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

Question

A blood transfusion is being set up in an emergency room for anaccident victim. Blood has a density of 1060kg/m3 and a viscosity of 4.0 ×10-3 Pa·s. The needle being used has alength of 3.0 cm and an inner radius of 0.25 mm. Thedoctor wishes to use a volume flow rate through the needle of5.0 × 10-8 m3/s. What isthe distance h above the victim's arm where the level ofthe blood in the transfusion bottle should be located? As anapproximation, assume that the level of the blood in thetransfusion bottle and the point where the needle enters the veinin the arm have the same pressure of one atmosphere. (In reality,the pressure in the vein is slightly above atmosphericpressure.)

Explanation / Answer

   in the given problem we can see that thepressure at the input of the needle is    P2 = Patmosphere+ g h    the pressure at the output of the needle is    P1 =Patmosphere    P2 - P1 = gh    with help pf the poisueills law we get    Q = R4 (P2 -P1) / 8 L        = R4 g h / 8 L    solve for the height h    h = ........ m    P1 =Patmosphere    P2 - P1 = gh    with help pf the poisueills law we get    Q = R4 (P2 -P1) / 8 L        = R4 g h / 8 L    solve for the height h    h = ........ m

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