Turbulence and Poiseuille's equation

Question

(P3) [8 points] Poiseuille’s equation does not hold if the flow velocity is high enough that turbulence sets in. The onset of turbulence occurs when the so-called Reynolds number Re, exceeds approximately 2000. (a) Determine if blood flow through the aorta is laminar or turbulent, when the average speed of blood in the aorta (r = 1.0 cm) during the resting part of the heart’s cycle is about 30 cm/s.

I've done this problem over five or so times and can't seem to get the correct answer. using Re=2*v*radius*density/viscosity of blood. We were told that the viscosity should be taken to be 2.8*10^-3 Pa seconds.

The answer is supposed to be 2300 apparently but I keep getting vastly different numbers. Can someone please walk me through it? I am probably using the wrong units but can't figure it out.

Answer 1

Here is what I get for the Reynolds number:

v = 0.30 m/s

r = 0.01 m

ρ = 1025 kg/m³ (for blood plasma; I had to look this up)

μ = 2.8 x 10^-3 Pa-s

Everything is in SI units now, so

Re = 2vrρ/μ = 2(0.30)(0.01)(1025) / (2.8 x 10^-3) ≅ 2196,

which is not far from 2300. What did you use for the density of blood? Could you have made a mistake in the units?