Poiseuille Flow Calculator
Blood through a 10 cm vessel of 2 mm radius with a 100 Pa pressure drop flows at 1.7952 mL/s, from Poiseuille’s law.
Blood about 3–4 mPa·s, water at 20 °C 1.0 mPa·s.
1.79519580205131 mL/s
Full answer, then cut to fewer decimals (not rounded):
- 1.79519580205131 mL/s
- 1.7951958020513 mL/s
- 1.795195802051 mL/s
- 1.79519580205 mL/s
- 1.7951958020 mL/s
- 1.795195802 mL/s
- 1.79519580 mL/s
- 1.7951958 mL/s
- 1.795195 mL/s
- 1.79519 mL/s
- 1.7951 mL/s
- 1.795 mL/s
- 1.79 mL/s
- 1.7 mL/s
- In m³/s
- 0.000001795195802 m³/s
- In mL/min
- 107.7117481 mL/min
- In L/min
- 0.1077117481 L/min
- Hydraulic resistance 8μL/(πr⁴)
- 55704230.08 Pa·s/m³
- Mean velocity Q/(πr²)
- 14.28571429 cm/s
- Radius effect
- halving r cuts flow 16-fold at the same ΔP
Step-by-step solution
- Convert units: r = 2 mm = 0.002 m; μ = 3.5 mPa·s = 0.0035 Pa·s; L = 10 cm = 0.1 m
- Q = π × r⁴ × ΔP ÷ (8 × μ × L)
- Q = π × 0.002⁴ × 100 ÷ (8 × 0.0035 × 0.1)
- Q = 0.000001795195802 m³/s = 1.795195802 mL/s
Poiseuille Flow Formula
Q = π r⁴ ΔP / (8 μ L)
resistance R = 8μL/(πr⁴); valid for steady laminar flow of a Newtonian fluid
Worked Example
Blood (3.5 mPa·s) through a 2 mm radius, 10 cm vessel with 100 Pa pressure difference:
- Convert units: r = 2 mm = 0.002 m; μ = 3.5 mPa·s = 0.0035 Pa·s; L = 10 cm = 0.1 m
- Q = π × r⁴ × ΔP ÷ (8 × μ × L)
- Q = π × 0.002⁴ × 100 ÷ (8 × 0.0035 × 0.1)
- Q = 0.000001795195802 m³/s = 1.795195802 mL/s
In mL/min: 107.7117481 mL/min · In L/min: 0.1077117481 L/min · Hydraulic resistance 8μL/(πr⁴): 55704230.08 Pa·s/m³ · Mean velocity Q/(πr²): 14.28571429 cm/s · Radius effect: halving r cuts flow 16-fold at the same ΔP
GATE tip
Vessel resistances combine like electrical ones: in series they add, in parallel the reciprocals add. Check the Reynolds number (below about 2000) to confirm laminar flow.
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Frequently asked questions
Why does radius matter so much?
Flow scales with r⁴: narrowing a vessel by 16 % halves the flow at the same pressure, which is why small changes in arteriole radius control blood flow.
Is blood Newtonian?
Not exactly: its viscosity falls at high shear rates and depends on haematocrit. Poiseuille’s law is a good first estimate in larger vessels.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Poiseuille Flow Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/poiseuille-flow-calculator/
IEEE
Scientific Converters, "Poiseuille Flow Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/poiseuille-flow-calculator/