Final answer:
Increasing the flow tube radius decreases resistance and allows the pump rate to decrease while maintaining the same pressure. This principle, derived from Poiseuille's law, is critical in biological systems such as the human cardiovascular system, where vessel diameter significantly influences blood flow and pressure.
Step-by-step explanation:
When the flow tube radius increased, the correct answer is resistance decreased and pump rate decreased to maintain pressure. This concept is based on the principles of fluid dynamics, especially Poiseuille's law, which describes how flow rate through a tube is related to factors such as pressure difference, tube length, fluid viscosity, and particularly the tube radius to the fourth power. The formula indicates that as the radius increases, resistance to flow decreases significantly, reducing the need for a high pump rate to maintain fluid pressure.
In biological systems like the cardiovascular system, an increase in blood vessel radius would lead to a decrease in resistance (due to less friction between the blood and vessel walls) and thus the heart rate could decrease or pump rate could slow down to maintain the same pressure because less force is required to push the blood through the larger vessels. This is analogous to a garden hose where increasing the diameter allows more water to flow with less resistance, and one does not need to increase the pressure to achieve a steady flow.