How to Calculate Poiseuille Law
What is Poiseuille Law?
Poiseuille's law quantifies laminar flow through cylindrical pipes. It shows how flow rate depends on pressure, pipe dimensions, and fluid viscosity.
Formula
The calculator applies Q = (π × ΔP × r⁴) / (8 × η × L)
- Q
- (π × ΔP × r⁴) / (8 × η × L) — (π × ΔP × r⁴) / (8 × η × L)
- L
- L value — Variable used in the calculation
Step-by-Step Guide
- 1Enter pressure difference, pipe radius, length, and dynamic viscosity
- 2The calculator applies Q = (π × ΔP × r⁴) / (8 × η × L)
- 3Results show volumetric flow rate
Worked Examples
Input
ΔP = 1000 Pa, r = 1 mm, L = 1 m, η = 0.001 Pa·s (water)
Result
Q ≈ 0.39 mL/s
Surprisingly slow
Common Mistakes to Avoid
- ✕Forgetting to use radius, not diameter, in the r⁴ term
- ✕Confusing dynamic viscosity (Pa·s) with kinematic viscosity (m²/s)
Frequently Asked Questions
Why is flow proportional to r⁴?
Small radius changes dramatically affect flow; doubling radius increases flow 16×, which is why plumbing uses large pipes.
How does viscosity affect flow?
Higher viscosity reduces flow; thick oils flow much slower than water at the same pressure difference.
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