Question 9.19: Turbulent Flow of Blood BIO GOAL Use the Reynolds number to ...
Turbulent Flow of Blood BIO
GOAL Use the Reynolds number to determine a speed associated with the onset of turbulence.
PROBLEM Determine the speed at which blood flowing through an artery of diameter 0.20 cm will become turbulent.
STRATEGY The solution requires only the substitution of values into Equation 9.26 giving the Reynolds number and then solving it for the speed υ.
R N={\frac{\rho v d}{\eta}} [9.26]
Solve Equation 9.26 for v, and substitute the viscosity and density of blood from Example 9.18, the diameter d of the artery, and a Reynolds number of 3.00 × 10³:
v=\frac{\eta(R N)}{\rho d}=\frac{\left(2.7 \times 10^{-3} N \cdot s / m ^2\right)\left(3.00 \times 10^3\right)}{\left(1.05 \times 10^3 kg / m ^3\right)\left(0.20 \times 10^{-2} m \right)}
υ = 3.9 m/s
REMARKS The exercise shows that rapid ingestion of soda through a straw may create a turbulent state