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 4.00 10-3 Pa·s. The needle being used has a length of 3.0 cm and an inner radius of 0.25 mm. The doctor wishes to use a volume flow rate through the needle of 4.70 10-8 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.)
h =

Answer 1

Answer:

The distance h above the victim's arm where the level of the blood in the transfusion bottle should be located is 0.254 m

Explanation:

given information:

density, ρ = 1060 $kg/m^{3}$

viscosity, η = 4 x $10^{-3}$ Pa.s

needle length, L = 3 cm = 0.03 m

radius, r = 0.25 mm = 0.00025 m

volume flow rate, Q = 4.70 x $10^{-8}$  $m^{3} /s$

according to  Poiseuille’s law

Q = (π$r^{4}$ΔP)/8ηL

ΔP = (8QηL)/(π$r^{4}$)

     = 8 (4.70 x $10^{-8}$)(4 x $10^{-3}$)(0.03)/(π$0.00025^{4}$)

     = 3676.71

Now we can calculate the distance h

ΔP = ρ g h

h = ΔP / ρ g

  = 3676.71/(1060)(9.8)

  = 0.354 m