Poiseuille Viscous Flow Calculator
Enter tube radius, length, pressure drop and viscosity to compute the viscous flow rate Q = π·r⁴·Δp/(8·η·L) of a Newtonian fluid.
Input Data
Results
At a glance:This calculator applies the Hagen–Poiseuille law for a Newtonian (viscous, constant-η) fluid in laminar tube flow: Q = π·r⁴·Δp/(8·η·L). It emphasizes the viscous parameters — viscosity η and geometry r, L — that set the resistance to flow. The strong r⁴ dependence means small radius changes dominate. As with the flow-rate variant, it is valid for laminar (Re < ~2300), fully developed, incompressible Newtonian flow. Outputs Q in m³/s, mL/s and L/min for convenience in lab and biomedical contexts.
Formula
Q = π·r⁴·Δp/(8·η·L)
$$Q = \frac{\pi r^4 \Delta P}{8\eta L}$$$$\Delta P = \frac{8\eta L Q}{\pi r^4}$$How to Use
- Enter tube radius r and length L.
- Enter pressure drop Δp and viscosity η.
- The calculator returns Q in m³/s, mL/s and L/min.
Case Studies
IV drip
r = 0.0005 m, L = 0.05 m, Δp = 500 Pa, η = 1e-3 Pa·s.
Q = π·(5e-4)⁴·500/(8·1e-3·0.05) ≈ 1.2e-7 m³/s.
≈ 0.12 mL/s (7.3 mL/min).
FAQ
What makes the fluid 'Newtonian'?
Its viscosity η is constant regardless of shear rate (water, blood at low shear approx., oils). Non-Newtonian fluids (paint, polymer melts) need a different law.
Why report three flow units?
m³/s for SI, mL/s and L/min for practical lab/biofluid volumes (e.g. IV drips, perfusion).
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References
Content review: Calculatorism Editorial Team. Results are for reference only; please refer to the relevant authorities for the official figures.