In a tube model, increasing radius reduces resistance and increases flow rate; which statement is true?

In a tube model, increasing radius reduces resistance and increases flow rate; which statement is true?

• A. Flow rate decreases and resistance increases
• B. Flow rate increases and resistance remains the same
• C. Flow rate increases and resistance decreases
• D. Flow rate remains constant and resistance increases

Answer: (C)

In laminar tube flow, the flow rate Q for a given pressure difference scales with the fourth power of the radius, while the resistance R scales inversely with the fourth power of the radius (R ∝ 1/r^4 and Q ∝ r^4). This means increasing the radius greatly reduces frictional resistance and, for the same driving pressure, increases how much fluid can pass per unit time. So the statement that flow rate increases and resistance decreases is the true one. The other options imply either flow or resistance changes that don’t follow the r^4 relationship (for example, flow rising while resistance stays the same, or flow decreasing while radius increases, or both flow and resistance changing in opposite directions that contradict the established dependence).

In laminar tube flow, the flow rate Q for a given pressure difference scales with the fourth power of the radius, while the resistance R scales inversely with the fourth power of the radius (R ∝ 1/r^4 and Q ∝ r^4). This means increasing the radius greatly reduces frictional resistance and, for the same driving pressure, increases how much fluid can pass per unit time. So the statement that flow rate increases and resistance decreases is the true one. The other options imply either flow or resistance changes that don’t follow the r^4 relationship (for example, flow rising while resistance stays the same, or flow decreasing while radius increases, or both flow and resistance changing in opposite directions that contradict the established dependence).