Poiseuille's Law Calculator

Poiseuille's law describes steady laminar flow of an incompressible Newtonian fluid through a long, straight, circular pipe. The volumetric flow rate is Q = π ΔP r⁴ / (8 μ L), where ΔP is the pressure difference, r is the internal pipe radius, μ is dynamic viscosity, and L is pipe length. The calculator uses SI units, so the resulting flow rate is in cubic metres per second. Average velocity follows from v = Q / (π r²), which divides the volume passing each second by the pipe cross-sectional area. Radius has an especially strong influence because it is raised to the fourth power. Doubling radius while all other values stay fixed increases predicted flow sixteenfold. Pressure difference changes flow linearly, while viscosity and length oppose flow linearly. This sensitivity makes accurate internal-diameter measurements important in capillary systems, laboratory tubing, lubrication lines, medical flow models, and microfluidic channels. A small radius error can produce a much larger error in flow rate. The law depends on restrictive assumptions. Flow should be fully developed and laminar, the pipe should be much longer than its diameter, the wall should be rigid with no slip, and fluid properties should remain approximately constant. The calculator reports Reynolds number using Re = ρvD / μ, where density is ρ and diameter D equals twice the radius. Values below about 2300 generally indicate laminar pipe flow; transition occurs above that range and turbulent models become necessary. Entrance effects, bends, fittings, roughness, pulsation, compressibility, and non-Newtonian behavior can also make measured flow differ from this ideal prediction. Dynamic viscosity must be entered in pascal-seconds, not centipoise unless converted first; one centipoise equals 0.001 pascal-second. Pressure difference is the inlet pressure minus outlet pressure across the entered length. Use internal radius rather than outside radius. Results are useful for study, preliminary design, comparison, and checking experiments, but safety-critical pipe sizing should include losses from fittings and use applicable engineering standards. Always confirm that Reynolds number supports the laminar assumption before relying on the calculated flow.