Blood flow with various sized tubing We are dealing with an issue I would like some help with.   We have 1/4 inch cannulas in a patient connected to 1/4 tubing to a centrifugal pump for cardiopulmonary support.    If we change the 1/4 inch tubing to 3/8 inch tubing ( but leave the 1/4 inch cannulas in the patient which drain into the tubing) will we get better flow?   
 A: I'm guessing your flow rates are slow enough that the flow is non-turbulent. In that case the relevant equation is the Hagen-Poiseuille equation:
$$ \text{Flow rate} = \frac{\pi }{8 \eta } \frac{\Delta P}{\ell} r^4 $$
In this equation $r$ is the internal radius of the tubing, $\eta$ is the viscosity and $\Delta P/\ell$ is the pressure drop per metre along the tube. I think that a centrifugal blood pump generates a constant pressure $\Delta P$, and presumably the length of the tubing, $\ell$, is constant so in that case we get:
$$ \text{Flow rate} \propto r^4 $$
and increasing the internal radius of the tube by even a small amount will make a big difference. There will still be a bottleneck at the cannula, but if the length of the cannula is small compared to the total length of the tubing you'll still see a big increase in flow rate.
But this assumes that the restricting factor is the internal diameter of the tube. If this isn't the case then you won't see as big an improvement as you expect. It isn't possible to say for certain without looking at the setup you're using.
