Hagen-Poiseuille

The Hagen-Poiseuille Resistance calculator computes the fluid resistance in a blood vessel or small tube based on the viscosity (η) and length (L) and radius (r) of the vessel.

INSTRUCTIONS: Choose your preferred units and enter the following:

• (η) Fluid Viscosity.
• (L) Length of Vessel.
• (r) Inner Radius of Vessel.

Tube/Vessel Resistance (R):   The calculator returns the resistance (R) in mmHg•min / L.

The Math / Science

Poiseuille's Law relates the fluid resistance of blood flow through a small blood vessel with the blood vessel's radius (r), the length (λ) of the artery, and the viscosity (η) of the blood. The formula for Poiseuille's Law of Blood Resistance is:

      `R = (8•η•λ) / (π•r^4)`

where:

• R is the Blood Flow Resistance
• η is the viscosity
• λ is the length of the blood vessel or artery
• r is the interior radius of the blood vessel or artery

Poiseuille's Law:

The volume of a homogeneous fluid passing per unit time through a capillary tube without turbulence is proportional to the pressure difference between its ends and is proportional to the fourth power of its internal radius.  

The volumetric flow rate is also inversely proportional to the length of the tube and the viscosity of the fluid.  This formula applies to the flow of blood in an artery because we can treat the  blood flow as a laminar flow of a uniformly viscous liquid.

Cardiac and Blood Flow Calculators

• Hagen-Poiseuille Resistance
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• Poiseuille's Velocity of Compressible Fluids
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