A blood transfusion is being set up in an emergency room for an accident victim.

Question

A blood transfusion is being set up in an emergency room for an accident victim. Blood has a density of 1060 kg/m3 and a viscosity of 4.00E-3 Pa*s. The needle being used has a length of 3.08 cm and an inner radius of 0.294 mm. The doctor wishes to use a volume flow rate through the needle of 4.35E-8 m3/s. What is the distance h above the victim's arm where the level of the blood in the transfusion bottle should be located? As an approximation, assume that the level of the blood in the transfusion bottle and the point where the needle enters the vein in the arm have the same pressure of one atmosphere. (In reality, the pressure in the vein is slightly above atmospheric pressure.)

Explanation / Answer

The pressure difference along the tube is P2 - P1 = q g h = (1060 kg/m^3) (9.8 m/s^2) h where q is the density of blood. For viscosity u, Poiseuille's law is V = pi (P2 - P1) r^4 / (8 L u) where V is the volume velocity, L is the length of the tube, and r is its radius. h = (8 V L u) / (pi q g r^4)

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