Question

The diameter of a renal artery lumen in humans is 5 mm. If the mean velocity of the blood flowing in the renal artery is 40 cm/s, the density of blood (ρ) is 1060 kg/m³, and the viscosity of blood (μ) is 3 cP, the Reynolds number for the blood flowing in the renal artery is \(\underline{\hspace{2cm}}\). (rounded off to the nearest integer)

Hint:

Reynolds number helps determine whether the flow is laminar or turbulent.

Answer 1

Correct Answer: 700

Reynolds number formula: \[ Re = \frac{\rho v D}{\mu} \] Where: \[ \rho = 1060\ \text{kg/m}^3, v = 40\ \text{cm/s} = 0.4\ \text{m/s}, D = 5\ \text{mm} = 0.005\ \text{m}, \mu = 3\ \text{cP} = 3 \times 10^{-3}\ \text{Pa.s} \] Substitute values: \[ Re = \frac{1060 \times 0.4 \times 0.005}{3 \times 10^{-3}} = \frac{2.12}{3 \times 10^{-3}} = 706.67 \] Thus: \[ \boxed{707} \]