The Reynolds number is a dimensionless quantity that characterizes the flow regime of a fluid. It is given by the formula:
Re = (ρvd) / μ
where ρ is the density of the fluid, v is the flow velocity, d is the diameter of the vessel, and μ is the dynamic viscosity of the fluid.
To find the Reynolds number for blood flow through the coronary artery, we can use the given values:
ρ = 50 kg/m^3 (density of blood)
v = 15 mL/s = 0.015 L/s = 0.000015 m^3/s (flow speed of blood)
d = 0.2 m (diameter of vessel)
The dynamic viscosity of blood varies with shear rate and is approximately 4 × 10^(-3) Pa·s at a shear rate of 100 s^(-1) for whole blood. However, the viscosity of plasma (the fluid component of blood) is much lower than that of whole blood, and since the Reynolds number for flow in the coronary artery is typically low (i.e., laminar flow), we can assume that the viscosity of blood is similar to that of water, which is about 10^(-3) Pa·s.
Substituting these values into the Reynolds number formula, we get:
Re = (ρvd) / μ
= (50 kg/m^3)(0.000015 m^3/s)(0.2 m) / (10^(-3) Pa·s)
= 1.5
Therefore, the Reynolds number for blood flow through the coronary artery is approximately 1.5, which is well below the critical value of 2,300 for the onset of turbulent flow. This suggests that blood flow through the coronary artery is likely to be laminar (smooth and orderly), which is important for maintaining efficient blood flow and preventing damage to the vessel walls