Final answer:
Doubling the radius of the blood vessels is the best way to increase the rate of blood flow as it is mathematically shown to have a more significant impact than the other options, by increasing the flow rate by 16 times according to Poiseuille's law.
Step-by-step explanation:
To determine the best way to increase the rate of blood flow from an original rate of 100ml/min, we can draw upon principles of fluid dynamics, in particular, Poiseuille's law, which relates the flow rate of a fluid in a pipe to the viscosity of the fluid, the length and radius of the pipe, and the pressure difference across the pipe. According to this law, the flow rate (Q) is directly proportional to the fourth power of the radius of the blood vessels (r) and the pressure difference (ΔP), and inversely proportional to the viscosity (η) of the blood and the length (L) of the blood vessels:
Q ≈ (r^4)ΔP / (ηL)
This means that if we double the radius of the blood vessels (option A), the rate of blood flow would increase by 2^4, which is 16 times, assuming all other factors remain constant. This would have a significantly greater impact on blood flow rate compared to doubling the blood pressure (option B), halving the viscosity of the blood (option C), or doubling the length of the blood vessels (option D), which each affect the flow rate linearly or inversely. Thus, doubling the radius of the blood vessels is the best way to increase the rate of blood flow.