A blood vessel is 25 cm long, and has a radius of 2.6 mm. If blood is flowing through it with a volume flow rate of 9 X10-7 m3/s, what is the difference in the pressures at the two ends of the blood vessel? Do NOT assume there is zero viscosity.
You can use Hagen–Poiseuille equation [1] to compute
the pressure drop for a fluid flowing through a pipe in viscous,
laminar, incompressible flow.
ΔP = 8∙µ∙L∙Q / (π∙R⁴)
with
µ - dynamic viscosity
L - pipe length
Q - volumetric flow rate
R - pipe radius
Average viscosity of blood is [2]:
µ = 3.5×10⁻³ Pa∙s
So the pressure difference between the ends of your blood vessel
is:
ΔP = 8 ∙ 3.5×10⁻³ Pa∙s ∙ 25×10⁻² m ∙ 9×10⁻⁷ m³∙s⁻¹ / (π∙(2.6×10⁻³
m)⁴)
= 43.88 Pa
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