In a flow-tube model, increasing the radius of the right flow tube affects flow rate, resistance, and pump rate. Which statements are true?

In a flow-tube model, increasing the radius of the right flow tube affects flow rate, resistance, and pump rate. Which statements are true?

• A. Flow rate increases, resistance decreases, pump rate increases to maintain pressure.
• B. Flow rate decreases, resistance increases, pump rate decreases to maintain pressure.
• C. Flow rate increases, resistance increases, pump rate decreases to maintain pressure.
• D. Flow rate decreases, resistance decreases, pump rate increases to maintain pressure.

Answer: (A)

Increasing the radius of the right flow tube lowers resistance sharply, since resistance in laminar flow goes as R ∝ 1/r^4. With a pump driving a pressure difference, a smaller resistance means more flow for the same ΔP, so the flow rate rises. To keep the pressure gradient steady while this larger flow occurs, the pump must raise its output. So the combination of flow rate increasing, resistance decreasing, and pump rate increasing to maintain pressure aligns with the physics of how resistance and flow relate to radius. The alternative scenarios would conflict with the fact that larger radius lowers resistance and that flow increases when driving pressure is the same but resistance drops.

Increasing the radius of the right flow tube lowers resistance sharply, since resistance in laminar flow goes as R ∝ 1/r^4. With a pump driving a pressure difference, a smaller resistance means more flow for the same ΔP, so the flow rate rises. To keep the pressure gradient steady while this larger flow occurs, the pump must raise its output. So the combination of flow rate increasing, resistance decreasing, and pump rate increasing to maintain pressure aligns with the physics of how resistance and flow relate to radius. The alternative scenarios would conflict with the fact that larger radius lowers resistance and that flow increases when driving pressure is the same but resistance drops.