In laminar flow through a cylindrical tube, what happens to flow when the tube radius increases?

In laminar flow through a cylindrical tube, what happens to flow when the tube radius increases?

• A. Flow decreases
• B. Flow remains the same
• C. Flow increases
• D. Flow becomes turbulent

Answer: (C)

In laminar flow through a round tube, the flow rate Q for a given pressure drop ΔP depends very strongly on the radius. Poiseuille’s law gives Q = π ΔP r^4 / (8 μ L). Because the radius r is raised to the fourth power, increasing the radius increases the flow dramatically. For example, doubling the radius multiplies the flow by 16. The average velocity U_mean = Q/(π r^2) also grows with radius (U_mean = ΔP r^2 / (8 μ L)), so the fluid moves faster overall as the tube gets wider. This assumes the flow remains laminar; turbulence would require a higher Reynolds number, which isn’t the focus here.

In laminar flow through a round tube, the flow rate Q for a given pressure drop ΔP depends very strongly on the radius. Poiseuille’s law gives Q = π ΔP r^4 / (8 μ L). Because the radius r is raised to the fourth power, increasing the radius increases the flow dramatically. For example, doubling the radius multiplies the flow by 16. The average velocity U_mean = Q/(π r^2) also grows with radius (U_mean = ΔP r^2 / (8 μ L)), so the fluid moves faster overall as the tube gets wider. This assumes the flow remains laminar; turbulence would require a higher Reynolds number, which isn’t the focus here.