increases Reynolds number increases too increasing the likelihood of turbulent flow.

Re = rho * V * d / mu

But you also have to see that for a constant mass flow system such as a blood vessel another relation is applied which contuinity of flow which mathematically is V * A = constant

so   V * d^2 = constant flow rate for a blood vessel

So the reynold number equation can be modified to

Re = rho * Constant / d * mu    (which implies that for a constant flow rate system , Re is inversely proportional to the dia of the vessel, hence smaller dia will have a large Re value (turbulent flow).

I hope you got the concept if you need further clarifications drop a comment.