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Blood Flow Physics Question. Help needed! Poiseuilles' Equation/Flow in tubes/Viscosity! A patient is to be...?
A patient is to be given a blood transfusion. The blood is to flow through a tube from a raised bottle to a needle inserted in the vein . The inside diameter of the 4.5 cm long needle is 0.44 mm, and the required flow rate is 4.8 cm^3 of blood per minute.
How high (h) should the bottle be placed above the needle? Use pho(blood)=1.05*10^3kg/m^3 and viscosity(blood)=4.0*10^-3kg/m^3 . Assume the blood pressure is 18 torr above atmospheric pressure.
--I was thinking that I use Poiseuille's Equation to calculate the change in pressure, and then use pgh to calculate height, but I just can't figure it out. I would really like some help please.
You have it Paul. Just as you say, except viscosity is in Pa∙s, not kg/m³
ΔP = 128µLQ / [π∙d^4]
= 128 ∙ 0.004 Pa∙s ∙ 0.045m ∙ 0.0000048m³/min ∙ min/60s / [π ∙ (0.00044m)^4]
= 15653.5 Pa
Now the pressure in the vein is 18 torr, so you need to add this:
= 18 torr *101325 Pa / 760 torr = 2399.8 Pa
P_total = 18053.3 Pa
Head = ΔP / ρg = 18053.3 Pa /(1050kg/m³ ∙ 9.80665 m/s²) = 1.75 m
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