Increasing the flow tube radius affects resistance how?

Increasing the flow tube radius affects resistance how?

• A. Increasing radius decreases resistance.
• B. Increasing radius increases resistance.
• C. Radius has no effect on resistance.
• D. Radius only affects velocity, not resistance.

Answer: (A)

The key idea is that resistance to flow in a cylindrical tube depends very strongly on the radius. Poiseuille’s law shows that resistance is inversely proportional to the fourth power of the radius (R ∝ 1/r^4). This means that increasing the radius drastically lowers resistance. For a given pressure difference, lower resistance allows more flow to pass. Radius does affect velocity as well (through changes in cross-sectional area, since v = Q/A), but that deals with how fast the fluid moves for a given flow, not the resistance itself. So the correct interpretation is that increasing the radius decreases resistance.

The key idea is that resistance to flow in a cylindrical tube depends very strongly on the radius. Poiseuille’s law shows that resistance is inversely proportional to the fourth power of the radius (R ∝ 1/r^4). This means that increasing the radius drastically lowers resistance. For a given pressure difference, lower resistance allows more flow to pass. Radius does affect velocity as well (through changes in cross-sectional area, since v = Q/A), but that deals with how fast the fluid moves for a given flow, not the resistance itself. So the correct interpretation is that increasing the radius decreases resistance.