Poiseuille Flow Calculator
poiseuille flow calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Poiseuille Flow Calculator
Calculator
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Formula: Q = πΔPr⁴ / (8μL)
Worked example — ~3.93×10⁻⁴ m³/s
Formula
Q = πΔPr⁴ / (8μL)
Laminar flow rate through a pipe. Flow increases with the 4th power of radius.
Worked Examples
Example 1: Small pipe
Problem:ΔP=1000Pa, r=0.01m, μ=0.001 Pa·s, L=1m
Solution:Q=π×1000×10⁻⁸/(8×0.001×1)
Result:~3.93×10⁻⁴ m³/s
Frequently Asked Questions
What is Poiseuille's law and when does it apply?
Poiseuille's law describes steady laminar flow of a viscous fluid through a cylindrical pipe: Q = πΔPr⁴/(8μL). It applies when the Reynolds number Re = ρvD/μ is below ~2100 (laminar regime). Above Re ≈ 4000 the flow becomes turbulent and the formula no longer holds.
How do you calculate volumetric flow rate using Poiseuille's law?
Plug in: Q = π × ΔP × r⁴ / (8 × μ × L). For ΔP = 1000 Pa, r = 0.01 m, μ = 0.001 Pa·s, L = 1 m: Q = π × 1000 × 10⁻⁸ / (8 × 0.001 × 1) ≈ 3.93×10⁻⁴ m³/s or 0.393 L/s.
What units are used in Poiseuille flow calculations?
Pressure drop ΔP in Pascals (Pa), pipe radius r in metres (m), dynamic viscosity μ in Pascal-seconds (Pa·s; water ≈ 0.001 Pa·s at 20°C), pipe length L in metres (m). The result Q is in m³/s; multiply by 1000 to get litres per second (L/s).
Why does pipe radius have such a large effect on flow rate?
Flow rate scales with the fourth power of radius (r⁴). Doubling the pipe radius increases flow by 2⁴ = 16 times. This means a 10% reduction in radius (e.g. from arterial plaque) reduces flow to 0.9⁴ ≈ 66% of normal — explaining why partial blockages significantly impair blood flow.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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