physics about flow rate

Assume that the infusion rate of blood is low, then using Bernouli's Principle,

pressure difference = gain in kinetic energy per unit volume of blood
1050g.(0.5) = (1/2)(1050)v^2
where v is the speed of blood flow in the needle
g is the acceleration due to gravity

hence, v = square-root[2g x 0.5] m/s = 3.162 m/s (taking g = 10 m/s2)

Blood flow rate = 3.162 x pi x (0.2/1000)^2 m^3/s = 3.92 x 10^-7 m^3/s