Poiseuille Flow Rate Calculator
Enter tube radius, pressure difference, viscosity and length to compute the volumetric flow rate Q = π·r⁴·Δp/(8·η·L).
Input Data
Results
At a glance:The Hagen–Poiseuille law gives the steady laminar volumetric flow rate through a circular tube: Q = π·r⁴·Δp/(8·η·L), where r is the tube radius, Δp the pressure drop over length L, and η the dynamic viscosity. The parabolic velocity profile has mean velocity v̄ = Q/(πr²) = r²·Δp/(8ηL). The hydraulic resistance R_h = Δp/Q = 8ηL/(πr⁴) — note the extreme r⁴ dependence: doubling the radius increases flow 16×. Valid for laminar (Re < ~2300), Newtonian, incompressible flow with fully developed profile. This tool returns Q (m³/s, L/min), v̄ and R_h.
Formula
Q = π·r⁴·Δp/(8·η·L)
v̄ = r²·Δp/(8ηL)
R_h = 8ηL/(πr⁴)
How to Use
- Enter tube radius r, pressure difference Δp, viscosity η and length L.
- The calculator returns Q, mean velocity and hydraulic resistance.
Case Studies
Capillary blood flow
r = 1e-3 m, Δp = 1000 Pa, η = 3e-3 Pa·s, L = 0.1 m.
Q = π·1e-12·1000/(8·3e-3·0.1) ≈ 1.31e-6 m³/s.
≈ 0.079 L/min.
FAQ
Why is flow so sensitive to radius?
Q ∝ r⁴ — a small change in vessel radius dramatically changes flow; this is why vasoconstriction strongly regulates blood flow.
When does Poiseuille's law apply?
Laminar, Newtonian, incompressible, fully developed flow (Re < ~2300) in a straight rigid tube; not for turbulent or pulsatile flow.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.