A glucose solution of viscosity $2\mathrm{.}2103103$ N$$s$/$m$2$N$$s$/$m$2$ and density $1030$ kg$/$m$3$kg$/$m$3$ flows from an elevated open bag into a vein. The needle into the vein has a radius of $0\mathrm{.}20$ mmmm and is $3\mathrm{.}0$ cmcm long. All other tubes leading to the needle have much larger radii, and viscous forces in them can be ignored. The pressure in the vein is $1000$ N$/$m$2$N$/$m$2$ above atmospheric pressure.

Part A

Determine the pressure relative to atmospheric pressure needed at the entrance of the needle to maintain a flow rate of $0\mathrm{.}10$ cm$3/$scm$3/$s$.$