Poiseuille Flow Rate Calculator
The Hagen-Poiseuille equation predicts how much viscous fluid flows through a pipe under a steady pressure difference, as long as the flow is smooth and laminar. It is fundamental to hydraulics, microfluidics, intravenous infusion and blood flow modelling. This calculator takes the pressure drop along the pipe, the pipe radius, the fluid dynamic viscosity and the pipe length, then returns the volumetric flow rate in cubic metres per second and litres per minute. Because flow scales with radius to the fourth power, the tool shows how sensitive flow is to even small changes in pipe diameter.
Hagen-Poiseuille formula
Q = pi * deltaP * r^4 / (8 * mu * L)
deltaP = pressure drop (Pa)
r = pipe radius (m), L = pipe length (m)
mu = dynamic viscosity (Pa*s)
Q is the volumetric flow rate in cubic metres per second. To convert to litres per minute, multiply by 60,000. The fourth-power dependence on radius makes flow extremely sensitive to pipe diameter.
Laminar flow context
- The equation holds only for laminar flow, typically Reynolds number below about 2,300.
- Flow rate scales with the fourth power of radius: doubling radius raises flow sixteen-fold.
- Dynamic viscosity of water at 20 degrees Celsius is approximately 0.001 pascal-seconds.
- The equation assumes a Newtonian fluid, a rigid straight pipe and fully developed flow.
- It underlies models of intravenous drip rates and blood flow in small vessels.
Poiseuille flow: frequently asked questions
What is the Hagen-Poiseuille equation?
The Hagen-Poiseuille equation gives the volumetric flow rate of an incompressible viscous fluid in steady laminar flow through a long cylindrical pipe: Q = pi * deltaP * r^4 / (8 * mu * L). Flow rate scales with the fourth power of radius, so a small change in pipe radius has a large effect.
When does Poiseuille flow apply?
It applies to steady, laminar, fully developed flow of a Newtonian fluid in a straight pipe of constant circular cross-section, where the Reynolds number is below about 2,300. It does not hold for turbulent flow, gases at high speed, or non-Newtonian fluids like blood at very small scales.
Why does flow depend on the fourth power of radius?
Both the cross-sectional area and the velocity profile depend on radius, and they combine so that flow rate scales as radius to the fourth power. Doubling the radius increases flow sixteen-fold at the same pressure. This is why even slight narrowing of a pipe or vessel sharply reduces flow.
What viscosity value should I enter?
Dynamic viscosity is a property of the fluid and temperature. Water at 20 degrees Celsius is about 0.001 pascal-seconds; air is about 0.0000181. Because it is empirical and temperature dependent, viscosity ships here as a user-editable input so you can match your fluid and conditions.
What units does this calculator use?
It uses SI units throughout: pressure drop in pascals, radius and length in metres, viscosity in pascal-seconds. The result is in cubic metres per second, and is also shown in litres per minute for convenience. Convert your inputs to these units before entering them.
Official sources
- U.S. National Institute of Standards and Technology: Fluid Metrology.
- NASA Glenn Research Center: Viscosity of a fluid.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.