Poiseuille's Law Calculator

Poiseuille's Law describes the physical relationship governing the laminar flow of an incompressible, Newtonian fluid through a long, cylindrical pipe of constant cross-section. The core equation relates volumetric flow rate ($Q$) to the pressure difference ($\Delta P$), pipe radius ($r$), fluid dynamic viscosity ($\mu$), and pipe length ($L$):

Q = (π × ΔP × r⁴) / (8 × μ × L)

Alternatively, fluid resistance ($R$) can be determined using the formula R = (8 × μ × L) / (π × r⁴), which simplifies the flow rate expression to Q = ΔP / R, mirroring Ohm's Law in electrical circuits.

Consider a medical scenario where a blood substitute (viscosity μ = 0.004 Pa·s) flows through a cylindrical catheter with a length ($L$) of 0.5 meters and an inner radius ($r$) of 0.002 meters. If the initial driving pressure is 1,200 Pa and the terminal end pressure is 200 Pa, the pressure drop (ΔP) equals 1,000 Pa.

Substituting these values into the Poiseuille's equation:

1. Calculate radius to the fourth power: (0.002)⁴ = 1.6 × 10^-11 m⁴.

2. Multiply numerator terms: 3.14159 × 1,000 × 1.6 × 10^-11 = 5.026 × 10^-8.

3. Multiply denominator terms: 8 × 0.004 × 0.5 = 0.016.

4. Divide numerator by denominator: (5.026 × 10^-8) / 0.016 = 3.14 × 10^-6 m³/s, or approximately 3.14 mL/s.

To ensure your calculations remain accurate, always convert your inputs into standard SI units—such as meters for length and radius, Pascals for pressure, and Pascal-seconds for dynamic viscosity. Keep in mind that Poiseuille's Law only applies strictly to steady, laminar flow of Newtonian fluids; if your fluid experiences turbulence or contains suspended particles that alter its viscosity profile at varying shear rates, alternative models should be used.