[L | t+ | ★★] | keywords: laminar flow, viscosity, flow rate
16-tube water tank to show relation between tube cross-section and flow rate.
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.
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How it works:
Poiseulle's law states that the flow rate Q is also dependent upon
fluid viscosity η, pipe length L, and the pressure difference
between the ends P, by
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.
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!
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