Poiseuille Flow (Viscous Flow in a Pipe)
Push a thick or thin liquid through a narrow pipe and watch the flow profile form — the fluid at the wall barely moves, the centre races, and halving the radius cuts the flow to a sixteenth.
Preview — sign up free to change the numbers yourself
What you can adjust
- Fluid
- 1 – 10000 mPa·s
- Pipe radius (R)
- 0.5 – 10 mm
- Pipe length (L)
- 5 – 100 cm
- Pressure difference (ΔP)
- 0.1 – 50 kPa
- Animation duration
- 2 – 6 s
How thick the liquid is. A thicker (more viscous) fluid drags far more at the wall, cutting the flow rate for the same push and pipe.
The flow rate depends on the FOURTH power of this radius — halving it cuts the flow to a sixteenth, everything else unchanged.
A longer pipe means more wall to drag against over the same pressure push, so the flow rate falls in direct proportion.
The pressure difference pushing fluid from one end of the pipe to the other. The flow rate rises in direct proportion to this.
How long the clip runs — long enough to watch the flat starting line bow out into the full parabolic velocity profile.
About this simulation
What it shows
A liquid is pushed through a narrow pipe, and the speed across the pipe is drawn as it develops: nearly still at the wall and fastest at the centre.
The key idea
Thick liquids drag more at the wall. The flow rate is Q = πR⁴ΔP / (8μL), so it depends on the radius to the fourth power: halving the radius cuts the flow to one sixteenth.
Try this
Halve Pipe radius (R) from 2 mm to 1 mm: the flow rate falls to one sixteenth, with everything else unchanged.
The formula only holds for smooth, steady (laminar) flow. The results include a laminar flag that shows whether your settings stay within it.