Как да изчислим Poiseuille Law
Какво е Poiseuille Law?
Poiseuille's law quantifies laminar flow through cylindrical pipes. It shows how flow rate depends on pressure, pipe dimensions, and fluid viscosity.
Формула
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
Ръководство стъпка по стъпка
- 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
Вход
ΔP = 1000 Pa, r = 1 mm, L = 1 m, η = 0.001 Pa·s (water)
Резултат
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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