An intravenous (IV) system is supplying saline solution to a patient at the rate of 0.120 cm3 /s through a needle of radius 0.150 mm and length 2.50 cm. What pressure is needed at the entrance of the needle to cause this flow, assuming the viscosity of the saline solution to be the same as that of water? The gauge pressure of the blood in the patient's vein is 8.00 mm Hg. (Assume that the temperature is 20°C .)
Assuming laminar flow, then the Poiseuille's law equation is 
where P2 is the pressure at the entrance of the needle and P1 is the
pressure in the vein. The only unknown is P2
Solving for P2
yields
P1 is given as 8.00 mm Hg, which converts to 1.066 × 103 N/m2. Substituting this and the other known values yields
