Poiseuille's Law Calculator

Our Hagen-Poiseuille's law calculator is a simple way to calculate the flow rate, resistance, or pressure change of a fluid or gas in a pipe.

Volumetric flow3.9192 ml/s235.149 ml a minute, 3.919e-6 m³/s

Mean velocity1.2475 m/s

Centreline velocity2.49501 m/sexactly twice the mean — laminar tube flow has a parabolic profile

Wall shear stress5 Pa

At twice the radius62.7064 ml/sSIXTEEN times the flow — the fourth power is why a slightly narrowed artery or a partly blocked pipe restricts so drastically

At 10% narrower2.5714 ml/s34.4% less flow for a 10% radius reduction

Resistance to flow2.552e+9 Pa·s/m³8µL ÷ πr⁴ — the hydraulic analogue of electrical resistance, and it adds in series just the same

Reynolds number2,485.55ABOVE 2300 — the flow is turbulent and Poiseuille's law no longer holds, so this answer overstates the flow

Viscosity used1.002 mPa·s1.002 centipoise

The formula

Stokes F = 6πµrv; Poiseuille Q = πΔPr⁴ ÷ 8µL

Fourth power, and square

Poiseuille's law has flow proportional to the fourth power of radius. Narrowing a tube by 10% cuts the flow by 34%; halving the radius cuts it to a sixteenth. This is why a modest arterial narrowing has such disproportionate consequences, and why pipe sizing dominates every other variable in a laminar system.

Stokes settling goes as the square of radius, which is why fine particles effectively never settle. Halving a particle's diameter quarters its settling speed, so clay-sized material stays suspended for days or years while sand drops out in seconds. It is the basis of sedimentation analysis and of every clarifier design.

Both laws have validity limits worth respecting. Poiseuille assumes laminar flow and fails above a Reynolds number of about 2300. Stokes assumes creeping flow and starts to fail above a Reynolds number of about 1 — a far stricter condition, and one that a 1 mm steel sphere in water already violates badly. Both modes report the Reynolds number so the answer can be judged rather than trusted.

Laminar tube flow has a parabolic velocity profile, so the centreline moves at exactly twice the mean. That factor of two matters whenever a measurement is taken at one point rather than averaged.