If radius increases from r to 2r, flow increases by how much? (Assuming constant pressure and viscosity)

If radius increases from r to 2r, flow increases by how much? (Assuming constant pressure and viscosity)

• A. Flow increases by 2x
• B. Flow increases by 4x
• C. Flow increases by 8x
• D. Flow increases by 16x

Answer: (D)

In laminar flow through a circular pipe, the flow rate is proportional to the fourth power of the radius when pressure difference, viscosity, and length are held constant. This is captured by Poiseuille’s law: Q ∝ r^4. If the radius doubles (r → 2r), the flow becomes (2r)^4 = 16 r^4, so the flow increases sixteenfold. This is why the correct increase is 16x, even though the cross-sectional area only grows by 4x; the r^4 relationship governs how much flow changes.

In laminar flow through a circular pipe, the flow rate is proportional to the fourth power of the radius when pressure difference, viscosity, and length are held constant. This is captured by Poiseuille’s law: Q ∝ r^4. If the radius doubles (r → 2r), the flow becomes (2r)^4 = 16 r^4, so the flow increases sixteenfold. This is why the correct increase is 16x, even though the cross-sectional area only grows by 4x; the r^4 relationship governs how much flow changes.