如何计算Poiseuille Law
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Poiseuille's law quantifies laminar flow through cylindrical pipes. It shows how flow rate depends on pressure, pipe dimensions, and fluid viscosity.
公式
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
分步指南
- 1Enter pressure difference, pipe radius, length, and dynamic viscosity
- 2The calculator applies Q = (π × ΔP × r⁴) / (8 × η × L)
- 3Results show volumetric flow rate
例题解析
输入
ΔP = 1000 Pa, r = 1 mm, L = 1 m, η = 0.001 Pa·s (water)
结果
Q ≈ 0.39 mL/s
Surprisingly slow
常见错误注意事项
- ✕Forgetting to use radius, not diameter, in the r⁴ term
- ✕Confusing dynamic viscosity (Pa·s) with kinematic viscosity (m²/s)
常见问题
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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