Which of the following results in an increase in fluid flow rate?

Which of the following results in an increase in fluid flow rate?

• A. Decrease in pressure and decrease in radius.
• B. Increase in pressure and increase in radius diameter.
• C. Increase in length and decrease in radius.
• D. Decrease in pressure and increase in length.

Answer: (B)

Flow rate through a tube is driven by the pressure difference and the tube’s radius, and it is opposed by the tube’s length and the fluid’s viscosity. Poiseuille’s law captures this: Q is proportional to ΔP and r^4, and inversely proportional to η and L (Q ∝ ΔP r^4 / (η L)). So increasing the driving pressure and widening the tube (increasing radius) both boost flow, with radius having a very strong effect because it is raised to the fourth power. The choice that increases both the pressure difference and the radius will thus raise flow the most. The other options either reduce pressure, reduce radius, or increase length (which slows flow), all of which decrease Q. Therefore, increasing pressure together with an increase in radius yields the greatest increase in fluid flow rate.

Flow rate through a tube is driven by the pressure difference and the tube’s radius, and it is opposed by the tube’s length and the fluid’s viscosity. Poiseuille’s law captures this: Q is proportional to ΔP and r^4, and inversely proportional to η and L (Q ∝ ΔP r^4 / (η L)). So increasing the driving pressure and widening the tube (increasing radius) both boost flow, with radius having a very strong effect because it is raised to the fourth power.

The choice that increases both the pressure difference and the radius will thus raise flow the most. The other options either reduce pressure, reduce radius, or increase length (which slows flow), all of which decrease Q. Therefore, increasing pressure together with an increase in radius yields the greatest increase in fluid flow rate.