Final answer:
The greatest average speed of blood flow in an artery to maintain laminar flow can be found using the Reynolds number formula, rearranged to solve for velocity. The flow rate is then calculated from the velocity and the cross-sectional area of the artery. This type of calculation is important in fields like Physics, biomedical engineering, and cardiovascular research.
Step-by-step explanation:
To determine the greatest average speed of blood flow in an artery where the flow is laminar, we can use the Reynolds number, which predicts the transition from laminar to turbulent flow. The critical Reynolds number for blood flow in vessels is generally taken to be around 2000. The Reynolds number (Re) is calculated by the formula:
Re = (Density x Velocity x Diameter) / Viscosity
Given that the density (ρ) of blood is 1025 kg/m³ and the viscosity (η) is 2.084 × 10⁻³ Pa·s, along with the artery diameter (2 x radius), we can rearrange the formula to solve for the velocity (V) as follows:
V = (Re × Viscosity) / (Density × Diameter)
Substituting the known values and a Reynolds number of 2000 for the onset of turbulent flow, we can find the maximum average speed.
Once the velocity is found, the flow rate can be determined using the formula:
Flow rate (Q) = Velocity x Area
Where Area is πr², with r being the radius of the artery. Calculating the flow rate will involve using the speed found previously and the cross-sectional area of the artery.
It is important to note that this analysis will provide an ideal case, with certain biological factors possibly causing deviations in actual scenarios. This example illustrates a fundamental Physics computation often relevant in biomedical engineering and cardiovascular research.