Question

Calculate the minimum speed would blood need to travel

through a small blood vessel with a radius of 1 mm before the flow

was turbulent?

Where the viscosity of the blood is ηblood = 2.7× 10−3 Pa s and its density is ρblood = 1050 kg m−3

Answer 1

For flow in a pipe of diameter $D = 2r = 2mm = 2\times 10^{-3}m$ laminar flow occurs when $Re_D= 2300$ (upper boundary), where $Re_D$ is the Reynolds number:

$$Re_D = \dfrac{\rho u_{max} D}{\mu} = 2300$$

where $\rho = 1050kg/m^3$ is the density of the blood, and $\mu = 2.7\times 10^{-3}Pa\cdot s$ is the dynamic viscosity of the blood, and $u_{max}$ is the maximum speed. Expressing $u_{max}$, obtain:

$$u_{max} = \dfrac{2300\mu}{\rho D}\\ u_{max} = \dfrac{2300\cdot 2.7\times 10^{-3}}{1050 \cdot 2\times 10^{-3}} \approx 4.1m/s$$

Answer. 4.1 m/s.