I want to calculate the improvement in flow rate that can be achieved with changing the tubing size when the tubing is sub-millimeter size.
I originally approached this using a simplification of Poiseuille's law which says $\Delta Q=\Delta r^4$
However, lets say I'm changing from 0.5 to 1.5 millimeter tubing. That gives $\Delta r=0.050$, which when raised to the 4th power is a tiny number (6.25E-05). This seems wrong intuitively, based on the relative increase in size (i.e. new tube is 300% of the original tube)
If I convert to micrometers first, the result jumps to 6.25E06, which seems really really large.
What am I missing here, because this doesn't seem like the right approach.