Kostenloser Viscous Durchfluss Rate Rechner
Berechnen Sie laminar flow rate through a pipe unter Verwendung von the Hagen-Poiseuille equation. Kostenloser fluid dynamics Rechner.
Durchflussrate
0.0039269908 m3/s
Flow Rate vs Pipe Radius
Formel
## Hagen-Poiseuille Flow For steady, laminar, incompressible flow through a long circular pipe, the flow rate depends strongly on the pipe radius. ### Formula **Q = pi R^4 dP / (8 mu L)** - *R* = pipe radius - *dP* = pressure drop along the pipe - *mu* = dynamic viscosity - *L* = pipe length The R^4 dependence means doubling the radius increases flow by 16 times.
Lösungsbeispiel
Water (mu = 0.001 Pa s) through a 1 cm radius, 1 m long pipe with 1 kPa pressure drop.
- 01Q = pi * (0.01)^4 * 1000 / (8 * 0.001 * 1)
- 02R^4 = 1e-8
- 03Q = pi * 1e-8 * 1000 / 0.008
- 04Q = pi * 1e-5 / 0.008 = 3.927e-3 m3/s
- 05Q = 235.6 L/min
Häufig Gestellte Fragen
Why does flow rate depend on R to the fourth power?
The velocity profile is parabolic: fluid moves fastest at the centre and is stationary at the walls. Integrating the parabolic profile over the circular cross-section gives the R^4 dependence.
When does this equation apply?
Only for laminar flow (Re < 2300 in the pipe), incompressible fluid, and fully developed flow far from the pipe entrance.
How does this relate to blood flow?
The Hagen-Poiseuille law governs blood flow in small vessels. Narrowing of arteries (stenosis) dramatically reduces flow because of the R^4 dependence.
Lernen