Poiseuille's Law

What it shows

Poiseulle determined that the laminar flow rate of an incompressible fluid along a pipe is proportional to the fourth power of the pipe's radius. To test his idea, we'll show that you need sixteen tubes to pass as much water as one tube twice their diameter.

How it works

Poiseulle's law states that the flow rate Q is also dependant upon fluid viscosity η, pipe length L, and the pressure difference between the ends P by

flow rate is proportional to the 4th power of radius

but all these factors are kept constant for this demo so that the effect of radius is clear.

The apparatus consists of two 12 liter Plexiglas tanks, one to be emptied through a single 6mm bore capillary tube and the other through sixteen 3mm bore tubes. All tubes are 60cm in length. For direct comparison, all tubes need to be opened to the tanks simultaneously and this is achieved using a valve consisting of a long steel rod with 17 holes drilled through it, corresponding to the 17 tubes (figure 1b). The rod runs the length of the tanks and has a handle that rotates it to align the holes in the rod with those in the tank.

figure 1a. Poiseulles's apparatus, and 1b. detail of valve.

top view of tanks and pipes

Setting it up

For convenience the two tanks are constructed separately but can be set up side by side with a connector linking the rod valves of each. The apparatus sets up on a bench with a catch tray angled at about 20°, just below the ends of the capillaries. There is a hole in one corner of the tray that allows it to empty to a bucket below. Food coloring can be added to the water to make the levels clear.

Comments

Very interesting effect visually, since the 6mm tube doesn't look that much bigger than the 3mm ones, and there are 16 of them!