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In laminar Poiseuille flow, how does tube radius affect flow rate?

Flow rate scales with the fourth power of radius.

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  1. Directly with radius
  2. With radius squared
  3. With radius to the fourth power ✔

Why: For a round tube in ideal laminar conditions, Q is proportional to r to the fourth power. Halving radius therefore reduces flow to one-sixteenth when other factors stay fixed.

Huh, didn't know that: The same law makes flow rate inversely proportional to viscosity and tube length.

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The pipe radius raised its influence to the fourth power.
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References

Answer: With radius to the fourth power. For a round tube in ideal laminar conditions, Q is proportional to r to the fourth power. Halving radius therefore reduces flow to one-sixteenth when other factors stay fixed.

  1. OpenStax University Physics Volume 1, Viscosity and Turbulence openstax.org/books/university-physics-volume-1/pages/14-7-viscosity-and-turbulence
    Flow rate increases with radius by a factor of r to the fourth power.
    Checked 2026-10-10.

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