Final answer:
During intense exercise, the body experiences vasodilation, which increases blood flow to supply muscles with more oxygen and nutrients. Using Poiseuille's law, one can determine how much the average vessel radius has increased given the changes in blood flow, viscosity, and pressure.
Step-by-step explanation:
During vigorous exercise such as a marathon race, the body undergoes several physiological changes to accommodate the increased demand for oxygen and nutrients. One important change is the dilation of blood vessels (vasodilation), which allows for increased blood flow. An increase in blood flow is typically associated with a decrease in blood viscosity and an increase in blood pressure. According to Poiseuille's law, the flow rate of a fluid through a cylindrical tube depends on the pressure difference between two ends, the radius of the tube to the fourth power, the length of the tube, and the viscosity of the fluid. In the context of human physiology, blood vessels can be considered tubes that carry blood.
Given the increase in blood flow by a factor of 10, a drop in blood viscosity to 95% of its normal value, and an increased blood pressure difference by 50%, we can deduce the change in the radii of the blood vessels through a modified version of Poiseuille's law. Assuming other factors such as the length of the blood vessels stay constant, any increase in blood flow can be attributed to changes in pressure difference, blood viscosity, and vessel radius.
To find the factor by which the average radius of the blood vessels has increased, we can set up a ratio using the known variables. The math involves solving for the radius in the modified Poiseuille equation. Taking into account the exercise-induced changes in blood flow, viscosity, and blood pressure, the calculation would reveal the factor by which the vessel radius must have increased to achieve the new flow rate.