I used the Hagen-Poiseuille law.
Volume flow rate = π X pressure difference X pipe radius^ 4 X liquid viscosity / 8 X viscosity X pipe length.
F = πPr^4 / 8nl
So after reviewing the equation your using I think 1 of use is using the wrong equation but my understanding of the question might be off. I don't fully understand the medical procedure, so is the blood discharging out of the cylinder into an open area, or is it within constant cylindrical shape equal to the radius?
You don't have velocity in the equation but instead your using pressure differential??? Velocity and flow rate are differently related. I think I've used this equation in the past to explain the liquid discharge rate where the cylinder ends and the liquid is poured into an open space.
Here is an easier problem on fluid dynamics to get us in the mood for the "difficult math problem."
A doctor places a stent in an artery that doubles the blood flow through that section of the artery. The artery before and the stent was perfectly circular. The pressure either way is the same (I know probably not realistic, but let's keep this simple).
Hint: The flow of liquid through a circular pipe is faster in the middle of the pipe than the edges. To be more specific, the rate of flow at any given location is proportional to the distance to the nearest edge.
How much did the stent increase the radius of the artery at the point of the stent?
So does the stent discharge at both ends or just 1?