Question

A patient receives a blood transfusion through a needle of radius 0.24 mm and length 2.3 cm, The density of blood is 1,050 kg/m3. The bottle supplying the blood is 0.500 m above the patient's arm. What is the rate of flow through the needle?

Answer 1

Poiseuille’s relation for blood in needle  ΔV/Δt = Δpie*R^4/8nblood*L

First, we have (see figure), even though the two points are at Pb>Pc the same level. It is due to viscosity and the fluid is flowing. Second, the last sentence in the question means that = PP CA . Therefore, we find  ΔP = Pb-Pc =Pb-Pa= ρBlood gh

so that the equation above becomes

ΔV/Δt = ρBlood ghR^4/8nblood*L

= 1,050 kg/m^3*9.81*0.5*3.14*(0.00024)^4/8*0.0027 *0.02

= 1.24*10^-7m^3/s

note : η Blood = 0.0027 N·s/m2